Browse by Mathematics Subject Classification

00 General (421 articles)
- 00 General
- 00-00 Difficult to classify at the second level (must be assigned at least one other classification number in this section) (2 articles)
- 00-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 00-02 Research exposition (monographs, survey articles)
- 00.0 (1940-1958) Bibliographical notes
- 00.00 (1959-1972) General (1 articles)
- 00.04 (1959-1972) translation volumes, etc.
- 00.20 (1959-1972) General bibliographies
- 00.30 (1959-1972) Dictionaries and other general reference works
- 00.50 (1959-1972) Methodology and philosophy of mathematics
- 00.99 (1959-1972) None of the above, but in this section
- 00Axx General and miscellaneous specific topics (392 articles)
  - 00Axx General and miscellaneous specific topics (7 articles)
  - 00A05 General mathematics (26 articles)
  - 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) (6 articles)
  - 00A07 Problem books (2 articles)
  - 00A08 Recreational mathematics (22 articles)
  - 00A15 Bibliographies (3 articles)
  - 00A17 External book reviews (158 articles)
  - 00A20 Dictionaries and other general reference works (2 articles)
  - 00A22 Formularies
  - 00A30 Philosophy of mathematics (34 articles)
  - 00A35 Methodology of mathematics, didactics (31 articles)
  - 00A69 General applied mathematics (35 articles)
  - 00A71 Theory of mathematical modeling (5 articles)
  - 00A72 General methods of simulation (1 articles)
  - 00A73 Dimensional analysis (2 articles)
  - 00A79 Physics (use more specific entries from Sections 70 through 86 when possible) (5 articles)
  - 00A99 Miscellaneous topics (53 articles)
- 00Bxx Conference proceedings and collections of papers (23 articles)
  - 00Bxx Conference proceedings and collections of papers
  - 00B05 Collections of abstracts of lectures
  - 00B10 Collections of articles of general interest
  - 00B15 Collections of articles of miscellaneous specific content
  - 00B20 Proceedings of conferences of general interest (1 articles)
  - 00B25 Proceedings of conferences of miscellaneous specific interest (20 articles)
  - 00B30 Festschriften (2 articles)
  - 00B50 Volumes of selected translations
  - 00B55 Miscellaneous volumes of translations
  - 00B60 Collections of reprinted articles
01 History and biography (1738 articles)
- 01 History and biography
- 01-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (10 articles)
- 01-01 Instructional exposition (textbooks, tutorial papers, etc.) (63 articles)
- 01-02 Research exposition (monographs, survey articles) (2 articles)
- 01-06 Proceedings, conferences, collections, etc. (9 articles)
- 01-08 Computational methods (1 articles)
- 01.0 (1940-1958) History, biography
- 01.00 (1959-1972) General (5 articles)
- 01.01 (1959-1972) General histories, source books
- 01.02 (1959-1972) Primitive
- 01.05 (1959-1972) Pre-Greek, Babylonian, Egyptian
- 01.08 (1959-1972) Greek
- 01.10 (1959-1972) Far East (1 articles)
- 01.12 (1959-1972) Islam
- 01.15 (1959-1972) Medieval
- 01.18 (1959-1972) 15th and 16th centuries, Renaissance
- 01.20 (1959-1972) 17th century
- 01.25 (1959-1972) 18th century
- 01.30 (1959-1972) 19th century
- 01.35 (1959-1972) 20th century (2 articles)
- 01.40 (1959-1972) Contemporary
- 01.50 (1959-1972) Biographies, obituaries, personalia (4 articles)
- 01.60 (1959-1972) Collected or selected works; reprintings or translations of classics
- 01.99 (1959-1972) None of the above, but in this section
- 01Axx History of mathematics and mathematicians (1641 articles)
  - 01Axx History of mathematics and mathematicians (25 articles)
  - 01A05 General histories, source books (9 articles)
  - 01A07 Ethnomathematics, general
  - 01A10 Paleolithic, Neolithic
  - 01A12 Indigenous cultures of the Americas (1 articles)
  - 01A13 Other indigenous cultures (non-European)
  - 01A15 Indigenous European cultures (pre-Greek, etc.) (1 articles)
  - 01A16 Egyptian (4 articles)
  - 01A17 Babylonian (1 articles)
  - 01A20 Greek, Roman (21 articles)
  - 01A25 China (1 articles)
  - 01A27 Japan (2 articles)
  - 01A29 Southeast Asia
  - 01A30 Islam (Medieval) (5 articles)
  - 01A32 India (5 articles)
  - 01A35 Medieval (9 articles)
  - 01A40 15th and 16th centuries, Renaissance (11 articles)
  - 01A45 17th century (17 articles)
  - 01A50 18th century (30 articles)
  - 01A55 19th century (133 articles)
  - 01A60 20th century (251 articles)
  - 01A61 Twenty-first century (12 articles)
  - 01A65 Contemporary (71 articles)
  - 01A67 Future prospectives (2 articles)
  - 01A70 Biographies, obituaries, personalia, bibliographies (873 articles)
  - 01A72 Schools of mathematics (9 articles)
  - 01A73 Universities (21 articles)
  - 01A74 Other institutions and academies (31 articles)
  - 01A75 Collected or selected works; reprintings or translations of classics (13 articles)
  - 01A80 Sociology (and profession) of mathematics (20 articles)
  - 01A85 Historiography (6 articles)
  - 01A90 Bibliographic studies (5 articles)
  - 01A99 Miscellaneous topics (52 articles)
02 (1940-1979) Logic and foundations (23 articles)
- 02 (1940-1979) Logic and foundations
- 02-00 (1973-1979) Difficult to classify at the second level (must be assigned at least one other classification number in this section) (6 articles)
- 02-01 (1973-1979) Elementary exposition (collegiate level)
- 02-02 (1973-1979) Advanced exposition (research surveys, etc.)
- 02-03 (1973-1979) Historical
- 02-04 (1973-1979) Explicit machine computation and programs (not the theory of computation or programming)
- 02-06 (1973-1979) Collections of papers; proceedings of conferences
- 02.0 (1940-1958) Foundations, logic, theory of sets
- 02.00 (1959-1972) General (5 articles)
- 02.10 (1959-1972) Classical deductive systems, general
- 02.12 (1959-1972) Propositional calculus, two-valued
- 02.16 (1959-1972) Predicate calculus
- 02.18 (1959-1972) Classical proof theory
- 02.20 (1959-1972) Nonclassical logic, general
- 02.23 (1959-1972) Intuitionism
- 02.25 (1959-1972) Many-valued logic
- 02.27 (1959-1972) Modal logic
- 02.30 (1959-1972) Formal syntax and linguistics, general (1 articles)
- 02.32 (1959-1972) Higher-order languages
- 02.35 (1959-1972) Infinitary languages
- 02.38 (1959-1972) Languages with additional quantifiers
- 02.40 (1959-1972) Algebraic logic, general
- 02.42 (1959-1972) Boolean algebras, lattices, topologies
- 02.45 (1959-1972) Algebra of relations
- 02.48 (1959-1972) Cylindric and polyadic algebras
- 02.50 (1959-1972) Model theory, general
- 02.52 (1959-1972) Semantics and metamathematics, categoricity (1 articles)
- 02.54 (1959-1972) Axiomatics and applications, decision methods
- 02.57 (1959-1972) Non-standard models
- 02.60 (1959-1972) Axiomatic set theory, general (1 articles)
- 02.63 (1959-1972) Formalization of set theory (1 articles)
- 02.65 (1959-1972) Consistency, independence, existence (2 articles)
- 02.68 (1959-1972) Measurability, accessibility, other special questions
- 02.70 (1959-1972) Recursive function theory, general (1 articles)
- 02.72 (1959-1972) Arithmetic and recursive analysis
- 02.74 (1959-1972) Undecidability
- 02.75 (1959-1972) Unsolvability in mathematical systems
- 02.77 (1959-1972) Hierarchies
- 02.80 (1959-1972) Algorithms and machines, general (3 articles)
- 02.82 (1959-1972) Turing, Post, Thue schemes
- 02.85 (1959-1972) Combinatory logic
- 02.88 (1959-1972) Abstract automaton theory (2 articles)
- 02.99 (1959-1972) None of the above, but in this section
03 Mathematical logic and foundations (1893 articles)
- 03 Mathematical logic and foundations
- 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 03-01 Instructional exposition (textbooks, tutorial papers, etc.) (8 articles)
- 03-02 Research exposition (monographs, survey articles) (6 articles)
- 03-03 Historical (must also be assigned at least one classification number from Section 01) (14 articles)
- 03-04 Explicit machine computation and programs (not the theory of computation or programming)
- 03-06 Proceedings, conferences, collections, etc. (4 articles)
- 03A05 Philosophical and critical (33 articles)
- 03Bxx General logic (277 articles)
  - 03Bxx General logic (1 articles)
  - 03B05 Classical propositional logic (12 articles)
  - 03B10 Classical first-order logic (5 articles)
  - 03B15 Higher-order logic and type theory (4 articles)
  - 03B20 Subsystems of classical logic (including intuitionistic logic) (4 articles)
  - 03B22 Abstract deductive systems (5 articles)
  - 03B25 Decidability of theories and sets of sentences (11 articles)
  - 03B30 Foundations of classical theories (including reverse mathematics) (10 articles)
  - 03B35 Mechanization of proofs and logical operations (12 articles)
  - 03B40 Combinatory logic and lambda-calculus (5 articles)
  - 03B42 Logic of knowledge and belief (1 articles)
  - 03B44 Temporal logic (1 articles)
  - 03B45 Modal logic (12 articles)
  - 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (5 articles)
  - 03B48 Probability and inductive logic (13 articles)
  - 03B50 Many-valued logic (34 articles)
  - 03B52 Fuzzy logic; logic of vagueness (97 articles)
  - 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) (2 articles)
  - 03B55 Intermediate logics (1 articles)
  - 03B60 Other nonclassical logic (11 articles)
  - 03B65 Logic of natural languages (8 articles)
  - 03B70 Logic in computer science (2 articles)
  - 03B80 Other applications of logic
  - 03B99 None of the above, but in this section (21 articles)
- 03Cxx Model theory (119 articles)
  - 03Cxx Model theory (2 articles)
  - 03C05 Equational classes, universal algebra (31 articles)
  - 03C07 Basic properties of first-order languages and structures (1 articles)
  - 03C10 Quantifier elimination, model completeness and related topics (1 articles)
  - 03C13 Finite structures (7 articles)
  - 03C15 Denumerable structures (3 articles)
  - 03C20 Ultraproducts and related constructions (10 articles)
  - 03C25 Model-theoretic forcing (1 articles)
  - 03C30 Other model constructions (5 articles)
  - 03C35 Categoricity and completeness of theories
  - 03C40 Interpolation, preservation, definability (2 articles)
  - 03C45 Classification theory, stability and related concepts (2 articles)
  - 03C50 Models with special properties (saturated, rigid, etc.) (9 articles)
  - 03C52 Properties of classes of models (2 articles)
  - 03C55 Set-theoretic model theory (1 articles)
  - 03C57 Effective and recursion-theoretic model theory (1 articles)
  - 03C60 Model-theoretic algebra (8 articles)
  - 03C62 Models of arithmetic and set theory (5 articles)
  - 03C64 Model theory of ordered structures; o-minimality
  - 03C65 Models of other mathematical theories (8 articles)
  - 03C68 Other classical first-order model theory (3 articles)
  - 03C70 Logic on admissible sets
  - 03C75 Other infinitary logic (1 articles)
  - 03C80 Logic with extra quantifiers and operators (1 articles)
  - 03C85 Second- and higher-order model theory (1 articles)
  - 03C90 Nonclassical models (Boolean-valued, sheaf, etc.) (2 articles)
  - 03C95 Abstract model theory (1 articles)
  - 03C98 Applications of model theory (4 articles)
  - 03C99 None of the above, but in this section (7 articles)
- 03Dxx Computability and recursion theory (104 articles)
  - 03Dxx Computability and recursion theory
  - 03D03 Thue and Post systems, etc.
  - 03D05 Automata and formal grammars in connection with logical questions (11 articles)
  - 03D10 Turing machines and related notions (13 articles)
  - 03D15 Complexity of computation (15 articles)
  - 03D20 Recursive functions and relations, subrecursive hierarchies (8 articles)
  - 03D25 Recursively (computably) enumerable sets and degrees (7 articles)
  - 03D28 Other Turing degree structures
  - 03D30 Other degrees and reducibilities (9 articles)
  - 03D35 Undecidability and degrees of sets of sentences (3 articles)
  - 03D40 Word problems, etc. (1 articles)
  - 03D45 Theory of numerations, effectively presented structures (2 articles)
  - 03D50 Recursive equivalence types of sets and structures, isols
  - 03D55 Hierarchies (12 articles)
  - 03D60 Computability and recursion theory on ordinals, admissible sets, etc. (9 articles)
  - 03D65 Higher-type and set recursion theory
  - 03D70 Inductive definability (3 articles)
  - 03D75 Abstract and axiomatic computability and recursion theory (1 articles)
  - 03D80 Applications of computability and recursion theory (3 articles)
  - 03D99 None of the above, but in this section (7 articles)
- 03Exx Set theory (866 articles)
  - 03Exx Set theory (3 articles)
  - 03E02 Partition relations (7 articles)
  - 03E04 Ordered sets and their cofinalities; pcf theory (5 articles)
  - 03E05 Other combinatorial set theory (93 articles)
  - 03E10 Ordinal and cardinal numbers (19 articles)
  - 03E15 Descriptive set theory (50 articles)
  - 03E17 Cardinal characteristics of the continuum (35 articles)
  - 03E20 Other classical set theory (including functions, relations, and set algebra) (52 articles)
  - 03E25 Axiom of choice and related propositions (52 articles)
  - 03E30 Axiomatics of classical set theory and its fragments (10 articles)
  - 03E35 Consistency and independence results (106 articles)
  - 03E40 Other aspects of forcing and Boolean-valued models (28 articles)
  - 03E45 Inner models, including constructibility, ordinal definability, and core models (10 articles)
  - 03E47 Other notions of set-theoretic definability (1 articles)
  - 03E50 Continuum hypothesis and Martin's axiom (38 articles)
  - 03E55 Large cardinals (28 articles)
  - 03E60 Determinacy principles (4 articles)
  - 03E65 Other hypotheses and axioms (15 articles)
  - 03E70 Nonclassical and second-order set theories (91 articles)
  - 03E72 Fuzzy set theory (184 articles)
  - 03E75 Applications of set theory (20 articles)
  - 03E99 None of the above, but in this section (15 articles)
- 03Fxx Proof theory and constructive mathematics (110 articles)
  - 03Fxx Proof theory and constructive mathematics
  - 03F03 Proof theory, general (1 articles)
  - 03F05 Cut-elimination and normal-form theorems (3 articles)
  - 03F07 Structure of proofs (6 articles)
  - 03F10 Functionals in proof theory
  - 03F15 Recursive ordinals and ordinal notations
  - 03F20 Complexity of proofs (5 articles)
  - 03F25 Relative consistency and interpretations (6 articles)
  - 03F30 First-order arithmetic and fragments (12 articles)
  - 03F35 Second- and higher-order arithmetic and fragments (4 articles)
  - 03F40 Gödel numberings in proof theory (1 articles)
  - 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) (1 articles)
  - 03F50 Metamathematics of constructive systems
  - 03F52 Linear logic and other substructural logics
  - 03F55 Intuitionistic mathematics (2 articles)
  - 03F60 Constructive and recursive analysis (17 articles)
  - 03F65 Other constructive mathematics (19 articles)
  - 03F99 None of the above, but in this section (33 articles)
- 03Gxx Algebraic logic (271 articles)
  - 03Gxx Algebraic logic
  - 03G05 Boolean algebras (26 articles)
  - 03G10 Lattices and related structures (36 articles)
  - 03G12 Quantum logic (107 articles)
  - 03G15 Cylindric and polyadic algebras; relation algebras (5 articles)
  - 03G20 Lukasiewicz and Post algebras (16 articles)
  - 03G25 Other algebras related to logic (76 articles)
  - 03G30 Categorical logic, topoi (3 articles)
  - 03G99 None of the above, but in this section (2 articles)
- 03Hxx Nonstandard models (81 articles)
  - 03Hxx Nonstandard models
  - 03H05 Nonstandard models in mathematics (31 articles)
  - 03H10 Other applications of nonstandard models (economics, physics, etc.) (3 articles)
  - 03H15 Nonstandard models of arithmetic (23 articles)
  - 03H99 None of the above, but in this section (24 articles)
04 Set theory (172 articles)
- 04 Set theory
- 04-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 04-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 04-02 Research exposition (monographs, survey articles)
- 04-03 Historical (must be assigned at least one classification number from Section 01) (1 articles)
- 04-04 Explicit machine computation and programs (not the theory of computation or programming)
- 04-06 Proceedings, conferences, collections, etc.
- 04.00 (1959-1972) General (3 articles)
- 04.15 (1959-1972) Point sets
- 04.20 (1959-1972) Relations (2 articles)
- 04.30 (1959-1972) Transfinite numbers (1 articles)
- 04.40 (1959-1972) Descriptive set theory; Borel classifications, Suslin schemes, etc. (4 articles)
- 04.60 (1959-1972) Combinatorial (4 articles)
- 04.99 (1959-1972) None of the above, but in this section (1 articles)
- 04A03 Set algebra
- 04A05 Relations, functions (35 articles)
- 04A10 Ordinal and cardinal numbers; generalizations (3 articles)
- 04A15 Descriptive set theory; Borel classifications, Suslin schemes, etc. (17 articles)
- 04A20 Combinatorial set theory (40 articles)
- 04A25 Axiom of choice and equivalent propositions (Zorn's lemma, etc.) (8 articles)
- 04A30 Continuum hypothesis, generalized continuum hypothesis (4 articles)
- 04A72 Fuzzy sets, fuzzy relations (43 articles)
- 04A99 Miscellaneous topics (5 articles)
05 Combinatorics (2513 articles)
- 05 Combinatorics
- 05-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (3 articles)
- 05-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 05-02 Research exposition (monographs, survey articles) (4 articles)
- 05-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 05-04 Explicit machine computation and programs (not the theory of computation or programming) (6 articles)
- 05-06 Proceedings, conferences, collections, etc.
- 05.0 (1940-1958) Combinatorial analysis
- 05.00 (1959-1972) General (5 articles)
- 05.04 (1959-1972) Combinatorial choice problems; subsets, representatives (4 articles)
- 05.05 (1959-1972) Factorials, binomial coefficients, combinatorial functions (6 articles)
- 05.10 (1959-1972) Combinatorial enumeration problems, generating functions (6 articles)
- 05.15 (1959-1972) Combinatorial inequalities
- 05.20 (1959-1972) Block designs (1 articles)
- 05.22 (1959-1972) Difference sets (number-theoretic, group-theoretic, etc.) (1 articles)
- 05.24 (1959-1972) Orthogonal arrays, Latin squares (1 articles)
- 05.25 (1959-1972) Matrices
- 05.27 (1959-1972) Finite geometries
- 05.30 (1959-1972) Other designs, configurations
- 05.35 (1959-1972) Matroids, geometric lattices
- 05.40 (1959-1972) Graphs, general theory (15 articles)
- 05.45 (1959-1972) Trees (1 articles)
- 05.50 (1959-1972) Topological graph theory, embedding (1 articles)
- 05.55 (1959-1972) Chromatic theory of graphs and maps (2 articles)
- 05.60 (1959-1972) Directed graphs (digraphs) (5 articles)
- 05.62 (1959-1972) Graphs and groups (4 articles)
- 05.65 (1959-1972) Enumeration of graphs and maps (1 articles)
- 05.99 (1959-1972) None of the above, but in this section
- 05Axx Enumerative combinatorics (200 articles)
  - 05Axx Enumerative combinatorics (3 articles)
  - 05A05 Combinatorial choice problems (subsets, representatives, permutations) (33 articles)
  - 05A10 Factorials, binomial coefficients, combinatorial functions (23 articles)
  - 05A15 Exact enumeration problems, generating functions (41 articles)
  - 05A16 Asymptotic enumeration (3 articles)
  - 05A17 Partitions of integers (31 articles)
  - 05A18 Partitions of sets (9 articles)
  - 05A19 Combinatorial identities (25 articles)
  - 05A20 Combinatorial inequalities (5 articles)
  - 05A30 $q$-calculus and related topics (8 articles)
  - 05A40 Umbral calculus (4 articles)
  - 05A99 None of the above, but in this section (15 articles)
- 05Bxx Designs and configurations (167 articles)
  - 05Bxx Designs and configurations (1 articles)
  - 05B05 Block designs (12 articles)
  - 05B07 Triple systems (7 articles)
  - 05B10 Difference sets (number-theoretic, group-theoretic, etc.) (3 articles)
  - 05B15 Orthogonal arrays, Latin squares, Room squares (36 articles)
  - 05B20 Matrices (incidence, Hadamard, etc.) (16 articles)
  - 05B25 Finite geometries (13 articles)
  - 05B30 Other designs, configurations (29 articles)
  - 05B35 Matroids, geometric lattices (21 articles)
  - 05B40 Packing and covering (6 articles)
  - 05B45 Tessellation and tiling problems (12 articles)
  - 05B50 Polyominoes (3 articles)
  - 05B99 None of the above, but in this section (8 articles)
- 05Cxx Graph theory (2026 articles)
  - 05Cxx Graph theory (21 articles)
  - 05C05 Trees (124 articles)
  - 05C07 Degree sequences (23 articles)
  - 05C10 Topological graph theory, imbedding (102 articles)
  - 05C12 Distance in graphs (101 articles)
  - 05C15 Coloring of graphs and hypergraphs (131 articles)
  - 05C17 Perfect graphs (2 articles)
  - 05C20 Directed graphs (digraphs), tournaments (157 articles)
  - 05C22 Signed, gain and biased graphs (11 articles)
  - 05C25 Graphs and groups (89 articles)
  - 05C30 Enumeration of graphs and maps (23 articles)
  - 05C35 Extremal problems (171 articles)
  - 05C38 Paths and cycles (121 articles)
  - 05C40 Connectivity (62 articles)
  - 05C45 Eulerian and Hamiltonian graphs (49 articles)
  - 05C50 Graphs and matrices (115 articles)
  - 05C55 Generalized Ramsey theory (29 articles)
  - 05C60 Isomorphism problems (reconstruction conjecture, etc.) (19 articles)
  - 05C62 Graph representations (geometric and intersection representations, etc.) (3 articles)
  - 05C65 Hypergraphs (44 articles)
  - 05C69 Dominating sets, independent sets, cliques (75 articles)
  - 05C70 Factorization, matching, covering and packing (92 articles)
  - 05C75 Structural characterization of types of graphs (123 articles)
  - 05C78 Graph labelling (graceful graphs, bandwidth, etc.) (30 articles)
  - 05C80 Random graphs (8 articles)
  - 05C83 Graph minors (2 articles)
  - 05C85 Graph algorithms (23 articles)
  - 05C90 Applications (11 articles)
  - 05C99 None of the above, but in this section (265 articles)
- 05Dxx Extremal combinatorics (25 articles)
  - 05Dxx Extremal combinatorics
  - 05D05 Extremal set theory (4 articles)
  - 05D10 Ramsey theory (15 articles)
  - 05D15 Transversal (matching) theory (2 articles)
  - 05D40 Probabilistic methods (1 articles)
  - 05D99 None of the above, but in this section (3 articles)
- 05Exx Algebraic combinatorics (23 articles)
  - 05Exx Algebraic combinatorics
  - 05E05 Symmetric functions (4 articles)
  - 05E10 Tableaux, representations of the symmetric group (4 articles)
  - 05E15 Combinatorial problems concerning the classical groups (4 articles)
  - 05E20 Group actions on designs, geometries and codes (1 articles)
  - 05E25 Group actions on posets and homology groups of posets
  - 05E30 Association schemes, strongly regular graphs (6 articles)
  - 05E35 Orthogonal polynomials
  - 05E99 None of the above, but in this section (4 articles)
06 Order, lattices, ordered algebraic structures (2272 articles)
- 06 Order, lattices, ordered algebraic structures
- 06-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (12 articles)
- 06-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 06-02 Research exposition (monographs, survey articles) (1 articles)
- 06-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 06-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 06-06 Proceedings, conferences, collections, etc.
- 06.0 (1940-1958) Partial order, lattices
- 06.00 (1959-1972) General (10 articles)
- 06.10 (1959-1972) Total order (1 articles)
- 06.20 (1959-1972) Partial order (5 articles)
- 06.30 (1959-1972) Lattices, generalizations (8 articles)
- 06.35 (1959-1972) Complemented lattices, generalizations
- 06.40 (1959-1972) Modular lattices, continuous geometries, generalizations (2 articles)
- 06.50 (1959-1972) Distributive lattices, generalizations (4 articles)
- 06.60 (1959-1972) Boolean algebras and rings (3 articles)
- 06.65 (1959-1972) Order topologies (3 articles)
- 06.70 (1959-1972) Ordered semigroups, other generalizations of groups (4 articles)
- 06.75 (1959-1972) Ordered groups (15 articles)
- 06.78 (1959-1972) Ordered abelian groups (1 articles)
- 06.80 (1959-1972) Ordered linear spaces
- 06.85 (1959-1972) Ordered rings, algebras, modules (See 12.70 for ordered fields)
- 06.90 (1959-1972) Other ordered algebraic structures
- 06.99 (1959-1972) None of the above, but in this section
- 06Axx Ordered sets (412 articles)
  - 06Axx Ordered sets (2 articles)
  - 06A05 Total order (18 articles)
  - 06A06 Partial order, general (183 articles)
  - 06A07 Combinatorics of partially ordered sets (32 articles)
  - 06A11 Algebraic aspects of posets (20 articles)
  - 06A12 Semilattices (79 articles)
  - 06A15 Galois correspondences, closure operators (49 articles)
  - 06A99 None of the above, but in this section (29 articles)
- 06Bxx Lattices (468 articles)
  - 06Bxx Lattices (1 articles)
  - 06B05 Structure theory (122 articles)
  - 06B10 Ideals, congruence relations (95 articles)
  - 06B15 Representation theory (30 articles)
  - 06B20 Varieties of lattices (39 articles)
  - 06B23 Complete lattices, completions (61 articles)
  - 06B25 Free lattices, projective lattices, word problems (12 articles)
  - 06B30 Topological lattices, order topologies (30 articles)
  - 06B35 Continuous lattices and posets, applications (24 articles)
  - 06B99 None of the above, but in this section (54 articles)
- 06Cxx Modular lattices, complemented lattices (200 articles)
  - 06Cxx Modular lattices, complemented lattices
  - 06C05 Modular lattices, Desarguesian lattices (51 articles)
  - 06C10 Semimodular lattices, geometric lattices (13 articles)
  - 06C15 Complemented lattices, orthocomplemented lattices and posets (121 articles)
  - 06C20 Complemented modular lattices, continuous geometries (7 articles)
  - 06C99 None of the above, but in this section (8 articles)
- 06Dxx Distributive lattices (400 articles)
  - 06Dxx Distributive lattices (1 articles)
  - 06D05 Structure and representation theory (72 articles)
  - 06D10 Complete distributivity (25 articles)
  - 06D15 Pseudocomplemented lattices (39 articles)
  - 06D20 Heyting algebras (29 articles)
  - 06D22 Frames, locales (21 articles)
  - 06D25 Post algebras (4 articles)
  - 06D30 De Morgan algebras, Lukasiewicz algebras (25 articles)
  - 06D35 MV-algebras (117 articles)
  - 06D50 Lattices and duality (8 articles)
  - 06D72 Fuzzy lattices (soft algebras) and related topics (5 articles)
  - 06D99 None of the above, but in this section (54 articles)
- 06Exx Boolean algebras (Boolean rings) (132 articles)
  - 06Exx Boolean algebras (Boolean rings) (3 articles)
  - 06E05 Structure theory (46 articles)
  - 06E10 Chain conditions, complete algebras (15 articles)
  - 06E15 Stone space and related constructions (16 articles)
  - 06E20 Ring-theoretic properties (9 articles)
  - 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.) (3 articles)
  - 06E30 Boolean functions (9 articles)
  - 06E99 None of the above, but in this section (31 articles)
- 06Fxx Ordered structures (589 articles)
  - 06Fxx Ordered structures
  - 06F05 Ordered semigroups and monoids (106 articles)
  - 06F07 Quantales (3 articles)
  - 06F10 Noether lattices (7 articles)
  - 06F15 Ordered groups (232 articles)
  - 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces (122 articles)
  - 06F25 Ordered rings, algebras, modules (45 articles)
  - 06F30 Topological lattices, order topologies (22 articles)
  - 06F35 BCK-algebras, BCI-algebras (30 articles)
  - 06F99 None of the above, but in this section (22 articles)
08 General algebraic systems (1100 articles)
- 08 General algebraic systems
- 08-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 08-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 08-02 Research exposition (monographs, survey articles) (2 articles)
- 08-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 08-04 Explicit machine computation and programs (not the theory of computation or programming) (2 articles)
- 08-06 Proceedings, conferences, collections, etc.
- 08.00 (1959-1972) General (3 articles)
- 08.10 (1959-1972) Concrete categories, structures (3 articles)
- 08.20 (1959-1972) Laws of composition
- 08.30 (1959-1972) Universal algebra, general algebraic structures (5 articles)
- 08.40 (1959-1972) Other (1 articles)
- 08.99 (1959-1972) None of the above, but in this section
- 08Axx Algebraic structures (735 articles)
  - 08Axx Algebraic structures (38 articles)
  - 08A02 Relational systems, laws of composition (69 articles)
  - 08A05 Structure theory (117 articles)
  - 08A30 Subalgebras, congruence relations (200 articles)
  - 08A35 Automorphisms, endomorphisms (48 articles)
  - 08A40 Operations, polynomials, primal algebras (44 articles)
  - 08A45 Equational compactness (3 articles)
  - 08A50 Word problems (4 articles)
  - 08A55 Partial algebras (44 articles)
  - 08A60 Unary algebras (91 articles)
  - 08A62 Finitary algebras (15 articles)
  - 08A65 Infinitary algebras (2 articles)
  - 08A68 Heterogeneous algebras (5 articles)
  - 08A70 Applications of universal algebra in computer science (4 articles)
  - 08A72 Fuzzy algebraic structures (23 articles)
  - 08A99 None of the above, but in this section (28 articles)
- 08Bxx Varieties (293 articles)
  - 08Bxx Varieties
  - 08B05 Equational logic, Malcev (Maltsev) conditions (90 articles)
  - 08B10 Congruence modularity, congruence distributivity (48 articles)
  - 08B15 Lattices of varieties (44 articles)
  - 08B20 Free algebras (37 articles)
  - 08B25 Products, amalgamated products, and other kinds of limits and colimits (9 articles)
  - 08B26 Subdirect products and subdirect irreducibility (13 articles)
  - 08B30 Injectives, projectives (2 articles)
  - 08B99 None of the above, but in this section (50 articles)
- 08Cxx Other classes of algebras (51 articles)
  - 08Cxx Other classes of algebras
  - 08C05 Categories of algebras (19 articles)
  - 08C10 Axiomatic model classes (6 articles)
  - 08C15 Quasivarieties (18 articles)
  - 08C99 None of the above, but in this section (8 articles)
09 (1940-1972) Classical algebra
- 09 (1940-1972) Classical algebra
- 09.0 (1940-1958) Algebra
- 09.00 (1959-1972) Classical algebra
- 09.1 (1940-1958) Abstract algebra
- 09.2 (1940-1958) Elementary algebra
- 09.3 (1940-1958) Rings, fields and algebras
10 (1940-1984) Number theory (41 articles)
- 10 (1940-1984) Number theory
- 10-00 (1973-1979) Difficult to classify at the second level (must be assigned at least one other classification number in this section) (2 articles)
- 10-01 (1973-1984) Elementary exposition, textbooks
- 10-02 (1973-1984) Advanced exposition (research surveys, monographs, etc.)
- 10-03 (1973-1984) Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 10-04 (1973-1984) Explicit machine computation and programs (not the theory of computation or programming)
- 10-06 (1973-1984) Proceedings, conferences, etc.
- 10.0 (1940-1958) Number theory
- 10.00 (1959-1972) General (7 articles)
- 10.01 (1959-1972) General books
- 10.02 (1959-1972) Tables
- 10.03 (1959-1972) Computations
- 10.05 (1959-1972) Elementary number theory, general (2 articles)
- 10.06 (1959-1972) Congruences, residues (1 articles)
- 10.07 (1959-1972) Special functions and sequences
- 10.08 (1959-1972) Elementary prime number theory
- 10.09 (1959-1972) Expansions and algorithms (2 articles)
- 10.1 (1940-1958) Analytic number theory
- 10.10 (1959-1972) Diophantine equations, general (1 articles)
- 10.11 (1959-1972) Linear and quadratic equations (2 articles)
- 10.12 (1959-1972) Cubic and quartic equations
- 10.13 (1959-1972) Equations of higher degree (1 articles)
- 10.14 (1959-1972) Local ($p$-adic) theory
- 10.15 (1959-1972) Forms, general
- 10.16 (1959-1972) Quadratic, Hermitian forms
- 10.17 (1959-1972) Forms of degree $\geq 3$ (1 articles)
- 10.18 (1959-1972) Multi-linear forms
- 10.2 (1940-1958) Algebraic number theory
- 10.20 (1959-1972) Modular functions and forms, automorphic functions
- 10.21 (1959-1972) Modular group, modular functions
- 10.22 (1959-1972) Automorphic forms, one variable
- 10.23 (1959-1972) Several variables
- 10.25 (1959-1972) Geometry of numbers
- 10.3 (1940-1958) Geometry of numbers, Diophantine approximation
- 10.30 (1959-1972) Diophantine approximation (1 articles)
- 10.31 (1959-1972) Linear approximation, continued fractions
- 10.32 (1959-1972) Algebraicity, irrationality and transcendence (1 articles)
- 10.33 (1959-1972) Distribution modulo 1, normal numbers (2 articles)
- 10.34 (1959-1972) Analytic and $p$-adic theory
- 10.4 (1940-1958) Continued fractions
- 10.40 (1959-1972) Analytic multiplicative theory, general
- 10.41 (1959-1972) Analytic tools (Zeta- and $L$-functions, exponential sums, etc.) (4 articles)
- 10.42 (1959-1972) Distribution of the integers with specified multiplicative structure (including primes) (2 articles)
- 10.43 (1959-1972) Number-theoretic functions
- 10.45 (1959-1972) Analytic additive theory, general (1 articles)
- 10.46 (1959-1972) Sums of powers, generalizations (4 articles)
- 10.47 (1959-1972) Additive questions concerning primes
- 10.48 (1959-1972) Partitions, generating functions (1 articles)
- 10.49 (1959-1972) Sequences
- 10.50 (1959-1972) Probabilistic number theory (2 articles)
- 10.55 (1959-1972) Combinatorial problems in number theory
- 10.60 (1959-1972) Sequences of integers, general (1 articles)
- 10.61 (1959-1972) Recursive and other special sequences
- 10.62 (1959-1972) Addition of sequences, basis, essential components, etc. (1 articles)
- 10.63 (1959-1972) Density of special sequences
- 10.64 (1959-1972) Sieves
- 10.65 (1959-1972) Algebraic number theory, general
- 10.66 (1959-1972) Individual algebraic number fields (quadratic, cubic, cyclotomic, Kummer, etc.) (1 articles)
- 10.67 (1959-1972) Local theory (valuations, finite extensions of $p$-adic fields)
- 10.68 (1959-1972) Class field theory, complex multiplication
- 10.69 (1959-1972) Arithmetic of general rings
- 10.75 (1959-1972) Arithmetic theory of algebraic objects
- 10.76 (1959-1972) Polynomials
- 10.77 (1959-1972) Finite fields, power series fields
- 10.78 (1959-1972) Valued fields, algebraic function fields
- 10.79 (1959-1972) Matrices
- 10.80 (1959-1972) Decidability, other logical questions
- 10.99 (1959-1972) None of the above, but in this section
11 Number theory (1760 articles)
- 11 Number theory
- 11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 11-01 Instructional exposition (textbooks, tutorial papers, etc.) (14 articles)
- 11-02 Research exposition (monographs, survey articles) (6 articles)
- 11-03 Historical (must also be assigned at least one classification number from Section 01) (13 articles)
- 11-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 11-06 Proceedings, conferences, collections, etc.
- 11Axx Elementary number theory (287 articles)
  - 11Axx Elementary number theory (2 articles)
  - 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors (38 articles)
  - 11A07 Congruences; primitive roots; residue systems (65 articles)
  - 11A15 Power residues, reciprocity (20 articles)
  - 11A25 Arithmetic functions; related numbers; inversion formulas (62 articles)
  - 11A41 Primes (28 articles)
  - 11A51 Factorization; primality (26 articles)
  - 11A55 Continued fractions (18 articles)
  - 11A63 Radix representation; digital problems (19 articles)
  - 11A67 Other representations (1 articles)
  - 11A99 None of the above, but in this section (8 articles)
- 11Bxx Sequences and sets (269 articles)
  - 11Bxx Sequences and sets (1 articles)
  - 11B05 Density, gaps, topology (34 articles)
  - 11B13 Additive bases (7 articles)
  - 11B25 Arithmetic progressions (13 articles)
  - 11B34 Representation functions (1 articles)
  - 11B37 Recurrences (25 articles)
  - 11B39 Fibonacci and Lucas numbers and polynomials and generalizations (57 articles)
  - 11B50 Sequences (mod $m$) (15 articles)
  - 11B57 Farey sequences; the sequences $ (2 articles)
  - 11B65 Binomial coefficients; factorials; $q$-identities (23 articles)
  - 11B68 Bernoulli and Euler numbers and polynomials (33 articles)
  - 11B73 Bell and Stirling numbers (3 articles)
  - 11B75 Other combinatorial number theory (8 articles)
  - 11B83 Special sequences and polynomials (33 articles)
  - 11B85 Automata sequences (3 articles)
  - 11B99 None of the above, but in this section (11 articles)
- 11Cxx Polynomials and matrices (28 articles)
  - 11Cxx Polynomials and matrices (1 articles)
  - 11C08 Polynomials (14 articles)
  - 11C20 Matrices, determinants (12 articles)
  - 11C99 None of the above, but in this section (1 articles)
- 11Dxx Diophantine equations (134 articles)
  - 11Dxx Diophantine equations
  - 11D04 Linear equations (15 articles)
  - 11D09 Quadratic and bilinear equations (15 articles)
  - 11D25 Cubic and quartic equations (12 articles)
  - 11D41 Higher degree equations; Fermat's equation (18 articles)
  - 11D45 Counting solutions of Diophantine equations (9 articles)
  - 11D57 Multiplicative and norm form equations (3 articles)
  - 11D59 Thue-Mahler equations (4 articles)
  - 11D61 Exponential equations (23 articles)
  - 11D68 Rational numbers as sums of fractions (4 articles)
  - 11D72 Equations in many variables (10 articles)
  - 11D75 Diophantine inequalities (9 articles)
  - 11D79 Congruences in many variables (4 articles)
  - 11D85 Representation problems (3 articles)
  - 11D88 $p$-adic and power series fields (1 articles)
  - 11D99 None of the above, but in this section (4 articles)
- 11Exx Forms and linear algebraic groups (84 articles)
  - 11Exx Forms and linear algebraic groups (1 articles)
  - 11E04 Quadratic forms over general fields (8 articles)
  - 11E08 Quadratic forms over local rings and fields (2 articles)
  - 11E10 Forms over real fields (4 articles)
  - 11E12 Quadratic forms over global rings and fields (10 articles)
  - 11E16 General binary quadratic forms (4 articles)
  - 11E20 General ternary and quaternary quadratic forms; forms of more than two variables (2 articles)
  - 11E25 Sums of squares and representations by other particular quadratic forms (5 articles)
  - 11E39 Bilinear and Hermitian forms (2 articles)
  - 11E41 Class numbers of quadratic and Hermitian forms (23 articles)
  - 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (2 articles)
  - 11E57 Classical groups (2 articles)
  - 11E70 $K$-theory of quadratic and Hermitian forms
  - 11E72 Galois cohomology of linear algebraic groups
  - 11E76 Forms of degree higher than two (1 articles)
  - 11E81 Algebraic theory of quadratic forms; Witt groups and rings (16 articles)
  - 11E88 Quadratic spaces; Clifford algebras
  - 11E95 $p$-adic theory (2 articles)
  - 11E99 None of the above, but in this section
- 11Fxx Discontinuous groups and automorphic forms (44 articles)
  - 11Fxx Discontinuous groups and automorphic forms
  - 11F03 Modular and automorphic functions (1 articles)
  - 11F06 Structure of modular groups and generalizations; arithmetic groups (2 articles)
  - 11F11 Modular forms, one variable (5 articles)
  - 11F12 Automorphic forms, one variable (2 articles)
  - 11F20 Dedekind eta function, Dedekind sums (7 articles)
  - 11F22 Relationship to Lie algebras and finite simple groups (1 articles)
  - 11F23 Relations with algebraic geometry and topology
  - 11F25 Hecke-Petersson operators, differential operators (one variable)
  - 11F27 Theta series; Weil representation (3 articles)
  - 11F30 Fourier coefficients of automorphic forms (10 articles)
  - 11F32 Modular correspondences, etc.
  - 11F33 Congruences for modular and $p$-adic modular forms
  - 11F37 Forms of half-integer weight; nonholomorphic modular forms (2 articles)
  - 11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (1 articles)
  - 11F46 Siegel modular groups and their modular and automorphic forms (1 articles)
  - 11F50 Jacobi forms (1 articles)
  - 11F52 Modular forms associated to Drinfel'd modules
  - 11F55 Other groups and their modular and automorphic forms (several variables)
  - 11F60 Hecke-Petersson operators, differential operators (several variables)
  - 11F66 Dirichlet series and functional equations in connection with modular forms (4 articles)
  - 11F67 Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols (1 articles)
  - 11F70 Representation-theoretic methods; automorphic representations over local and global fields
  - 11F72 Spectral theory; Selberg trace formula
  - 11F75 Cohomology of arithmetic groups
  - 11F80 Galois representations (3 articles)
  - 11F85 $p$-adic theory, local fields
  - 11F99 None of the above, but in this section
- 11Gxx Arithmetic algebraic geometry (Diophantine geometry) (21 articles)
  - 11Gxx Arithmetic algebraic geometry (Diophantine geometry)
  - 11G05 Elliptic curves over global fields (12 articles)
  - 11G07 Elliptic curves over local fields (1 articles)
  - 11G09 Drinfeld modules; higher-dimensional motives, etc.
  - 11G10 Abelian varieties of dimension $gtr 1$ (1 articles)
  - 11G15 Complex multiplication and moduli of abelian varieties
  - 11G16 Elliptic and modular units (1 articles)
  - 11G18 Arithmetic aspects of modular and Shimura varieties (2 articles)
  - 11G20 Curves over finite and local fields (2 articles)
  - 11G25 Varieties over finite and local fields
  - 11G30 Curves of arbitrary genus or genus $ e 1$ over global fields (1 articles)
  - 11G35 Varieties over global fields
  - 11G40 $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (1 articles)
  - 11G45 Geometric class field theory
  - 11G50 Heights
  - 11G55 Polylogarithms and relations with $K$-theory
  - 11G99 None of the above, but in this section
- 11Hxx Geometry of numbers (20 articles)
  - 11Hxx Geometry of numbers
  - 11H06 Lattices and convex bodies (10 articles)
  - 11H16 Nonconvex bodies (4 articles)
  - 11H31 Lattice packing and covering (2 articles)
  - 11H46 Products of linear forms
  - 11H50 Minima of forms (2 articles)
  - 11H55 Quadratic forms (reduction theory, extreme forms, etc.)
  - 11H56 Automorphism groups of lattices (1 articles)
  - 11H60 Mean value and transfer theorems
  - 11H71 Relations with coding theory
  - 11H99 None of the above, but in this section (1 articles)
- 11Jxx Diophantine approximation, transcendental number theory (102 articles)
  - 11Jxx Diophantine approximation, transcendental number theory (5 articles)
  - 11J04 Homogeneous approximation to one number (5 articles)
  - 11J06 Markov and Lagrange spectra and generalizations
  - 11J13 Simultaneous homogeneous approximation, linear forms (12 articles)
  - 11J17 Approximation by numbers from a fixed field (2 articles)
  - 11J20 Inhomogeneous linear forms (2 articles)
  - 11J25 Diophantine inequalities (3 articles)
  - 11J54 Small fractional parts of polynomials and generalizations (1 articles)
  - 11J61 Approximation in non-Archimedean valuations (3 articles)
  - 11J68 Approximation to algebraic numbers (4 articles)
  - 11J70 Continued fractions and generalizations (6 articles)
  - 11J71 Distribution modulo one (6 articles)
  - 11J72 Irrationality; linear independence over a field (5 articles)
  - 11J81 Transcendence (general theory) (13 articles)
  - 11J82 Measures of irrationality and of transcendence (3 articles)
  - 11J83 Metric theory (5 articles)
  - 11J85 Algebraic independence; Gelfond's method (4 articles)
  - 11J86 Linear forms in logarithms; Baker's method (15 articles)
  - 11J89 Transcendence theory of elliptic and abelian functions (1 articles)
  - 11J91 Transcendence theory of other special functions (4 articles)
  - 11J93 Transcendence theory of Drinfel'd and $t$-modules
  - 11J95 Results involving abelian varieties
  - 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)
  - 11J99 None of the above, but in this section (3 articles)
- 11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms (80 articles)
  - 11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms
  - 11K06 General theory of distribution modulo $1$ (18 articles)
  - 11K16 Normal numbers, radix expansions, etc. (5 articles)
  - 11K31 Special sequences (11 articles)
  - 11K36 Well-distributed sequences and other variations (2 articles)
  - 11K38 Irregularities of distribution, discrepancy (9 articles)
  - 11K41 Continuous, $p$-adic and abstract analogues
  - 11K45 Pseudo-random numbers; Monte Carlo methods (7 articles)
  - 11K50 Metric theory of continued fractions (1 articles)
  - 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension (15 articles)
  - 11K60 Diophantine approximation (1 articles)
  - 11K65 Arithmetic functions (6 articles)
  - 11K70 Harmonic analysis and almost periodicity (2 articles)
  - 11K99 None of the above, but in this section (3 articles)
- 11Lxx Exponential sums and character sums (57 articles)
  - 11Lxx Exponential sums and character sums
  - 11L03 Trigonometric and exponential sums, general (6 articles)
  - 11L05 Gauss and Kloosterman sums; generalizations (24 articles)
  - 11L07 Estimates on exponential sums (10 articles)
  - 11L10 Jacobsthal and Brewer sums; other complete character sums (2 articles)
  - 11L15 Weyl sums (1 articles)
  - 11L20 Sums over primes (3 articles)
  - 11L26 Sums over arbitrary intervals
  - 11L40 Estimates on character sums (11 articles)
  - 11L99 None of the above, but in this section
- 11Mxx Zeta and $L$-functions: analytic theory (65 articles)
  - 11Mxx Zeta and $L$-functions: analytic theory
  - 11M06 $zeta (s)$ and $L(s, chi)$ (27 articles)
  - 11M20 Real zeros of $L(s, chi)$; results on $L(1, chi)$ (6 articles)
  - 11M26 Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses (8 articles)
  - 11M35 Hurwitz and Lerch zeta functions (6 articles)
  - 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas (2 articles)
  - 11M38 Zeta and $L$-functions in characteristic $p$ (2 articles)
  - 11M41 Other Dirichlet series and zeta functions (10 articles)
  - 11M45 Tauberian theorems (1 articles)
  - 11M99 None of the above, but in this section (3 articles)
- 11Nxx Multiplicative number theory (105 articles)
  - 11Nxx Multiplicative number theory
  - 11N05 Distribution of primes (19 articles)
  - 11N13 Primes in progressions (7 articles)
  - 11N25 Distribution of integers with specified multiplicative constraints (9 articles)
  - 11N30 Turán theory (1 articles)
  - 11N32 Primes represented by polynomials; other multiplicative structure of polynomial values (4 articles)
  - 11N35 Sieves (5 articles)
  - 11N36 Applications of sieve methods (5 articles)
  - 11N37 Asymptotic results on arithmetic functions (29 articles)
  - 11N45 Asymptotic results on counting functions for algebraic and topological structures (6 articles)
  - 11N56 Rate of growth of arithmetic functions (2 articles)
  - 11N60 Distribution functions associated with additive and positive multiplicative functions (3 articles)
  - 11N64 Other results on the distribution of values or the characterization of arithmetic functions (4 articles)
  - 11N69 Distribution of integers in special residue classes (6 articles)
  - 11N75 Applications of automorphic functions and forms to multiplicative problems (1 articles)
  - 11N80 Generalized primes and integers (4 articles)
  - 11N99 None of the above, but in this section
- 11Pxx Additive number theory; partitions (83 articles)
  - 11Pxx Additive number theory; partitions
  - 11P05 Waring's problem and variants (5 articles)
  - 11P21 Lattice points in specified regions (55 articles)
  - 11P32 Goldbach-type theorems; other additive questions involving primes (6 articles)
  - 11P55 Applications of the Hardy-Littlewood method (6 articles)
  - 11P70 Inverse problems of additive number theory (1 articles)
  - 11P81 Elementary theory of partitions (3 articles)
  - 11P82 Analytic theory of partitions (3 articles)
  - 11P83 Partitions; congruences and congruential restrictions (1 articles)
  - 11P99 None of the above, but in this section (3 articles)
- 11Rxx Algebraic number theory: global fields (243 articles)
  - 11Rxx Algebraic number theory: global fields (1 articles)
  - 11R04 Algebraic numbers; rings of algebraic integers (16 articles)
  - 11R06 PV-numbers and generalizations; other special algebraic numbers (5 articles)
  - 11R09 Polynomials (irreducibility, etc.) (10 articles)
  - 11R11 Quadratic extensions (22 articles)
  - 11R16 Cubic and quartic extensions (14 articles)
  - 11R18 Cyclotomic extensions (29 articles)
  - 11R20 Other abelian and metabelian extensions (18 articles)
  - 11R21 Other number fields (8 articles)
  - 11R23 Iwasawa theory (7 articles)
  - 11R27 Units and factorization (22 articles)
  - 11R29 Class numbers, class groups, discriminants (46 articles)
  - 11R32 Galois theory (4 articles)
  - 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers (7 articles)
  - 11R34 Galois cohomology
  - 11R37 Class field theory (12 articles)
  - 11R39 Langlands-Weil conjectures, nonabelian class field theory
  - 11R42 Zeta functions and $L$-functions of number fields (4 articles)
  - 11R44 Distribution of prime ideals (1 articles)
  - 11R45 Density theorems
  - 11R47 Other analytic theory (3 articles)
  - 11R52 Quaternion and other division algebras: arithmetic, zeta functions (6 articles)
  - 11R54 Other algebras and orders, and their zeta and $L$-functions (3 articles)
  - 11R56 Adèle rings and groups
  - 11R58 Arithmetic theory of algebraic function fields (3 articles)
  - 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.) (1 articles)
  - 11R65 Class groups and Picard groups of orders
  - 11R70 $K$-theory of global fields (1 articles)
  - 11R80 Totally real and totally positive fields
  - 11R99 None of the above, but in this section
- 11Sxx Algebraic number theory: local and $p$-adic fields (15 articles)
  - 11Sxx Algebraic number theory: local and $p$-adic fields
  - 11S05 Polynomials (8 articles)
  - 11S15 Ramification and extension theory (1 articles)
  - 11S20 Galois theory (1 articles)
  - 11S23 Integral representations (1 articles)
  - 11S25 Galois cohomology (1 articles)
  - 11S31 Class field theory; $p$-adic formal groups
  - 11S37 Langlands-Weil conjectures, nonabelian class field theory
  - 11S40 Zeta functions and $L$-functions
  - 11S45 Algebras and orders, and their zeta functions (1 articles)
  - 11S70 $K$-theory of local fields
  - 11S80 Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.) (2 articles)
  - 11S85 Other nonanalytic theory
  - 11S90 Prehomogeneous vector spaces
  - 11S99 None of the above, but in this section
- 11Txx Finite fields and commutative rings (number-theoretic aspects) (31 articles)
  - 11Txx Finite fields and commutative rings (number-theoretic aspects)
  - 11T06 Polynomials (6 articles)
  - 11T22 Cyclotomy
  - 11T23 Exponential sums (1 articles)
  - 11T24 Other character sums and Gauss sums (3 articles)
  - 11T30 Structure theory (2 articles)
  - 11T55 Arithmetic theory of polynomial rings over finite fields (7 articles)
  - 11T60 Finite upper half-planes
  - 11T71 Algebraic coding theory; cryptography (7 articles)
  - 11T99 None of the above, but in this section (5 articles)
- 11Uxx Connections with logic (9 articles)
  - 11Uxx Connections with logic
  - 11U05 Decidability (4 articles)
  - 11U07 Ultraproducts (1 articles)
  - 11U09 Model theory
  - 11U10 Nonstandard arithmetic (3 articles)
  - 11U99 None of the above, but in this section (1 articles)
- 11Yxx Computational number theory (46 articles)
  - 11Yxx Computational number theory
  - 11Y05 Factorization (5 articles)
  - 11Y11 Primality (1 articles)
  - 11Y16 Algorithms; complexity (5 articles)
  - 11Y35 Analytic computations (3 articles)
  - 11Y40 Algebraic number theory computations (11 articles)
  - 11Y50 Computer solution of Diophantine equations (11 articles)
  - 11Y55 Calculation of integer sequences (1 articles)
  - 11Y60 Evaluation of constants (4 articles)
  - 11Y65 Continued fraction calculations (2 articles)
  - 11Y70 Values of arithmetic functions; tables
  - 11Y99 None of the above, but in this section (3 articles)
- 11Z05 Miscellaneous applications of number theory (3 articles)
12 Field theory and polynomials (120 articles)
- 12 Field theory and polynomials
- 12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 12-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 12-02 Research exposition (monographs, survey articles) (1 articles)
- 12-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 12-04 Explicit machine computation and programs (not the theory of computation or programming)
- 12-06 Proceedings, conferences, collections, etc.
- 12.00 (1959-1972) General
- 12.10 (1959-1972) Division rings
- 12.20 (1959-1972) Finite fields
- 12.25 (1959-1972) Polynomials over finite fields (4 articles)
- 12.30 (1959-1972) Polynomials (1 articles)
- 12.40 (1959-1972) Galois theory
- 12.45 (1959-1972) Algebraic extension fields
- 12.50 (1959-1972) Algebraic number fields
- 12.70 (1959-1972) Valuations, topological fields, ordered fields
- 12.75 (1959-1972) Transcendental extension fields
- 12.78 (1959-1972) Algebraic function fields
- 12.80 (1959-1972) Differential and difference algebra; Galois theory
- 12.99 (1959-1972) None of the above, but in this section
- 12Dxx Real and complex fields (27 articles)
  - 12Dxx Real and complex fields
  - 12D05 Polynomials: factorization (4 articles)
  - 12D10 Polynomials: location of zeros (algebraic theorems) (15 articles)
  - 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (4 articles)
  - 12D99 None of the above, but in this section (4 articles)
- 12Exx General field theory (28 articles)
  - 12Exx General field theory
  - 12E05 Polynomials (irreducibility, etc.) (6 articles)
  - 12E10 Special polynomials (1 articles)
  - 12E12 Equations (12 articles)
  - 12E15 Skew fields, division rings (3 articles)
  - 12E20 Finite fields (field-theoretic aspects) (3 articles)
  - 12E25 Hilbertian fields; Hilbert's irreducibility theorem
  - 12E30 Field arithmetic (1 articles)
  - 12E99 None of the above, but in this section (2 articles)
- 12Fxx Field extensions (10 articles)
  - 12Fxx Field extensions
  - 12F05 Algebraic extensions (4 articles)
  - 12F10 Separable extensions, Galois theory (2 articles)
  - 12F12 Inverse Galois theory
  - 12F15 Inseparable extensions (1 articles)
  - 12F20 Transcendental extensions (2 articles)
  - 12F99 None of the above, but in this section (1 articles)
- 12Gxx Homological methods (field theory)
  - 12Gxx Homological methods (field theory)
  - 12G05 Galois cohomology
  - 12G10 Cohomological dimension
  - 12G99 None of the above, but in this section
- 12Hxx Differential and difference algebra (10 articles)
  - 12Hxx Differential and difference algebra
  - 12H05 Differential algebra (8 articles)
  - 12H10 Difference algebra (1 articles)
  - 12H20 Abstract differential equations
  - 12H25 $p$-adic differential equations
  - 12H99 None of the above, but in this section (1 articles)
- 12Jxx Topological fields (17 articles)
  - 12Jxx Topological fields
  - 12J05 Normed fields
  - 12J10 Valued fields (2 articles)
  - 12J12 Formally $p$-adic fields
  - 12J15 Ordered fields (8 articles)
  - 12J17 Topological semifields
  - 12J20 General valuation theory (3 articles)
  - 12J25 Non-Archimedean valued fields (2 articles)
  - 12J27 Krasner-Tate algebras
  - 12J99 None of the above, but in this section (2 articles)
- 12Kxx Generalizations of fields (13 articles)
  - 12Kxx Generalizations of fields
  - 12K05 Near-fields (6 articles)
  - 12K10 Semifields (5 articles)
  - 12K99 None of the above, but in this section (2 articles)
- 12Lxx Connections with logic (2 articles)
  - 12Lxx Connections with logic
  - 12L05 Decidability
  - 12L10 Ultraproducts
  - 12L12 Model theory
  - 12L15 Nonstandard arithmetic (1 articles)
  - 12L99 None of the above, but in this section (1 articles)
- 12Y05 Computational aspects of field theory and polynomials (4 articles)
13 Commutative rings and algebras (568 articles)
- 13 Commutative rings and algebras
- 13-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 13-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 13-02 Research exposition (monographs, survey articles)
- 13-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 13-04 Explicit machine computation and programs (not the theory of computation or programming)
- 13-06 Proceedings, conferences, collections, etc.
- 13.00 (1959-1972) General (3 articles)
- 13.10 (1959-1972) General theory
- 13.15 (1959-1972) Integral domains, unique factorization domains
- 13.20 (1959-1972) Ideal theory (1 articles)
- 13.25 (1959-1972) Chain conditions; Artinian rings, Noetherian rings
- 13.30 (1959-1972) Radical theory
- 13.40 (1959-1972) Modules, representation
- 13.50 (1959-1972) Structure, classification
- 13.60 (1959-1972) Automorphisms, derivations
- 13.70 (1959-1972) Galois theory
- 13.80 (1959-1972) Extension theory
- 13.90 (1959-1972) Homological methods
- 13.93 (1959-1972) Rings of polynomials, formal power series
- 13.95 (1959-1972) Local rings
- 13.98 (1959-1972) Valuations
- 13.99 (1959-1972) None of the above, but in this section
- 13Axx General commutative ring theory (111 articles)
  - 13Axx General commutative ring theory (1 articles)
  - 13A02 Graded rings (3 articles)
  - 13A05 Divisibility (11 articles)
  - 13A10 Radical theory (5 articles)
  - 13A15 Ideals; multiplicative ideal theory (53 articles)
  - 13A18 Valuations and their generalizations (12 articles)
  - 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (6 articles)
  - 13A35 Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure (2 articles)
  - 13A50 Actions of groups on commutative rings; invariant theory (6 articles)
  - 13A99 None of the above, but in this section (12 articles)
- 13Bxx Ring extensions and related topics (54 articles)
  - 13Bxx Ring extensions and related topics
  - 13B02 Extension theory (10 articles)
  - 13B05 Galois theory (2 articles)
  - 13B10 Morphisms (6 articles)
  - 13B21 Integral dependence
  - 13B22 Integral closure of rings and ideals (8 articles)
  - 13B24 Going up; going down; going between
  - 13B25 Polynomials over commutative rings (15 articles)
  - 13B30 Quotients and localization (8 articles)
  - 13B35 Completion (2 articles)
  - 13B40 Étale and flat extensions; Henselization; Artin approximation (1 articles)
  - 13B99 None of the above, but in this section (2 articles)
- 13Cxx Theory of modules and ideals (114 articles)
  - 13Cxx Theory of modules and ideals
  - 13C05 Structure, classification theorems (25 articles)
  - 13C10 Projective and free modules and ideals (16 articles)
  - 13C11 Injective and flat modules and ideals (13 articles)
  - 13C12 Torsion modules and ideals (3 articles)
  - 13C13 Other special types (22 articles)
  - 13C14 Cohen-Macaulay modules (8 articles)
  - 13C15 Dimension theory, depth, related rings (catenary, etc.) (14 articles)
  - 13C20 Class groups
  - 13C40 Linkage, complete intersections and determinantal ideals
  - 13C99 None of the above, but in this section (13 articles)
- 13Dxx Homological methods (82 articles)
  - 13Dxx Homological methods
  - 13D02 Syzygies and resolutions (20 articles)
  - 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (1 articles)
  - 13D05 Homological dimension (16 articles)
  - 13D07 Homological functors on modules (Tor, Ext, etc.) (9 articles)
  - 13D10 Deformations and infinitesimal methods (1 articles)
  - 13D15 Grothendieck groups, $K$-theory (1 articles)
  - 13D22 Homological conjectures (intersection theorems)
  - 13D25 Complexes (1 articles)
  - 13D30 Torsion theory (3 articles)
  - 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (2 articles)
  - 13D45 Local cohomology (27 articles)
  - 13D99 None of the above, but in this section (1 articles)
- 13Exx Chain conditions, finiteness conditions (40 articles)
  - 13Exx Chain conditions, finiteness conditions
  - 13E05 Noetherian rings and modules (21 articles)
  - 13E10 Artinian rings and modules, finite-dimensional algebras (8 articles)
  - 13E15 Rings and modules of finite generation or presentation; number of generators (4 articles)
  - 13E99 None of the above, but in this section (7 articles)
- 13Fxx Arithmetic rings and other special rings (83 articles)
  - 13Fxx Arithmetic rings and other special rings (1 articles)
  - 13F05 Dedekind, Prüfer and Krull rings and their generalizations (26 articles)
  - 13F07 Euclidean rings and generalizations
  - 13F10 Principal ideal rings (3 articles)
  - 13F15 Factorial rings, unique factorization domains (3 articles)
  - 13F20 Polynomial rings and ideals; rings of integer-valued polynomials (22 articles)
  - 13F25 Formal power series rings (8 articles)
  - 13F30 Valuation rings (13 articles)
  - 13F40 Excellent rings
  - 13F45 Seminormal rings
  - 13F50 Rings with straightening laws, Hodge algebras (1 articles)
  - 13F55 Face and Stanley-Reisner rings; simplicial complexes (4 articles)
  - 13F99 None of the above, but in this section (2 articles)
- 13G05 Integral domains (12 articles)
- 13Hxx Local rings and semilocal rings (23 articles)
  - 13Hxx Local rings and semilocal rings
  - 13H05 Regular local rings (2 articles)
  - 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13 articles)
  - 13H15 Multiplicity theory and related topics (5 articles)
  - 13H99 None of the above, but in this section (3 articles)
- 13Jxx Topological rings and modules (13 articles)
  - 13Jxx Topological rings and modules
  - 13J05 Power series rings (2 articles)
  - 13J07 Analytical algebras and rings
  - 13J10 Complete rings, completion (5 articles)
  - 13J15 Henselian rings
  - 13J20 Global topological rings
  - 13J25 Ordered rings (4 articles)
  - 13J30 Real algebra
  - 13J99 None of the above, but in this section (2 articles)
- 13K05 Witt vectors and related rings
- 13L05 Applications of logic to commutative algebra (1 articles)
- 13Mxx Finite commutative rings (7 articles)
  - 13Mxx Finite commutative rings
  - 13M05 Structure (5 articles)
  - 13M10 Polynomials (1 articles)
  - 13M99 None of the above, but in this section (1 articles)
- 13Nxx Differential algebra (13 articles)
  - 13Nxx Differential algebra
  - 13N05 Modules of differentials (3 articles)
  - 13N10 Rings of differential operators and their modules (1 articles)
  - 13N15 Derivations (9 articles)
  - 13N99 None of the above, but in this section
- 13Pxx Computational aspects of commutative algebra (9 articles)
  - 13Pxx Computational aspects of commutative algebra
  - 13P05 Polynomials, factorization (2 articles)
  - 13P10 Polynomial ideals, Gröbner bases (7 articles)
  - 13P99 None of the above, but in this section
14 Algebraic geometry (205 articles)
- 14 Algebraic geometry
- 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (2 articles)
- 14-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 14-02 Research exposition (monographs, survey articles)
- 14-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 14-04 Explicit machine computation and programs (not the theory of computation or programming)
- 14-06 Proceedings, conferences, collections, etc.
- 14.0 (1940-1958) Algebraic geometry
- 14.00 (1959-1972) General (1 articles)
- 14.01 (1959-1972) Algebraic varieties in real and complex spaces, classical algebraic geometry
- 14.05 (1959-1972) Algebraic geometry over abstract fields and rings, general
- 14.08 (1959-1972) Foundational questions
- 14.10 (1959-1972) Theories of equivalence
- 14.15 (1959-1972) Transformations and correspondences
- 14.18 (1959-1972) Singularities
- 14.20 (1959-1972) Algebraic curves, surfaces and special varieties (1 articles)
- 14.35 (1959-1972) Algebraic function fields
- 14.40 (1959-1972) Arithmetic properties of varieties
- 14.45 (1959-1972) Rationality questions
- 14.47 (1959-1972) Weil conjectures, Riemann hypotheses
- 14.48 (1959-1972) Zeta functions for varieties (including $mod p$ questions)
- 14.49 (1959-1972) Geometric analogues of arithmetic questions
- 14.50 (1959-1972) Group varieties (algebraic groups), abstract analytic groups
- 14.51 (1959-1972) Abelian varieties
- 14.52 (1959-1972) Abstract derivations and differentials
- 14.55 (1959-1972) Sheaf-theoretic and homological methods
- 14.99 (1959-1972) None of the above, but in this section
- 14Axx Foundations (7 articles)
  - 14Axx Foundations
  - 14A05 Relevant commutative algebra
  - 14A10 Varieties and morphisms (2 articles)
  - 14A15 Schemes and morphisms (2 articles)
  - 14A20 Generalizations (algebraic spaces, stacks)
  - 14A22 Noncommutative algebraic geometry
  - 14A25 Elementary questions (2 articles)
  - 14A99 None of the above, but in this section (1 articles)
- 14Bxx Local theory (7 articles)
  - 14Bxx Local theory
  - 14B05 Singularities (3 articles)
  - 14B07 Deformations of singularities
  - 14B10 Infinitesimal methods
  - 14B12 Local deformation theory, Artin approximation, etc.
  - 14B15 Local cohomology (4 articles)
  - 14B20 Formal neighborhoods
  - 14B25 Local structure of morphisms: étale, flat, etc.
  - 14B99 None of the above, but in this section
- 14Cxx Cycles and subschemes (7 articles)
  - 14Cxx Cycles and subschemes
  - 14C05 Parametrization (Chow and Hilbert schemes)
  - 14C15 Chow groups and rings (1 articles)
  - 14C17 Intersection theory, characteristic classes, intersection multiplicities
  - 14C20 Divisors, linear systems, invertible sheaves (3 articles)
  - 14C21 Pencils, nets, webs
  - 14C22 Picard groups
  - 14C25 Algebraic cycles
  - 14C30 Transcendental methods, Hodge theory
  - 14C34 Torelli problem
  - 14C35 Applications of methods of algebraic $K$-theory (1 articles)
  - 14C40 Riemann-Roch theorems (2 articles)
  - 14C99 None of the above, but in this section
- 14Dxx Families, fibrations (3 articles)
  - 14Dxx Families, fibrations
  - 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
  - 14D06 Fibrations, degenerations (1 articles)
  - 14D07 Variation of Hodge structures
  - 14D10 Arithmetic ground fields (finite, local, global)
  - 14D15 Formal methods; deformations (1 articles)
  - 14D20 Algebraic moduli problems, moduli of vector bundles
  - 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (1 articles)
  - 14D22 Fine and coarse moduli spaces
  - 14D99 None of the above, but in this section
- 14Exx Birational geometry (10 articles)
  - 14Exx Birational geometry
  - 14E05 Rational and birational maps (6 articles)
  - 14E07 Birational automorphisms, Cremona group and generalizations (1 articles)
  - 14E08 Rationality questions
  - 14E15 Global theory and resolution of singularities
  - 14E20 Coverings (1 articles)
  - 14E22 Ramification problems (1 articles)
  - 14E25 Embeddings
  - 14E30 Minimal model program (Mori theory, extremal rays)
  - 14E99 None of the above, but in this section (1 articles)
- 14Fxx (Co)homology theory (10 articles)
  - 14Fxx (Co)homology theory
  - 14F05 Vector bundles, sheaves, related constructions (4 articles)
  - 14F10 Differentials and other special sheaves (2 articles)
  - 14F17 Vanishing theorems (1 articles)
  - 14F20 Étale and other Grothendieck topologies and cohomologies
  - 14F22 Brauer groups of schemes
  - 14F25 Classical real and complex cohomology
  - 14F30 $p$-adic cohomology, crystalline cohomology
  - 14F35 Homotopy theory; fundamental groups (2 articles)
  - 14F40 de Rham cohomology (1 articles)
  - 14F42 Motivic cohomology
  - 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
  - 14F45 Topological properties
  - 14F99 None of the above, but in this section
- 14Gxx Arithmetic problems. Diophantine geometry (9 articles)
  - 14Gxx Arithmetic problems. Diophantine geometry
  - 14G05 Rational points (3 articles)
  - 14G10 Zeta-functions and related questions
  - 14G15 Finite ground fields
  - 14G20 Local ground fields (1 articles)
  - 14G22 Rigid analytic geometry (1 articles)
  - 14G25 Global ground fields
  - 14G27 Other nonalgebraically closed ground fields
  - 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
  - 14G35 Modular and Shimura varieties (1 articles)
  - 14G40 Arithmetic varieties and schemes; Arakelov theory; heights
  - 14G50 Applications to coding theory and cryptography (2 articles)
  - 14G99 None of the above, but in this section (1 articles)
- 14Hxx Curves (51 articles)
  - 14Hxx Curves (2 articles)
  - 14H05 Algebraic functions; function fields (2 articles)
  - 14H10 Families, moduli (algebraic) (1 articles)
  - 14H15 Families, moduli (analytic)
  - 14H20 Singularities, local rings (5 articles)
  - 14H25 Arithmetic ground fields (2 articles)
  - 14H30 Coverings, fundamental group (1 articles)
  - 14H37 Automorphisms
  - 14H40 Jacobians, Prym varieties (1 articles)
  - 14H42 Theta functions; Schottky problem
  - 14H45 Special curves and curves of low genus (11 articles)
  - 14H50 Plane and space curves (15 articles)
  - 14H51 Special divisors (gonality, Brill-Noether theory) (1 articles)
  - 14H52 Elliptic curves (7 articles)
  - 14H55 Riemann surfaces; Weierstrass points; gap sequences (1 articles)
  - 14H60 Vector bundles on curves and their moduli
  - 14H70 Relationships with integrable systems (1 articles)
  - 14H81 Relationships with physics
  - 14H99 None of the above, but in this section (1 articles)
- 14Jxx Surfaces and higher-dimensional varieties (20 articles)
  - 14Jxx Surfaces and higher-dimensional varieties (1 articles)
  - 14J10 Families, moduli, classification: algebraic theory
  - 14J15 Moduli, classification: analytic theory; relations with modular forms
  - 14J17 Singularities (1 articles)
  - 14J20 Arithmetic ground fields (1 articles)
  - 14J25 Special surfaces (9 articles)
  - 14J26 Rational and ruled surfaces (4 articles)
  - 14J27 Elliptic surfaces
  - 14J28 $K3$ surfaces and Enriques surfaces
  - 14J29 Surfaces of general type
  - 14J30 $3$-folds
  - 14J32 Calabi-Yau manifolds, mirror symmetry
  - 14J35 $4$-folds
  - 14J40 $n$-folds ($n>4$)
  - 14J45 Fano varieties (1 articles)
  - 14J50 Automorphisms of surfaces and higher-dimensional varieties
  - 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli (2 articles)
  - 14J70 Hypersurfaces (1 articles)
  - 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
  - 14J81 Relationships with physics
  - 14J99 None of the above, but in this section
- 14Kxx Abelian varieties and schemes (1 articles)
  - 14Kxx Abelian varieties and schemes
  - 14K02 Isogeny
  - 14K05 Algebraic theory
  - 14K10 Algebraic moduli, classification
  - 14K12 Subvarieties
  - 14K15 Arithmetic ground fields
  - 14K20 Analytic theory; abelian integrals and differentials
  - 14K22 Complex multiplication
  - 14K25 Theta functions (1 articles)
  - 14K30 Picard schemes, higher Jacobians
  - 14K99 None of the above, but in this section
- 14Lxx Algebraic groups (11 articles)
  - 14Lxx Algebraic groups (1 articles)
  - 14L05 Formal groups, $p$-divisible groups
  - 14L10 Group varieties
  - 14L15 Group schemes (2 articles)
  - 14L17 Affine algebraic groups, hyperalgebra constructions
  - 14L24 Geometric invariant theory (5 articles)
  - 14L30 Group actions on varieties or schemes (quotients) (3 articles)
  - 14L35 Classical groups (geometric aspects)
  - 14L40 Other algebraic groups (geometric aspects)
  - 14L99 None of the above, but in this section
- 14Mxx Special varieties (20 articles)
  - 14Mxx Special varieties
  - 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (3 articles)
  - 14M06 Linkage
  - 14M07 Low codimension problems
  - 14M10 Complete intersections (4 articles)
  - 14M12 Determinantal varieties (1 articles)
  - 14M15 Grassmannians, Schubert varieties, flag manifolds (8 articles)
  - 14M17 Homogeneous spaces and generalizations (3 articles)
  - 14M20 Rational and unirational varieties
  - 14M25 Toric varieties, Newton polyhedra
  - 14M30 Supervarieties (1 articles)
  - 14M99 None of the above, but in this section
- 14Nxx Projective and enumerative geometry (21 articles)
  - 14Nxx Projective and enumerative geometry
  - 14N05 Projective techniques (13 articles)
  - 14N10 Enumerative problems (combinatorial problems) (2 articles)
  - 14N15 Classical problems, Schubert calculus
  - 14N20 Configurations of linear subspaces (1 articles)
  - 14N25 Varieties of low degree (3 articles)
  - 14N30 Adjunction problems
  - 14N35 Gromov-Witten invariants, quantum cohomology
  - 14N99 None of the above, but in this section (2 articles)
- 14Pxx Real algebraic and real analytic geometry (9 articles)
  - 14Pxx Real algebraic and real analytic geometry (1 articles)
  - 14P05 Real algebraic sets (4 articles)
  - 14P10 Semialgebraic sets and related spaces (1 articles)
  - 14P15 Real analytic and semianalytic sets
  - 14P20 Nash functions and manifolds
  - 14P25 Topology of real algebraic varieties
  - 14P99 None of the above, but in this section (3 articles)
- 14Qxx Computational aspects in algebraic geometry (5 articles)
  - 14Qxx Computational aspects in algebraic geometry
  - 14Q05 Curves (3 articles)
  - 14Q10 Surfaces, hypersurfaces
  - 14Q15 Higher-dimensional varieties (1 articles)
  - 14Q20 Effectivity (1 articles)
  - 14Q99 None of the above, but in this section
- 14Rxx Affine geometry (4 articles)
  - 14Rxx Affine geometry
  - 14R05 Classification of affine varieties (1 articles)
  - 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (2 articles)
  - 14R15 Jacobian problem (1 articles)
  - 14R20 Group actions on affine varieties
  - 14R25 Affine fibrations
  - 14R99 None of the above, but in this section
15 Linear and multilinear algebra; matrix theory (731 articles)
- 15 Linear and multilinear algebra; matrix theory
- 15-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 15-01 Instructional exposition (textbooks, tutorial papers, etc.) (4 articles)
- 15-02 Research exposition (monographs, survey articles)
- 15-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 15-04 Explicit machine computation and programs (not the theory of computation or programming)
- 15-06 Proceedings, conferences, collections, etc.
- 15.0 (1940-1958) Linear algebra, polynomials, invariants
- 15.00 (1959-1972) General (7 articles)
- 15.05 (1959-1972) Vector spaces, linear dependence, rank
- 15.10 (1959-1972) Linear equations
- 15.15 (1959-1972) Matrix inversion, generalized inverses (1 articles)
- 15.20 (1959-1972) Determinants, permanents, other special matrix functions (1 articles)
- 15.25 (1959-1972) Eigenvalues and eigenvectors (2 articles)
- 15.30 (1959-1972) Canonical forms, reductions, classification (1 articles)
- 15.35 (1959-1972) Matrix equations and identities
- 15.38 (1959-1972) Commutativity
- 15.40 (1959-1972) Algebraic systems of matrices (2 articles)
- 15.45 (1959-1972) Matrices over special rings (quaternions, finite fields, etc.)
- 15.48 (1959-1972) Matrices of integers
- 15.50 (1959-1972) Linear inequalities
- 15.55 (1959-1972) Inequalities involving eigenvalues and eigenvectors (1 articles)
- 15.58 (1959-1972) Miscellaneous inequalities involving matrices (2 articles)
- 15.60 (1959-1972) Positive matrices (6 articles)
- 15.65 (1959-1972) Stochastic matrices (2 articles)
- 15.70 (1959-1972) Quadratic and bilinear forms, inner products
- 15.75 (1959-1972) Clifford algebras
- 15.80 (1959-1972) Multilinear algebra, tensor products
- 15.85 (1959-1972) Vector and tensor algebra, theory of invariants
- 15.90 (1959-1972) Exterior algebra, Grassmann algebras (1 articles)
- 15.99 (1959-1972) None of the above, but in this section
- 15A03 Vector spaces, linear dependence, rank (41 articles)
- 15A04 Linear transformations, semilinear transformations (36 articles)
- 15A06 Linear equations (32 articles)
- 15A09 Matrix inversion, generalized inverses (49 articles)
- 15A12 Conditioning of matrices (6 articles)
- 15A15 Determinants, permanents, other special matrix functions (53 articles)
- 15A18 Eigenvalues, singular values, and eigenvectors (92 articles)
- 15A21 Canonical forms, reductions, classification (23 articles)
- 15A22 Matrix pencils (6 articles)
- 15A23 Factorization of matrices (22 articles)
- 15A24 Matrix equations and identities (35 articles)
- 15A27 Commutativity (7 articles)
- 15A29 Inverse problems (3 articles)
- 15A30 Algebraic systems of matrices (10 articles)
- 15A33 Matrices over special rings (quaternions, finite fields, etc.) (22 articles)
- 15A36 Matrices of integers (10 articles)
- 15A39 Linear inequalities (9 articles)
- 15A42 Inequalities involving eigenvalues and eigenvectors (31 articles)
- 15A45 Miscellaneous inequalities involving matrices (17 articles)
- 15A48 Positive matrices and their generalizations; cones of matrices (33 articles)
- 15A51 Stochastic matrices (19 articles)
- 15A52 Random matrices (2 articles)
- 15A54 Matrices over function rings in one or more variables (6 articles)
- 15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.) (21 articles)
- 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory (30 articles)
- 15A63 Quadratic and bilinear forms, inner products (16 articles)
- 15A66 Clifford algebras, spinors (21 articles)
- 15A69 Multilinear algebra, tensor products (15 articles)
- 15A72 Vector and tensor algebra, theory of invariants (6 articles)
- 15A75 Exterior algebra, Grassmann algebras (6 articles)
- 15A78 Other algebras built from modules (4 articles)
- 15A90 Applications of matrix theory to physics (4 articles)
- 15A99 Miscellaneous topics (11 articles)
16 Associative rings and algebras (1046 articles)
- 16 Associative rings and algebras
- 16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 16-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 16-02 Research exposition (monographs, survey articles) (2 articles)
- 16-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 16-04 Explicit machine computation and programs (not the theory of computation or programming)
- 16-06 Proceedings, conferences, collections, etc.
- 16.00 (1959-1972) General (2 articles)
- 16.10 (1959-1972) General theory
- 16.15 (1959-1972) Integral domains, unique factorization domains (noncommutative)
- 16.20 (1959-1972) Ideal theory (1 articles)
- 16.25 (1959-1972) Chain conditions; Artinian rings, Noetherian rings (1 articles)
- 16.30 (1959-1972) Radical theory
- 16.32 (1959-1972) Nil, nilpotent, radical rings
- 16.40 (1959-1972) Modules, representation (2 articles)
- 16.42 (1959-1972) Primitive rings
- 16.44 (1959-1972) Semisimple rings
- 16.46 (1959-1972) Simple rings, division rings
- 16.48 (1959-1972) Matrix rings
- 16.49 (1959-1972) Rings with polynomial identity
- 16.50 (1959-1972) Structure, classification
- 16.53 (1959-1972) Prime rings
- 16.55 (1959-1972) Rings with annihilator conditions
- 16.56 (1959-1972) Regular rings
- 16.58 (1959-1972) Rings with involution
- 16.60 (1959-1972) Automorphisms, derivations
- 16.70 (1959-1972) Galois theory
- 16.80 (1959-1972) Extension theory
- 16.90 (1959-1972) Homological methods (1 articles)
- 16.94 (1959-1972) Finite rings
- 16.96 (1959-1972) Semirings, other generalizations of rings
- 16.98 (1959-1972) Topological rings
- 16.99 (1959-1972) None of the above, but in this section
- 16Bxx General and miscellaneous (7 articles)
  - 16Bxx General and miscellaneous
  - 16B50 Category-theoretic methods and results (except as in 16D90) (5 articles)
  - 16B70 Applications of logic (1 articles)
  - 16B99 None of the above, but in this section (1 articles)
- 16Dxx Modules, bimodules and ideals (265 articles)
  - 16Dxx Modules, bimodules and ideals (6 articles)
  - 16D10 General module theory (26 articles)
  - 16D20 Bimodules (3 articles)
  - 16D25 Ideals (12 articles)
  - 16D30 Infinite-dimensional simple rings (except as in 16Kxx) (4 articles)
  - 16D40 Free, projective, and flat modules and ideals (43 articles)
  - 16D50 Injective modules, self-injective rings (51 articles)
  - 16D60 Simple and semisimple modules, primitive rings and ideals (9 articles)
  - 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation (46 articles)
  - 16D80 Other classes of modules and ideals (34 articles)
  - 16D90 Module categories (25 articles)
  - 16D99 None of the above, but in this section (6 articles)
- 16Exx Homological methods (117 articles)
  - 16Exx Homological methods (9 articles)
  - 16E05 Syzygies, resolutions, complexes (6 articles)
  - 16E10 Homological dimension (17 articles)
  - 16E20 Grothendieck groups, $K$-theory, etc. (7 articles)
  - 16E30 Homological functors on modules (Tor, Ext, etc.) (19 articles)
  - 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) (10 articles)
  - 16E45 Differential graded algebras and applications (5 articles)
  - 16E50 von Neumann regular rings and generalizations (38 articles)
  - 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (2 articles)
  - 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (3 articles)
  - 16E99 None of the above, but in this section (1 articles)
- 16Gxx Representation theory of rings and algebras (45 articles)
  - 16Gxx Representation theory of rings and algebras (10 articles)
  - 16G10 Representations of Artinian rings (10 articles)
  - 16G20 Representations of quivers and partially ordered sets (10 articles)
  - 16G30 Representations of orders, lattices, algebras over commutative rings (2 articles)
  - 16G50 Cohen-Macaulay modules
  - 16G60 Representation type (finite, tame, wild, etc.) (2 articles)
  - 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (8 articles)
  - 16G99 None of the above, but in this section (3 articles)
- 16H05 Orders and arithmetic, separable algebras, Azumaya algebras (2 articles)
- 16Kxx Division rings and semisimple Artin rings (12 articles)
  - 16Kxx Division rings and semisimple Artin rings (2 articles)
  - 16K20 Finite-dimensional (6 articles)
  - 16K40 Infinite-dimensional and general (1 articles)
  - 16K50 Brauer groups (2 articles)
  - 16K99 None of the above, but in this section (1 articles)
- 16Lxx Local rings and generalizations (17 articles)
  - 16Lxx Local rings and generalizations
  - 16L30 Noncommutative local and semilocal rings, perfect rings (7 articles)
  - 16L60 Quasi-Frobenius rings (9 articles)
  - 16L99 None of the above, but in this section (1 articles)
- 16Nxx Radicals and radical properties of rings (67 articles)
  - 16Nxx Radicals and radical properties of rings (13 articles)
  - 16N20 Jacobson radical, quasimultiplication (6 articles)
  - 16N40 Nil and nilpotent radicals, sets, ideals, rings (12 articles)
  - 16N60 Prime and semiprime rings (30 articles)
  - 16N80 General radicals and rings (6 articles)
  - 16N99 None of the above, but in this section
- 16Pxx Chain conditions, growth conditions, and other forms of finiteness (31 articles)
  - 16Pxx Chain conditions, growth conditions, and other forms of finiteness
  - 16P10 Finite rings and finite-dimensional algebras (5 articles)
  - 16P20 Artinian rings and modules (4 articles)
  - 16P40 Noetherian rings and modules (8 articles)
  - 16P50 Localization and Noetherian rings
  - 16P60 Chain conditions on annihilators and summands: Goldie-type conditions (3 articles)
  - 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (10 articles)
  - 16P90 Growth rate, Gelfand-Kirillov dimension (1 articles)
  - 16P99 None of the above, but in this section
- 16Rxx Rings with polynomial identity (25 articles)
  - 16Rxx Rings with polynomial identity (5 articles)
  - 16R10 $T$-ideals, identities, varieties of rings and algebras (6 articles)
  - 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
  - 16R30 Trace rings and invariant theory (1 articles)
  - 16R40 Identities other than those of matrices over commutative rings (2 articles)
  - 16R50 Other kinds of identities (generalized polynomial, rational, involution) (11 articles)
  - 16R99 None of the above, but in this section
- 16Sxx Rings and algebras arising under various constructions (149 articles)
  - 16Sxx Rings and algebras arising under various constructions
  - 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (6 articles)
  - 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (4 articles)
  - 16S20 Centralizing and normalizing extensions (2 articles)
  - 16S30 Universal enveloping algebras of Lie algebras (2 articles)
  - 16S32 Rings of differential operators (2 articles)
  - 16S34 Group rings (38 articles)
  - 16S35 Twisted and skew group rings, crossed products (3 articles)
  - 16S36 Ordinary and skew polynomial rings and semigroup rings (13 articles)
  - 16S37 Quadratic and Koszul algebras (1 articles)
  - 16S38 Rings arising from non-commutative algebraic geometry
  - 16S40 Smash products of general Hopf actions (5 articles)
  - 16S50 Endomorphism rings; matrix rings (28 articles)
  - 16S60 Rings of functions, subdirect products, sheaves of rings (4 articles)
  - 16S70 Extensions of rings by ideals (1 articles)
  - 16S80 Deformations of rings (7 articles)
  - 16S90 Maximal ring of quotients, torsion theories, radicals on module categories (25 articles)
  - 16S99 None of the above, but in this section (8 articles)
- 16Uxx Conditions on elements (92 articles)
  - 16Uxx Conditions on elements
  - 16U10 Integral domains (2 articles)
  - 16U20 Ore rings, multiplicative sets, Ore localization (4 articles)
  - 16U30 Divisibility, noncommutative UFDs (2 articles)
  - 16U60 Units, groups of units (28 articles)
  - 16U70 Center, normalizer (invariant elements) (20 articles)
  - 16U80 Generalizations of commutativity (19 articles)
  - 16U99 None of the above, but in this section (17 articles)
- 16Wxx Rings and algebras with additional structure (136 articles)
  - 16Wxx Rings and algebras with additional structure
  - 16W10 Rings with involution; Lie, Jordan and other nonassociative structures (25 articles)
  - 16W20 Automorphisms and endomorphisms (17 articles)
  - 16W22 Actions of groups and semigroups; invariant theory (2 articles)
  - 16W25 Derivations, actions of Lie algebras (31 articles)
  - 16W30 Coalgebras, bialgebras, Hopf algebras (17 articles)
  - 16W35 Ring-theoretic aspects of quantum groups (2 articles)
  - 16W50 Graded rings and modules (14 articles)
  - 16W55 ``Super'' (or ``skew'') structure (2 articles)
  - 16W60 Valuations, completions, formal power series and related constructions (6 articles)
  - 16W70 Filtered rings; filtrational and graded techniques (3 articles)
  - 16W80 Topological and ordered rings and modules (11 articles)
  - 16W99 None of the above, but in this section (6 articles)
- 16Yxx Generalizations (66 articles)
  - 16Yxx Generalizations
  - 16Y30 Near-rings (7 articles)
  - 16Y60 Semirings (52 articles)
  - 16Y99 None of the above, but in this section (7 articles)
- 16Z05 Computational aspects of associative rings (4 articles)
17 Nonassociative rings and algebras (416 articles)
- 17 Nonassociative rings and algebras
- 17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 17-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 17-02 Research exposition (monographs, survey articles)
- 17-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 17-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 17-06 Proceedings, conferences, collections, etc.
- 17-08 Computational methods (2 articles)
- 17.0 (1940-1958) Lie groups and algebras
- 17.00 (1959-1972) General (1 articles)
- 17.10 (1959-1972) General theory
- 17.20 (1959-1972) Power associative
- 17.30 (1959-1972) Lie
- 17.40 (1959-1972) Jordan
- 17.50 (1959-1972) Alternative (1 articles)
- 17.60 (1959-1972) Other
- 17.99 (1959-1972) None of the above, but in this section
- 17Axx General nonassociative rings (97 articles)
  - 17Axx General nonassociative rings
  - 17A01 General theory (6 articles)
  - 17A05 Power-associative rings
  - 17A15 Noncommutative Jordan algebras (3 articles)
  - 17A20 Flexible algebras
  - 17A30 Algebras satisfying other identities (23 articles)
  - 17A32 Leibniz algebras (7 articles)
  - 17A35 Division algebras (7 articles)
  - 17A36 Automorphisms, derivations, other operators (7 articles)
  - 17A40 Ternary compositions (8 articles)
  - 17A42 Other $n$-ary compositions $(n ge 3)$ (5 articles)
  - 17A45 Quadratic algebras (but not quadratic Jordan algebras) (3 articles)
  - 17A50 Free algebras (2 articles)
  - 17A60 Structure theory (6 articles)
  - 17A65 Radical theory (1 articles)
  - 17A70 Superalgebras (9 articles)
  - 17A75 Composition algebras (3 articles)
  - 17A80 Valued algebras
  - 17A99 None of the above, but in this section (7 articles)
- 17Bxx Lie algebras and Lie superalgebras (274 articles)
  - 17Bxx Lie algebras and Lie superalgebras (1 articles)
  - 17B01 Identities, free Lie (super)algebras (3 articles)
  - 17B05 Structure theory (15 articles)
  - 17B10 Representations, algebraic theory (weights) (25 articles)
  - 17B15 Representations, analytic theory
  - 17B20 Simple, semisimple, reductive (super)algebras (roots) (17 articles)
  - 17B25 Exceptional (super)algebras (5 articles)
  - 17B30 Solvable, nilpotent (super)algebras (18 articles)
  - 17B35 Universal enveloping (super)algebras (8 articles)
  - 17B37 Quantum groups (quantized enveloping algebras) and related deformations (20 articles)
  - 17B40 Automorphisms, derivations, other operators (12 articles)
  - 17B45 Lie algebras of linear algebraic groups (6 articles)
  - 17B50 Modular Lie (super)algebras (10 articles)
  - 17B55 Homological methods in Lie (super)algebras (8 articles)
  - 17B56 Cohomology of Lie (super)algebras (21 articles)
  - 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) (13 articles)
  - 17B62 Lie bialgebras (1 articles)
  - 17B63 Poisson algebras (3 articles)
  - 17B65 Infinite-dimensional Lie (super)algebras (19 articles)
  - 17B66 Lie algebras of vector fields and related (super) algebras (16 articles)
  - 17B67 Kac-Moody (super)algebras (structure and representation theory) (7 articles)
  - 17B68 Virasoro and related algebras (1 articles)
  - 17B69 Vertex operators; vertex operator algebras and related structures (4 articles)
  - 17B70 Graded Lie (super)algebras (25 articles)
  - 17B75 Color Lie (super)algebras
  - 17B80 Applications to integrable systems
  - 17B81 Applications to physics (5 articles)
  - 17B99 None of the above, but in this section (11 articles)
- 17Cxx Jordan algebras (algebras, triples and pairs) (17 articles)
  - 17Cxx Jordan algebras (algebras, triples and pairs)
  - 17C05 Identities and free Jordan structures (3 articles)
  - 17C10 Structure theory
  - 17C17 Radicals
  - 17C20 Simple, semisimple algebras (1 articles)
  - 17C27 Idempotents, Peirce decompositions
  - 17C30 Associated groups, automorphisms (1 articles)
  - 17C36 Associated manifolds
  - 17C37 Associated geometries (1 articles)
  - 17C40 Exceptional Jordan structures (1 articles)
  - 17C50 Jordan structures associated with other structures (4 articles)
  - 17C55 Finite-dimensional structures (1 articles)
  - 17C60 Division algebras
  - 17C65 Jordan structures on Banach spaces and algebras (3 articles)
  - 17C70 Super structures
  - 17C90 Applications to physics (1 articles)
  - 17C99 None of the above, but in this section (1 articles)
- 17Dxx Other nonassociative rings and algebras (20 articles)
  - 17Dxx Other nonassociative rings and algebras (1 articles)
  - 17D05 Alternative rings (5 articles)
  - 17D10 Malcev (Maltsev) rings and algebras (3 articles)
  - 17D15 Right alternative rings (1 articles)
  - 17D20 $(gamma, delta)$-rings, including $(1,-1)$-rings
  - 17D25 Lie-admissible algebras (2 articles)
  - 17D92 Genetic algebras (1 articles)
  - 17D99 None of the above, but in this section (7 articles)
18 Category theory; homological algebra (869 articles)
- 18 Category theory; homological algebra
- 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (3 articles)
- 18-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 18-02 Research exposition (monographs, survey articles) (1 articles)
- 18-03 Historical (must also be assigned at least one classification number from Section 01)
- 18-04 Explicit machine computation and programs (not the theory of computation or programming)
- 18-06 Proceedings, conferences, collections, etc.
- 18.0 (1940-1958) Homological algebra
- 18.00 (1959-1972) General
- 18.10 (1959-1972) Abstract categories and functors (10 articles)
- 18.15 (1959-1972) Abelian categories
- 18.20 (1959-1972) Homological algebra
- 18.99 (1959-1972) None of the above, but in this section
- 18Axx General theory of categories and functors (270 articles)
  - 18Axx General theory of categories and functors (17 articles)
  - 18A05 Definitions, generalizations (10 articles)
  - 18A10 Graphs, diagram schemes, precategories (3 articles)
  - 18A15 Foundations, relations to logic and deductive systems (11 articles)
  - 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms (34 articles)
  - 18A22 Special properties of functors (faithful, full, etc.) (11 articles)
  - 18A23 Natural morphisms, dinatural morphisms (2 articles)
  - 18A25 Functor categories, comma categories (12 articles)
  - 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) (47 articles)
  - 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgams (9 articles)
  - 18A35 Categories admitting limits (complete categories), functors preserving limits, completions (18 articles)
  - 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (68 articles)
  - 18A99 None of the above, but in this section (28 articles)
- 18Bxx Special categories (282 articles)
  - 18Bxx Special categories (21 articles)
  - 18B05 Category of sets, characterizations (20 articles)
  - 18B10 Category of relations, additive relations (17 articles)
  - 18B15 Embedding theorems, universal categories (48 articles)
  - 18B20 Categories of machines, automata, operative categories (19 articles)
  - 18B25 Topoi (7 articles)
  - 18B30 Categories of topological spaces and continuous mappings (61 articles)
  - 18B35 Preorders, orders and lattices (viewed as categories) (17 articles)
  - 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) (5 articles)
  - 18B99 None of the above, but in this section (67 articles)
- 18Cxx Categories and theories (65 articles)
  - 18Cxx Categories and theories
  - 18C05 Equational categories (9 articles)
  - 18C10 Theories (e.g. algebraic theories), structure, and semantics (15 articles)
  - 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples (21 articles)
  - 18C20 Algebras and Kleisli categories associated with monads (7 articles)
  - 18C30 Sketches and generalizations
  - 18C35 Accessible and locally presentable categories (4 articles)
  - 18C50 Categorical semantics of formal languages
  - 18C99 None of the above, but in this section (9 articles)
- 18Dxx Categories with structure (89 articles)
  - 18Dxx Categories with structure (2 articles)
  - 18D05 Double categories, $2$-categories, bicategories and generalizations (7 articles)
  - 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories (15 articles)
  - 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) (26 articles)
  - 18D20 Enriched categories (over closed or monoidal categories) (6 articles)
  - 18D25 Strong functors, strong adjunctions
  - 18D30 Fibered categories (6 articles)
  - 18D35 Structured objects in a category (group objects, etc.) (6 articles)
  - 18D50 Operads (16 articles)
  - 18D99 None of the above, but in this section (5 articles)
- 18Exx Abelian categories (61 articles)
  - 18Exx Abelian categories
  - 18E05 Preadditive, additive categories (6 articles)
  - 18E10 Exact categories, abelian categories (11 articles)
  - 18E15 Grothendieck categories (1 articles)
  - 18E20 Embedding theorems (1 articles)
  - 18E25 Derived functors and satellites (1 articles)
  - 18E30 Derived categories, triangulated categories (5 articles)
  - 18E35 Localization of categories (1 articles)
  - 18E40 Torsion theories, radicals (33 articles)
  - 18E99 None of the above, but in this section (2 articles)
- 18Fxx Categories and geometry (26 articles)
  - 18Fxx Categories and geometry
  - 18F05 Local categories and functors (1 articles)
  - 18F10 Grothendieck topologies (1 articles)
  - 18F15 Abstract manifolds and fiber bundles (7 articles)
  - 18F20 Presheaves and sheaves (11 articles)
  - 18F25 Algebraic $K$-theory and $L$-theory (2 articles)
  - 18F30 Grothendieck groups
  - 18F99 None of the above, but in this section (4 articles)
- 18Gxx Homological algebra (62 articles)
  - 18Gxx Homological algebra
  - 18G05 Projectives and injectives (11 articles)
  - 18G10 Resolutions; derived functors (6 articles)
  - 18G15 Ext and Tor, generalizations, Künneth formula (6 articles)
  - 18G20 Homological dimension (5 articles)
  - 18G25 Relative homological algebra, projective classes (11 articles)
  - 18G30 Simplicial sets, simplicial objects (in a category) (3 articles)
  - 18G35 Chain complexes (5 articles)
  - 18G40 Spectral sequences, hypercohomology
  - 18G50 Nonabelian homological algebra (3 articles)
  - 18G55 Homotopical algebra (7 articles)
  - 18G60 Other (co)homology theories (2 articles)
  - 18G99 None of the above, but in this section (3 articles)
19 $K$-theory (41 articles)
- 19 $K$-theory
- 19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 19-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 19-02 Research exposition (monographs, survey articles) (1 articles)
- 19-03 Historical (must also be assigned at least one classification number from Section 01)
- 19-04 Explicit machine computation and programs (not the theory of computation or programming)
- 19-06 Proceedings, conferences, collections, etc.
- 19Axx Grothendieck groups and $K_0$ (8 articles)
  - 19Axx Grothendieck groups and $K_0$
  - 19A13 Stability for projective modules (1 articles)
  - 19A15 Efficient generation
  - 19A22 Frobenius induction, Burnside and representation rings (7 articles)
  - 19A31 $K_0$ of group rings and orders
  - 19A49 $K_0$ of other rings
  - 19A99 None of the above, but in this section
- 19Bxx Whitehead groups and $K_1$ (3 articles)
  - 19Bxx Whitehead groups and $K_1$
  - 19B10 Stable range conditions (3 articles)
  - 19B14 Stability for linear groups
  - 19B28 $K_1$ of group rings and orders
  - 19B37 Congruence subgroup problems
  - 19B99 None of the above, but in this section
- 19Cxx Steinberg groups and $K_2$
  - 19Cxx Steinberg groups and $K_2$
  - 19C09 Central extensions and Schur multipliers
  - 19C20 Symbols, presentations and stability of $K_2$
  - 19C30 $K_2$ and the Brauer group
  - 19C40 Excision for $K_2$
  - 19C99 None of the above, but in this section
- 19Dxx Higher algebraic $K$-theory (6 articles)
  - 19Dxx Higher algebraic $K$-theory
  - 19D06 $Q$- and plus-constructions (1 articles)
  - 19D10 Algebraic $K$-theory of spaces
  - 19D23 Symmetric monoidal categories
  - 19D25 Karoubi-Villamayor-Gersten $K$-theory
  - 19D35 Negative $K$-theory, NK and Nil
  - 19D45 Higher symbols, Milnor $K$-theory
  - 19D50 Computations of higher $K$-theory of rings (2 articles)
  - 19D55 $K$-theory and homology; cyclic homology and cohomology (3 articles)
  - 19D99 None of the above, but in this section
- 19Exx $K$-theory in geometry (1 articles)
  - 19Exx $K$-theory in geometry
  - 19E08 $K$-theory of schemes
  - 19E15 Algebraic cycles and motivic cohomology
  - 19E20 Relations with cohomology theories
  - 19E99 None of the above, but in this section (1 articles)
- 19Fxx $K$-theory in number theory (1 articles)
  - 19Fxx $K$-theory in number theory
  - 19F05 Generalized class field theory
  - 19F15 Symbols and arithmetic
  - 19F27 Étale cohomology, higher regulators, zeta and $L$-functions (1 articles)
  - 19F99 None of the above, but in this section
- 19Gxx $K$-theory of forms (4 articles)
  - 19Gxx $K$-theory of forms
  - 19G05 Stability for quadratic modules
  - 19G12 Witt groups of rings (2 articles)
  - 19G24 $L$-theory of group rings (2 articles)
  - 19G38 Hermitian $K$-theory, relations with $K$-theory of rings
  - 19G99 None of the above, but in this section
- 19Jxx Obstructions from topology (2 articles)
  - 19Jxx Obstructions from topology
  - 19J05 Finiteness and other obstructions in $K_0$
  - 19J10 Whitehead (and related) torsion
  - 19J25 Surgery obstructions (2 articles)
  - 19J35 Obstructions to group actions
  - 19J99 None of the above, but in this section
- 19Kxx $K$-theory and operator algebras (1 articles)
  - 19Kxx $K$-theory and operator algebras
  - 19K14 $K_0$ as an ordered group, traces
  - 19K33 EXT and $K$-homology
  - 19K35 Kasparov theory ($KK$-theory)
  - 19K56 Index theory
  - 19K99 None of the above, but in this section (1 articles)
- 19Lxx Topological $K$-theory (12 articles)
  - 19Lxx Topological $K$-theory
  - 19L10 Riemann-Roch theorems, Chern characters (3 articles)
  - 19L20 $J$-homomorphism, Adams operations
  - 19L41 Connective $K$-theory, cobordism
  - 19L47 Equivariant $K$-theory (1 articles)
  - 19L64 Computations, geometric applications (7 articles)
  - 19L99 None of the above, but in this section (1 articles)
- 19M05 Miscellaneous applications of $K$-theory (1 articles)
20 Group theory and generalizations (2044 articles)
- 20 Group theory and generalizations
- 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (12 articles)
- 20-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 20-02 Research exposition (monographs, survey articles) (1 articles)
- 20-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 20-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 20-06 Proceedings, conferences, collections, etc. (2 articles)
- 20.0 (1940-1958) Group theory and generalizations
- 20.00 (1959-1972) General (35 articles)
- 20.08 (1959-1972) Varieties of groups (1 articles)
- 20.10 (1959-1972) Group presentations; free groups, generators, relations
- 20.15 (1959-1972) Periodic groups
- 20.18 (1959-1972) Groups with local properties
- 20.20 (1959-1972) Groups acting on sets, permutation groups
- 20.22 (1959-1972) Automorphism groups
- 20.25 (1959-1972) Finite group theory (1 articles)
- 20.27 (1959-1972) Structure of groups, classification
- 20.29 (1959-1972) Simple groups
- 20.30 (1959-1972) Abelian groups (22 articles)
- 20.40 (1959-1972) Nilpotent, solvable, $p$-groups
- 20.43 (1959-1972) Sylow subgroups, $Pi$-subgroups
- 20.48 (1959-1972) Group extensions
- 20.50 (1959-1972) Homological methods in group theory
- 20.51 (1959-1972) Limits of systems of groups
- 20.52 (1959-1972) General products of groups (including semidirect, wreath, free, amalgamated) (1 articles)
- 20.54 (1959-1972) Special subgroups (1 articles)
- 20.56 (1959-1972) Series of subgroups (1 articles)
- 20.58 (1959-1972) Lattices of subgroups
- 20.60 (1959-1972) Crystallographic and discrete geometric groups
- 20.65 (1959-1972) Modular groups, discrete subgroups of classical groups
- 20.70 (1959-1972) Classical groups
- 20.72 (1959-1972) Collineation groups
- 20.75 (1959-1972) Linear groups, general
- 20.80 (1959-1972) Representations, characters, group algebras (1 articles)
- 20.85 (1959-1972) Representations of symmetric groups
- 20.90 (1959-1972) Semigroup algebras, representations, characters (2 articles)
- 20.92 (1959-1972) Semigroups, general theory (35 articles)
- 20.93 (1959-1972) Semigroups, structure and classification (20 articles)
- 20.95 (1959-1972) Other binary systems; groupoids, quasigroups, loops (1 articles)
- 20.97 (1959-1972) Ternary systems; heaps, semiheaps, heapoids
- 20.98 (1959-1972) $n$-ary systems
- 20.99 (1959-1972) None of the above, but in this section (4 articles)
- 20Axx Foundations (9 articles)
  - 20Axx Foundations
  - 20A05 Axiomatics and elementary properties (5 articles)
  - 20A10 Metamathematical considerations
  - 20A15 Applications of logic to group theory (2 articles)
  - 20A99 None of the above, but in this section (2 articles)
- 20Bxx Permutation groups (39 articles)
  - 20Bxx Permutation groups
  - 20B05 General theory for finite groups (2 articles)
  - 20B07 General theory for infinite groups
  - 20B10 Characterization theorems (1 articles)
  - 20B15 Primitive groups (4 articles)
  - 20B20 Multiply transitive finite groups (1 articles)
  - 20B22 Multiply transitive infinite groups
  - 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures (15 articles)
  - 20B27 Infinite automorphism groups (5 articles)
  - 20B30 Symmetric groups (3 articles)
  - 20B35 Subgroups of symmetric groups (4 articles)
  - 20B40 Computational methods (1 articles)
  - 20B99 None of the above, but in this section (3 articles)
- 20Cxx Representation theory of groups (74 articles)
  - 20Cxx Representation theory of groups
  - 20C05 Group rings of finite groups and their modules (17 articles)
  - 20C07 Group rings of infinite groups and their modules (17 articles)
  - 20C08 Hecke algebras and their representations
  - 20C10 Integral representations of finite groups (1 articles)
  - 20C11 $p$-adic representations of finite groups
  - 20C12 Integral representations of infinite groups
  - 20C15 Ordinary representations and characters (20 articles)
  - 20C20 Modular representations and characters (4 articles)
  - 20C25 Projective representations and multipliers
  - 20C30 Representations of finite symmetric groups (5 articles)
  - 20C32 Representations of infinite symmetric groups
  - 20C33 Representations of finite groups of Lie type (2 articles)
  - 20C34 Representations of sporadic groups
  - 20C35 Applications of group representations to physics (1 articles)
  - 20C40 Computational methods (1 articles)
  - 20C99 None of the above, but in this section (6 articles)
- 20Dxx Abstract finite groups (182 articles)
  - 20Dxx Abstract finite groups
  - 20D05 Classification of simple and nonsolvable groups (14 articles)
  - 20D06 Simple groups: alternating groups and groups of Lie type (19 articles)
  - 20D08 Simple groups: sporadic groups (10 articles)
  - 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks (38 articles)
  - 20D15 Nilpotent groups, $p$-groups (21 articles)
  - 20D20 Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure (19 articles)
  - 20D25 Special subgroups (Frattini, Fitting, etc.) (3 articles)
  - 20D30 Series and lattices of subgroups (7 articles)
  - 20D35 Subnormal subgroups (3 articles)
  - 20D40 Products of subgroups (8 articles)
  - 20D45 Automorphisms (3 articles)
  - 20D60 Arithmetic and combinatorial problems (29 articles)
  - 20D99 None of the above, but in this section (8 articles)
- 20Exx Structure and classification of infinite or finite groups (99 articles)
  - 20Exx Structure and classification of infinite or finite groups (2 articles)
  - 20E05 Free nonabelian groups (9 articles)
  - 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (5 articles)
  - 20E07 Subgroup theorems; subgroup growth (10 articles)
  - 20E08 Groups acting on trees (1 articles)
  - 20E10 Quasivarieties and varieties of groups (14 articles)
  - 20E15 Chains and lattices of subgroups, subnormal subgroups (19 articles)
  - 20E18 Limits, profinite groups (2 articles)
  - 20E22 Extensions, wreath products, and other compositions (8 articles)
  - 20E25 Local properties (3 articles)
  - 20E26 Residual properties and generalizations (2 articles)
  - 20E28 Maximal subgroups (3 articles)
  - 20E32 Simple groups (3 articles)
  - 20E34 General structure theorems (7 articles)
  - 20E36 General theorems concerning automorphisms of groups (3 articles)
  - 20E42 Groups with a $BN$-pair; buildings (1 articles)
  - 20E45 Conjugacy classes (5 articles)
  - 20E99 None of the above, but in this section (2 articles)
- 20Fxx Special aspects of infinite or finite groups (135 articles)
  - 20Fxx Special aspects of infinite or finite groups
  - 20F05 Generators, relations, and presentations (11 articles)
  - 20F06 Cancellation theory; application of van Kampen diagrams
  - 20F10 Word problems, other decision problems, connections with logic and automata (1 articles)
  - 20F12 Commutator calculus (6 articles)
  - 20F14 Derived series, central series, and generalizations (8 articles)
  - 20F16 Solvable groups, supersolvable groups (5 articles)
  - 20F17 Formations of groups, Fitting classes
  - 20F18 Nilpotent groups (4 articles)
  - 20F19 Generalizations of solvable and nilpotent groups (9 articles)
  - 20F22 Other classes of groups defined by subgroup chains (5 articles)
  - 20F24 FC-groups and their generalizations (1 articles)
  - 20F28 Automorphism groups of groups (3 articles)
  - 20F29 Representations of groups as automorphism groups of algebraic systems (3 articles)
  - 20F34 Fundamental groups and their automorphisms (1 articles)
  - 20F36 Braid groups; Artin groups (3 articles)
  - 20F38 Other groups related to topology or analysis (4 articles)
  - 20F40 Associated Lie structures
  - 20F45 Engel conditions (2 articles)
  - 20F50 Periodic groups; locally finite groups (3 articles)
  - 20F55 Reflection and Coxeter groups (4 articles)
  - 20F60 Ordered groups (47 articles)
  - 20F65 Geometric group theory (3 articles)
  - 20F67 Hyperbolic groups and nonpositively curved groups
  - 20F69 Asymptotic properties of groups (1 articles)
  - 20F99 None of the above, but in this section (11 articles)
- 20Gxx Linear algebraic groups (classical groups) (28 articles)
  - 20Gxx Linear algebraic groups (classical groups) (1 articles)
  - 20G05 Representation theory (5 articles)
  - 20G10 Cohomology theory (2 articles)
  - 20G15 Linear algebraic groups over arbitrary fields (2 articles)
  - 20G20 Linear algebraic groups over the reals, the complexes, the quaternions (4 articles)
  - 20G25 Linear algebraic groups over local fields and their integers
  - 20G30 Linear algebraic groups over global fields and their integers
  - 20G35 Linear algebraic groups over adèles and other rings and schemes
  - 20G40 Linear algebraic groups over finite fields (9 articles)
  - 20G42 Quantum groups (quantized function algebras) and their representations (3 articles)
  - 20G45 Applications to physics
  - 20G99 None of the above, but in this section (2 articles)
- 20Hxx Other groups of matrices (20 articles)
  - 20Hxx Other groups of matrices
  - 20H05 Unimodular groups, congruence subgroups (1 articles)
  - 20H10 Fuchsian groups and their generalizations (3 articles)
  - 20H15 Other geometric groups, including crystallographic groups (9 articles)
  - 20H20 Other matrix groups over fields (3 articles)
  - 20H25 Other matrix groups over rings (2 articles)
  - 20H30 Other matrix groups over finite fields (1 articles)
  - 20H99 None of the above, but in this section (1 articles)
- 20Jxx Connections with homological algebra and category theory (2 articles)
  - 20Jxx Connections with homological algebra and category theory
  - 20J05 Homological methods in group theory (1 articles)
  - 20J06 Cohomology of groups (1 articles)
  - 20J15 Category of groups
  - 20J99 None of the above, but in this section
- 20Kxx Abelian groups (297 articles)
  - 20Kxx Abelian groups (10 articles)
  - 20K01 Finite abelian groups (14 articles)
  - 20K10 Torsion groups, primary groups and generalized primary groups (30 articles)
  - 20K15 Torsion-free groups, finite rank (29 articles)
  - 20K20 Torsion-free groups, infinite rank (34 articles)
  - 20K21 Mixed groups (25 articles)
  - 20K25 Direct sums, direct products, etc. (40 articles)
  - 20K27 Subgroups (38 articles)
  - 20K30 Automorphisms, homomorphisms, endomorphisms, etc. (10 articles)
  - 20K35 Extensions (18 articles)
  - 20K40 Homological and categorical methods (13 articles)
  - 20K45 Topological methods (12 articles)
  - 20K99 None of the above, but in this section (24 articles)
- 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) (49 articles)
- 20Mxx Semigroups (560 articles)
  - 20Mxx Semigroups (9 articles)
  - 20M05 Free semigroups, generators and relations, word problems (32 articles)
  - 20M07 Varieties of semigroups (30 articles)
  - 20M10 General structure theory (166 articles)
  - 20M11 Radical theory (11 articles)
  - 20M12 Ideal theory (59 articles)
  - 20M14 Commutative semigroups (59 articles)
  - 20M15 Mappings of semigroups (22 articles)
  - 20M17 Regular semigroups (18 articles)
  - 20M18 Inverse semigroups (6 articles)
  - 20M19 Orthodox semigroups (1 articles)
  - 20M20 Semigroups of transformations, etc. (42 articles)
  - 20M25 Semigroup rings, multiplicative semigroups of rings (8 articles)
  - 20M30 Representation of semigroups; actions of semigroups on sets (40 articles)
  - 20M35 Semigroups in automata theory, linguistics, etc. (11 articles)
  - 20M50 Connections of semigroups with homological algebra and category theory (10 articles)
  - 20M99 None of the above, but in this section (36 articles)
- 20Nxx Other generalizations of groups (406 articles)
  - 20Nxx Other generalizations of groups (3 articles)
  - 20N02 Sets with a single binary operation (groupoids) (59 articles)
  - 20N05 Loops, quasigroups (254 articles)
  - 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.) (21 articles)
  - 20N15 $n$-ary systems $(nge 3)$ (21 articles)
  - 20N20 Hypergroups (11 articles)
  - 20N25 Fuzzy groups
  - 20N99 None of the above, but in this section (37 articles)
- 20P05 Probabilistic methods in group theory
21 (1940-1958) Topological algebraic structures
- 21 (1940-1958) Topological algebraic structures
- 21.0 (1940-1958) Topological algebraic structures
22 Topological groups, Lie groups (392 articles)
- 22 Topological groups, Lie groups
- 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 22-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 22-02 Research exposition (monographs, survey articles) (1 articles)
- 22-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 22-04 Explicit machine computation and programs (not the theory of computation or programming)
- 22-06 Proceedings, conferences, collections, etc.
- 22.00 (1959-1972) General (4 articles)
- 22.05 (1959-1972) Topological semigroups and other generalizations of groups (18 articles)
- 22.10 (1959-1972) Topological groups (6 articles)
- 22.20 (1959-1972) Locally compact groups
- 22.40 (1959-1972) Transformation groups
- 22.50 (1959-1972) Lie groups (2 articles)
- 22.55 (1959-1972) Classical groups
- 22.57 (1959-1972) Representations and analysis of classical groups (1 articles)
- 22.60 (1959-1972) Representations and analysis, general
- 22.65 (1959-1972) Harmonic analysis on non-abelian groups (See 42.50 for LCA groups)
- 22.70 (1959-1972) Homogeneous spaces, symmetric spaces (1 articles)
- 22.80 (1959-1972) Lie algebras of Lie groups
- 22.90 (1959-1972) Other Lie theory
- 22.99 (1959-1972) None of the above, but in this section
- 22Axx Topological and differentiable algebraic systems (175 articles)
  - 22Axx Topological and differentiable algebraic systems (1 articles)
  - 22A05 Structure of general topological groups (73 articles)
  - 22A10 Analysis on general topological groups (9 articles)
  - 22A15 Structure of topological semigroups (25 articles)
  - 22A20 Analysis on topological semigroups (7 articles)
  - 22A22 Topological groupoids (including differentiable and Lie groupoids) (12 articles)
  - 22A25 Representations of general topological groups and semigroups (7 articles)
  - 22A26 Topological semilattices, lattices and applications (5 articles)
  - 22A30 Other topological algebraic systems and their representations (20 articles)
  - 22A99 None of the above, but in this section (16 articles)
- 22Bxx Locally compact abelian groups (LCA groups) (8 articles)
  - 22Bxx Locally compact abelian groups (LCA groups)
  - 22B05 General properties and structure of LCA groups (4 articles)
  - 22B10 Structure of group algebras of LCA groups
  - 22B99 None of the above, but in this section (4 articles)
- 22C05 Compact groups (12 articles)
- 22Dxx Locally compact groups and their algebras (25 articles)
  - 22Dxx Locally compact groups and their algebras
  - 22D05 General properties and structure of locally compact groups (11 articles)
  - 22D10 Unitary representations of locally compact groups (1 articles)
  - 22D12 Other representations of locally compact groups
  - 22D15 Group algebras of locally compact groups (4 articles)
  - 22D20 Representations of group algebras
  - 22D25 $C^*$-algebras and $W$*-algebras in relation to group representations
  - 22D30 Induced representations (1 articles)
  - 22D35 Duality theorems (5 articles)
  - 22D40 Ergodic theory on groups (2 articles)
  - 22D45 Automorphism groups of locally compact groups (1 articles)
  - 22D99 None of the above, but in this section
- 22Exx Lie groups (129 articles)
  - 22Exx Lie groups (4 articles)
  - 22E05 Local Lie groups (3 articles)
  - 22E10 General properties and structure of complex Lie groups (2 articles)
  - 22E15 General properties and structure of real Lie groups (12 articles)
  - 22E20 General properties and structure of other Lie groups (1 articles)
  - 22E25 Nilpotent and solvable Lie groups (8 articles)
  - 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (1 articles)
  - 22E30 Analysis on real and complex Lie groups (13 articles)
  - 22E35 Analysis on $p$-adic Lie groups
  - 22E40 Discrete subgroups of Lie groups (1 articles)
  - 22E41 Continuous cohomology
  - 22E43 Structure and representation of the Lorentz group
  - 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods (6 articles)
  - 22E46 Semisimple Lie groups and their representations (27 articles)
  - 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (7 articles)
  - 22E50 Representations of Lie and linear algebraic groups over local fields
  - 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
  - 22E60 Lie algebras of Lie groups (9 articles)
  - 22E65 Infinite-dimensional Lie groups and their Lie algebras (12 articles)
  - 22E67 Loop groups and related constructions, group-theoretic treatment (1 articles)
  - 22E70 Applications of Lie groups to physics; explicit representations (16 articles)
  - 22E99 None of the above, but in this section (6 articles)
- 22Fxx Noncompact transformation groups (7 articles)
  - 22Fxx Noncompact transformation groups
  - 22F05 General theory of group and pseudogroup actions (2 articles)
  - 22F10 Measurable group actions
  - 22F30 Homogeneous spaces (2 articles)
  - 22F50 Groups as automorphisms of other structures (3 articles)
26 Real functions (1448 articles)
- 26 Real functions
- 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (11 articles)
- 26-01 Instructional exposition (textbooks, tutorial papers, etc.) (92 articles)
- 26-02 Research exposition (monographs, survey articles) (2 articles)
- 26-03 Historical (must also be assigned at least one classification number from Section 01) (12 articles)
- 26-04 Explicit machine computation and programs (not the theory of computation or programming) (2 articles)
- 26-06 Proceedings, conferences, collections, etc. (1 articles)
- 26.0 (1940-1958) Functions of real variables
- 26.00 (1959-1972) General (2 articles)
- 26.1 (1940-1958) Calculus
- 26.10 (1959-1972) Foundations: limits and generalizations, elementary topology of the line (2 articles)
- 26.20 (1959-1972) Calculus (1 articles)
- 26.21 (1959-1972) Elementary functions
- 26.30 (1959-1972) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) (1 articles)
- 26.35 (1959-1972) (5 articles)
- 26.40 (1959-1972) Differentiation, general theory; mean-value theorems (3 articles)
- 26.41 (1959-1972) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
- 26.43 (1959-1972) Generalized derivatives, derivatives of fractional order
- 26.44 (1959-1972) Antidifferentiation
- 26.45 (1959-1972) Denjoy integral, other special integrals (1 articles)
- 26.46 (1959-1972) Integrals of Riemann, Stieltjes and Lebesgue type (1 articles)
- 26.49 (1959-1972) Functions of bounded variation, generalizations
- 26.50 (1959-1972) Monotonic functions, generalizations
- 26.52 (1959-1972) Convexity, generalizations (1 articles)
- 26.54 (1959-1972) Fixed-point theorems
- 26.55 (1959-1972) Several variables, implicit function theorems, Jacobians, transformations with several variables
- 26.56 (1959-1972) Length, area, volume (1 articles)
- 26.60 (1959-1972) Polynomials
- 26.70 (1959-1972) Inequalities (of a general and miscellaneous character) (1 articles)
- 26.80 (1959-1972) Real-analytic functions, $C^infty$ functions
- 26.99 (1959-1972) None of the above, but in this section
- 26Axx Functions of one variable (880 articles)
  - 26Axx Functions of one variable (9 articles)
  - 26A03 Foundations: limits and generalizations, elementary topology of the line (18 articles)
  - 26A06 One-variable calculus (98 articles)
  - 26A09 Elementary functions (5 articles)
  - 26A12 Rate of growth of functions, orders of infinity, slowly varying functions (10 articles)
  - 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) (99 articles)
  - 26A16 Lipschitz (Hölder) classes (11 articles)
  - 26A18 Iteration (27 articles)
  - 26A21 Classification of real functions; Baire classification of sets and functions (84 articles)
  - 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems (102 articles)
  - 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (28 articles)
  - 26A30 Singular functions, Cantor functions, functions with other special properties (14 articles)
  - 26A33 Fractional derivatives and integrals (52 articles)
  - 26A36 Antidifferentiation (5 articles)
  - 26A39 Denjoy and Perron integrals, other special integrals (136 articles)
  - 26A42 Integrals of Riemann, Stieltjes and Lebesgue type (95 articles)
  - 26A45 Functions of bounded variation, generalizations (33 articles)
  - 26A46 Absolutely continuous functions (6 articles)
  - 26A48 Monotonic functions, generalizations (11 articles)
  - 26A51 Convexity, generalizations (19 articles)
  - 26A99 None of the above, but in this section (18 articles)
- 26Bxx Functions of several variables (204 articles)
  - 26Bxx Functions of several variables
  - 26B05 Continuity and differentiation questions (42 articles)
  - 26B10 Implicit function theorems, Jacobians, transformations with several variables (14 articles)
  - 26B12 Calculus of vector functions (4 articles)
  - 26B15 Integration: length, area, volume (23 articles)
  - 26B20 Integral formulas (Stokes, Gauss, Green, etc.) (22 articles)
  - 26B25 Convexity, generalizations (25 articles)
  - 26B30 Absolutely continuous functions, functions of bounded variation (16 articles)
  - 26B35 Special properties of functions of several variables, Hölder conditions, etc. (20 articles)
  - 26B40 Representation and superposition of functions (15 articles)
  - 26B99 None of the above, but in this section (23 articles)
- 26Cxx Polynomials, rational functions (19 articles)
  - 26Cxx Polynomials, rational functions
  - 26C05 Polynomials: analytic properties, etc. (5 articles)
  - 26C10 Polynomials: location of zeros (11 articles)
  - 26C15 Rational functions (2 articles)
  - 26C99 None of the above, but in this section (1 articles)
- 26Dxx Inequalities (123 articles)
  - 26Dxx Inequalities
  - 26D05 Inequalities for trigonometric functions and polynomials (4 articles)
  - 26D07 Inequalities involving other types of functions (2 articles)
  - 26D10 Inequalities involving derivatives and differential and integral operators (44 articles)
  - 26D15 Inequalities for sums, series and integrals (64 articles)
  - 26D20 Other analytical inequalities (4 articles)
  - 26D99 None of the above, but in this section (5 articles)
- 26Exx Miscellaneous topics (83 articles)
  - 26Exx Miscellaneous topics
  - 26E05 Real-analytic functions (4 articles)
  - 26E10 $C^infty$-functions, quasi-analytic functions (4 articles)
  - 26E15 Calculus of functions on infinite-dimensional spaces (5 articles)
  - 26E20 Calculus of functions taking values in infinite-dimensional spaces (6 articles)
  - 26E25 Set-valued functions (29 articles)
  - 26E30 Non-Archimedean analysis (2 articles)
  - 26E35 Nonstandard analysis (8 articles)
  - 26E40 Constructive real analysis (1 articles)
  - 26E50 Fuzzy real analysis (9 articles)
  - 26E60 Means (11 articles)
  - 26E99 None of the above, but in this section (4 articles)
27 (1940-1958) Analysis
- 27 (1940-1958) Analysis
- 27.0 (1940-1958) Analysis
- 27.1 (1940-1958) Foundations of analysis
- 27.2 (1940-1958) Theory of sets, theory of functions of real variables
- 27.3 (1940-1958) Theory of functions of real variables, theory of measure and integration
- 27.4 (1940-1958) Geometrical analysis
- 27.5 (1940-1958) Functions with particular properties
28 Measure and integration (1207 articles)
- 28 Measure and integration
- 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (9 articles)
- 28-01 Instructional exposition (textbooks, tutorial papers, etc.) (17 articles)
- 28-02 Research exposition (monographs, survey articles) (3 articles)
- 28-03 Historical (must also be assigned at least one classification number from Section 01) (4 articles)
- 28-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 28-06 Proceedings, conferences, collections, etc. (1 articles)
- 28.0 (1940-1958) Measure and integration
- 28.00 (1959-1972) General (15 articles)
- 28.10 (1959-1972) sets, analytic sets (4 articles)
- 28.13 (1959-1972) Real- or complex-valued set functions, contents, measures, outer measures, capacities, etc. (7 articles)
- 28.16 (1959-1972) Abstract differentiation theory, differentiation of set functions
- 28.20 (1959-1972) Measurable and non-measurable functions; modes of convergence (2 articles)
- 28.25 (1959-1972) Integration with respect to measures and other set functions (3 articles)
- 28.30 (1959-1972) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.)
- 28.40 (1959-1972) Measures and integrals in product spaces (3 articles)
- 28.46 (1959-1972) Measures and integrals in function spaces, linear spaces; Wiener measure (1 articles)
- 28.50 (1959-1972) Vector-valued measures and integrals, integration of vector-valued functions (7 articles)
- 28.55 (1959-1972) Integration and disintegration of measures, lifting theory
- 28.60 (1959-1972) Measures and integrals with values in general ordered systems
- 28.65 (1959-1972) Measures on Boolean rings, measure algebras (1 articles)
- 28.70 (1959-1972) Measure-preserving transformations, flows (dynamical systems), ergodic theory (3 articles)
- 28.75 (1959-1972) Invariant measures, Haar measure (1 articles)
- 28.80 (1959-1972) Length, area, volume; other geometric measure theory (3 articles)
- 28.99 (1959-1972) None of the above, but in this section (3 articles)
- 28Axx Classical measure theory (582 articles)
  - 28Axx Classical measure theory (15 articles)
  - 28A05 Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets (126 articles)
  - 28A10 Real- or complex-valued set functions (71 articles)
  - 28A12 Contents, measures, outer measures, capacities (64 articles)
  - 28A15 Abstract differentiation theory, differentiation of set functions (14 articles)
  - 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (70 articles)
  - 28A25 Integration with respect to measures and other set functions (29 articles)
  - 28A33 Spaces of measures, convergence of measures (33 articles)
  - 28A35 Measures and integrals in product spaces (29 articles)
  - 28A50 Integration and disintegration of measures (2 articles)
  - 28A51 Lifting theory (2 articles)
  - 28A60 Measures on Boolean rings, measure algebras (29 articles)
  - 28A75 Length, area, volume, other geometric measure theory (35 articles)
  - 28A78 Hausdorff and packing measures (25 articles)
  - 28A80 Fractals (23 articles)
  - 28A99 None of the above, but in this section (15 articles)
- 28Bxx Set functions, measures and integrals with values in abstract spaces (228 articles)
  - 28Bxx Set functions, measures and integrals with values in abstract spaces
  - 28B05 Vector-valued set functions, measures and integrals (127 articles)
  - 28B10 Group- or semigroup-valued set functions, measures and integrals (28 articles)
  - 28B15 Set functions, measures and integrals with values in ordered spaces (33 articles)
  - 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections (35 articles)
  - 28B99 None of the above, but in this section (5 articles)
- 28Cxx Set functions and measures on spaces with additional structure (122 articles)
  - 28Cxx Set functions and measures on spaces with additional structure (2 articles)
  - 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (35 articles)
  - 28C10 Set functions and measures on topological groups, Haar measures, invariant measures (10 articles)
  - 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) (38 articles)
  - 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (27 articles)
  - 28C99 None of the above, but in this section (10 articles)
- 28Dxx Measure-theoretic ergodic theory (102 articles)
  - 28Dxx Measure-theoretic ergodic theory (1 articles)
  - 28D05 Measure-preserving transformations (51 articles)
  - 28D10 One-parameter continuous families of measure-preserving transformations (10 articles)
  - 28D15 General groups of measure-preserving transformations (7 articles)
  - 28D20 Entropy and other invariants (27 articles)
  - 28D99 None of the above, but in this section (6 articles)
- 28Exx Miscellaneous topics in measure theory (85 articles)
  - 28Exx Miscellaneous topics in measure theory
  - 28E05 Nonstandard measure theory (13 articles)
  - 28E10 Fuzzy measure theory (54 articles)
  - 28E15 Other connections with logic and set theory (7 articles)
  - 28E99 None of the above, but in this section (11 articles)
30 Functions of a complex variable (468 articles)
- 30 Functions of a complex variable
- 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (2 articles)
- 30-01 Instructional exposition (textbooks, tutorial papers, etc.) (5 articles)
- 30-02 Research exposition (monographs, survey articles) (4 articles)
- 30-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 30-04 Explicit machine computation and programs (not the theory of computation or programming)
- 30-06 Proceedings, conferences, collections, etc.
- 30.0 (1940-1958) Functions of a complex variable
- 30.00 (1959-1972) General (2 articles)
- 30.01 (1959-1972) General questions, foundations
- 30.02 (1959-1972) Monogenic properties of complex functions (also polygenic and areolar monogenic functions)
- 30.09 (1959-1972) Inequalities in the complex domain
- 30.10 (1959-1972) Polynomials (1 articles)
- 30.11 (1959-1972) Zeros of polynomials
- 30.20 (1959-1972) Power series
- 30.21 (1959-1972) Behavior on the boundary of convergence. Over-convergence
- 30.24 (1959-1972) Dirichlet series
- 30.25 (1959-1972) Continued fractions
- 30.28 (1959-1972) Analytic continuation
- 30.30 (1959-1972) Sequences and series of analytic functions; uniform convergence, normal families, normal functions
- 30.35 (1959-1972) Integration; integral representations; Cauchy integral, Poisson and Poisson-Stieltjes integrals (1 articles)
- 30.36 (1959-1972) Moment problems; interpolation problems
- 30.40 (1959-1972) Conformal mapping, general theory (1 articles)
- 30.41 (1959-1972) Capacity, harmonic measure (1 articles)
- 30.42 (1959-1972) Univalent functions (2 articles)
- 30.43 (1959-1972) Coefficient problems
- 30.44 (1959-1972) Multivalent functions
- 30.45 (1959-1972) Riemann surfaces, uniformization (1 articles)
- 30.46 (1959-1972) Algebraic functions, Abelian integrals
- 30.47 (1959-1972) Quasiconformal mapping
- 30.49 (1959-1972) Automorphic functions and modular functions
- 30.50 (1959-1972) Maximum principle. Schwarz's lemma, Phragmen-Lindel of theorems
- 30.52 (1959-1972) Extremal problems in the complex domain
- 30.55 (1959-1972) Entire functions, general theory
- 30.56 (1959-1972) Entire functions, representation by Dirichlet series
- 30.57 (1959-1972) Entire functions, growth estimates
- 30.58 (1959-1972) Entire functions, distribution of values
- 30.60 (1959-1972) Meromorphic functions, general theory
- 30.61 (1959-1972) Distribution of values, Picard-type theorems, Nevanlinna theory, defect (deficiency) theory
- 30.62 (1959-1972) Theory of cluster sets, prime ends, boundary behavior
- 30.65 (1959-1972) Bounded functions, positive real part, Blaschke products
- 30.66 (1959-1972) Bounded mean modulus, bounded characteristic
- 30.67 (1959-1972) $H_p$ classes and other restrictions
- 30.70 (1959-1972) Approximation by polynomials and rational functions in the complex domain
- 30.75 (1959-1972) Boundary value problems, Dirichlet problem
- 30.77 (1959-1972) Special boundary value problems; Riemann-Hilbert problem. Inverse boundary problems (2 articles)
- 30.79 (1959-1972) Algebroidal functions
- 30.80 (1959-1972) Topological function theory, functions topologically equivalent to analytic mappings
- 30.81 (1959-1972) Generalized analytic mappings. Pseudo-analytic functions of Bers, Vekua, etc.
- 30.83 (1959-1972) Functions of hypercomplex variables and generalized variables
- 30.85 (1959-1972) Spaces of analytic functions
- 30.86 (1959-1972) Kernel function and applications
- 30.87 (1959-1972) Algebras of analytic functions
- 30.99 (1959-1972) None of the above, but in this section
- 30Axx General properties (9 articles)
 - 30Axx General properties
 - 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic functions) (3 articles)
 - 30A10 Inequalities in the complex domain (2 articles)
 - 30A99 None of the above, but in this section (4 articles)
- 30Bxx Series expansions (66 articles)
 - 30Bxx Series expansions
 - 30B10 Power series (including lacunary series) (30 articles)
 - 30B20 Random power series (3 articles)
 - 30B30 Boundary behavior of power series, over-convergence (7 articles)
 - 30B40 Analytic continuation (11 articles)
 - 30B50 Dirichlet series and other series expansions, exponential series (9 articles)
 - 30B60 Completeness problems, closure of a system of functions (1 articles)
 - 30B70 Continued fractions (4 articles)
 - 30B99 None of the above, but in this section (1 articles)
- 30Cxx Geometric function theory (140 articles)
 - 30Cxx Geometric function theory (2 articles)
 - 30C10 Polynomials (6 articles)
 - 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) (23 articles)
 - 30C20 Conformal mappings of special domains (6 articles)
 - 30C25 Covering theorems in conformal mapping theory
 - 30C30 Numerical methods in conformal mapping theory (2 articles)
 - 30C35 General theory of conformal mappings (6 articles)
 - 30C40 Kernel functions and applications (4 articles)
 - 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) (40 articles)
 - 30C50 Coefficient problems for univalent and multivalent functions (16 articles)
 - 30C55 General theory of univalent and multivalent functions (2 articles)
 - 30C62 Quasiconformal mappings in the plane (5 articles)
 - 30C65 Quasiconformal mappings in $R^n$, other generalizations (8 articles)
 - 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods (4 articles)
 - 30C75 Extremal problems for conformal and quasiconformal mappings, other methods (3 articles)
 - 30C80 Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (6 articles)
 - 30C85 Capacity and harmonic measure in the complex plane (4 articles)
 - 30C99 None of the above, but in this section (3 articles)
- 30Dxx Entire and meromorphic functions, and related topics (115 articles)
 - 30Dxx Entire and meromorphic functions, and related topics (1 articles)
 - 30D05 Functional equations in the complex domain, iteration and composition of analytic functions (9 articles)
 - 30D10 Representations of entire functions by series and integrals (9 articles)
 - 30D15 Special classes of entire functions and growth estimates (9 articles)
 - 30D20 Entire functions, general theory (6 articles)
 - 30D30 Meromorphic functions, general theory (8 articles)
 - 30D35 Distribution of values, Nevanlinna theory (52 articles)
 - 30D40 Cluster sets, prime ends, boundary behavior (5 articles)
 - 30D45 Bloch functions, normal functions, normal families (4 articles)
 - 30D50 Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part (5 articles)
 - 30D55 $ (4 articles)
 - 30D60 Quasi-analytic and other classes of functions (3 articles)
 - 30D99 None of the above, but in this section
- 30Exx Miscellaneous topics of analysis in the complex domain (46 articles)
 - 30Exx Miscellaneous topics of analysis in the complex domain (1 articles)
 - 30E05 Moment problems, interpolation problems (5 articles)
 - 30E10 Approximation in the complex domain (13 articles)
 - 30E15 Asymptotic representations in the complex domain (1 articles)
 - 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions (21 articles)
 - 30E25 Boundary value problems (4 articles)
 - 30E99 None of the above, but in this section (1 articles)
- 30Fxx Riemann surfaces (8 articles)
 - 30Fxx Riemann surfaces
 - 30F10 Compact Riemann surfaces and uniformization (1 articles)
 - 30F15 Harmonic functions on Riemann surfaces (1 articles)
 - 30F20 Classification theory of Riemann surfaces
 - 30F25 Ideal boundary theory
 - 30F30 Differentials on Riemann surfaces
 - 30F35 Fuchsian groups and automorphic functions (1 articles)
 - 30F40 Kleinian groups (2 articles)
 - 30F45 Conformal metrics (hyperbolic, Poincaré, distance functions) (1 articles)
 - 30F50 Klein surfaces (1 articles)
 - 30F60 Teichmüller theory
 - 30F99 None of the above, but in this section (1 articles)
- 30Gxx Generalized function theory (48 articles)
 - 30Gxx Generalized function theory
 - 30G06 Non-Archimedean function theory
 - 30G12 Finely holomorphic functions and topological function theory (1 articles)
 - 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.) (2 articles)
 - 30G25 Discrete analytic functions
 - 30G30 Other generalizations of analytic functions (including abstract-valued functions) (4 articles)
 - 30G35 Functions of hypercomplex variables and generalized variables (41 articles)
 - 30G99 None of the above, but in this section
- 30H05 Spaces and algebras of analytic functions (12 articles)
31 Potential theory (314 articles)
- 31 Potential theory
- 31-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (3 articles)
- 31-01 Instructional exposition (textbooks, tutorial papers, etc.) (2 articles)
- 31-02 Research exposition (monographs, survey articles) (2 articles)
- 31-03 Historical (must also be assigned at least one classification number from Section 01) (5 articles)
- 31-04 Explicit machine computation and programs (not the theory of computation or programming)
- 31-06 Proceedings, conferences, collections, etc.
- 31.0 (1940-1958) Harmonic functions, potential theory
- 31.00 (1959-1972) General (3 articles)
- 31.10 (1959-1972) Harmonic functions in the plane (5 articles)
- 31.11 (1959-1972) Harmonic functions, general
- 31.15 (1959-1972) Subharmonic, superharmonic functions
- 31.20 (1959-1972) Boundary value problems, Dirichlet problem (3 articles)
- 31.21 (1959-1972) Capacity and harmonic measure
- 31.22 (1959-1972) Generalized capacity and potential (1 articles)
- 31.30 (1959-1972) Biharmonic and polyharmonic functions and equations
- 31.35 (1959-1972) Poisson's equation
- 31.50 (1959-1972) Axiomatic potential theory
- 31.99 (1959-1972) None of the above, but in this section
- 31Axx Two-dimensional theory (68 articles)
  - 31Axx Two-dimensional theory (4 articles)
  - 31A05 Harmonic, subharmonic, superharmonic functions (8 articles)
  - 31A10 Integral representations, integral operators, integral equations methods (12 articles)
  - 31A15 Potentials and capacity, harmonic measure, extremal length (11 articles)
  - 31A20 Boundary behavior (theorems of Fatou type, etc.) (10 articles)
  - 31A25 Boundary value and inverse problems (11 articles)
  - 31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation (10 articles)
  - 31A35 Connections with differential equations (1 articles)
  - 31A99 None of the above, but in this section (1 articles)
- 31Bxx Higher-dimensional theory (128 articles)
  - 31Bxx Higher-dimensional theory (1 articles)
  - 31B05 Harmonic, subharmonic, superharmonic functions (23 articles)
  - 31B10 Integral representations, integral operators, integral equations methods (33 articles)
  - 31B15 Potentials and capacities, extremal length (18 articles)
  - 31B20 Boundary value and inverse problems (26 articles)
  - 31B25 Boundary behavior (6 articles)
  - 31B30 Biharmonic and polyharmonic equations and functions (14 articles)
  - 31B35 Connections with differential equations (5 articles)
  - 31B99 None of the above, but in this section (2 articles)
- 31Cxx Other generalizations (52 articles)
  - 31Cxx Other generalizations (1 articles)
  - 31C05 Harmonic, subharmonic, superharmonic functions (8 articles)
  - 31C10 Pluriharmonic and plurisubharmonic functions (3 articles)
  - 31C12 Potential theory on Riemannian manifolds (5 articles)
  - 31C15 Potentials and capacities (15 articles)
  - 31C20 Discrete potential theory and numerical methods
  - 31C25 Dirichlet spaces
  - 31C35 Martin boundary theory (4 articles)
  - 31C40 Fine potential theory (7 articles)
  - 31C45 Other generalizations (nonlinear potential theory, etc.) (7 articles)
  - 31C99 None of the above, but in this section (2 articles)
- 31D05 Axiomatic potential theory (42 articles)
32 Several complex variables and analytic spaces (264 articles)
- 32 Several complex variables and analytic spaces
- 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 32-01 Instructional exposition (textbooks, tutorial papers, etc.) (8 articles)
- 32-02 Research exposition (monographs, survey articles)
- 32-03 Historical (must also be assigned at least one classification number from Section 01)
- 32-04 Explicit machine computation and programs (not the theory of computation or programming)
- 32-06 Proceedings, conferences, collections, etc.
- 32.0 (1940-1958) Analytic functions of several variables
- 32.00 (1959-1972) General (1 articles)
- 32.02 (1959-1972) Foundations, general questions
- 32.05 (1959-1972) Polynomials, entire functions
- 32.10 (1959-1972) Power series, formal theory
- 32.12 (1959-1972) General analysis in several complex variables
- 32.15 (1959-1972) Integral representations
- 32.17 (1959-1972) Inequalities
- 32.20 (1959-1972) Domains of holomorphy
- 32.22 (1959-1972) Pseudoconvexity
- 32.25 (1959-1972) Local properties of holomorphic functions
- 32.27 (1959-1972) Removable singularities
- 32.32 (1959-1972) Complex symmetric spaces
- 32.35 (1959-1972) Bergman kernel function (1 articles)
- 32.40 (1959-1972) Analytic manifolds
- 32.44 (1959-1972) Analytic varieties
- 32.47 (1959-1972) Analytic spaces
- 32.49 (1959-1972) Stein spaces
- 32.50 (1959-1972) Analytic sheaves and cohomology theory
- 32.60 (1959-1972) Holomorphic mappings (1 articles)
- 32.65 (1959-1972) Automorphic functions
- 32.70 (1959-1972) Approximation theorems
- 32.80 (1959-1972) Non-Archimedean function theory
- 32.99 (1959-1972) None of the above, but in this section
- 32Axx Holomorphic functions of several complex variables (85 articles)
  - 32Axx Holomorphic functions of several complex variables (1 articles)
  - 32A05 Power series, series of functions (2 articles)
  - 32A07 Special domains (Reinhardt, Hartogs, circular, tube) (2 articles)
  - 32A10 Holomorphic functions (11 articles)
  - 32A12 Multifunctions
  - 32A15 Entire functions (3 articles)
  - 32A17 Special families of functions (2 articles)
  - 32A18 Bloch functions, normal functions (5 articles)
  - 32A19 Normal families of functions, mappings
  - 32A20 Meromorphic functions (1 articles)
  - 32A22 Nevanlinna theory (local); growth estimates; other inequalities (2 articles)
  - 32A25 Integral representations; canonical kernels (Szegö, Bergman, etc.) (12 articles)
  - 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels) (2 articles)
  - 32A27 Local theory of residues (2 articles)
  - 32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) (6 articles)
  - 32A35 $ (1 articles)
  - 32A36 Bergman spaces (12 articles)
  - 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (9 articles)
  - 32A38 Algebras of holomorphic functions (1 articles)
  - 32A40 Boundary behavior of holomorphic functions (2 articles)
  - 32A45 Hyperfunctions (1 articles)
  - 32A50 Harmonic analysis of several complex variables (1 articles)
  - 32A55 Singular integrals
  - 32A60 Zero sets of holomorphic functions
  - 32A65 Banach algebra techniques (1 articles)
  - 32A70 Functional analysis techniques
  - 32A99 None of the above, but in this section (6 articles)
- 32Bxx Local analytic geometry
  - 32Bxx Local analytic geometry
  - 32B05 Analytic algebras and generalizations, preparation theorems
  - 32B10 Germs of analytic sets, local parametrization
  - 32B15 Analytic subsets of affine space
  - 32B20 Semi-analytic sets and subanalytic sets
  - 32B25 Triangulation and related questions
  - 32B99 None of the above, but in this section
- 32Cxx Analytic spaces (9 articles)
  - 32Cxx Analytic spaces
  - 32C05 Real-analytic manifolds, real-analytic spaces (2 articles)
  - 32C07 Real-analytic sets, complex Nash functions
  - 32C09 Embedding of real analytic manifolds
  - 32C11 Complex supergeometry (1 articles)
  - 32C15 Complex spaces (1 articles)
  - 32C18 Topology of analytic spaces
  - 32C20 Normal analytic spaces
  - 32C22 Embedding of analytic spaces
  - 32C25 Analytic subsets and submanifolds
  - 32C30 Integration on analytic sets and spaces, currents
  - 32C35 Analytic sheaves and cohomology groups (3 articles)
  - 32C36 Local cohomology of analytic spaces
  - 32C37 Duality theorems (1 articles)
  - 32C38 Sheaves of differential operators and their modules, $D$-modules (1 articles)
  - 32C55 The Levi problem in complex spaces; generalizations
  - 32C81 Applications to physics
  - 32C99 None of the above, but in this section
- 32Dxx Analytic continuation (16 articles)
  - 32Dxx Analytic continuation
  - 32D05 Domains of holomorphy (3 articles)
  - 32D10 Envelopes of holomorphy (2 articles)
  - 32D15 Continuation of analytic objects (4 articles)
  - 32D20 Removable singularities (5 articles)
  - 32D26 Riemann domains
  - 32D99 None of the above, but in this section (2 articles)
- 32Exx Holomorphic convexity (9 articles)
  - 32Exx Holomorphic convexity
  - 32E05 Holomorphically convex complex spaces, reduction theory (1 articles)
  - 32E10 Stein spaces, Stein manifolds (3 articles)
  - 32E20 Polynomial convexity (1 articles)
  - 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation (2 articles)
  - 32E35 Global boundary behavior of holomorphic functions
  - 32E40 The Levi problem
  - 32E99 None of the above, but in this section (2 articles)
- 32Fxx Geometric convexity (12 articles)
  - 32Fxx Geometric convexity
  - 32F10 $q$-convexity, $q$-concavity (3 articles)
  - 32F17 Other notions of convexity (2 articles)
  - 32F18 Finite-type conditions (1 articles)
  - 32F27 Topological consequences of geometric convexity
  - 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.) (1 articles)
  - 32F45 Invariant metrics and pseudodistances (5 articles)
  - 32F99 None of the above, but in this section
- 32Gxx Deformations of analytic structures (2 articles)
  - 32Gxx Deformations of analytic structures
  - 32G05 Deformations of complex structures
  - 32G07 Deformations of special (e.g. CR) structures
  - 32G08 Deformations of fiber bundles
  - 32G10 Deformations of submanifolds and subspaces
  - 32G13 Analytic moduli problems (1 articles)
  - 32G15 Moduli of Riemann surfaces, Teichmüller theory
  - 32G20 Period matrices, variation of Hodge structure; degenerations
  - 32G34 Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) (1 articles)
  - 32G81 Applications to physics
  - 32G99 None of the above, but in this section
- 32Hxx Holomorphic mappings and correspondences (13 articles)
  - 32Hxx Holomorphic mappings and correspondences
  - 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions (4 articles)
  - 32H04 Meromorphic mappings (1 articles)
  - 32H12 Boundary uniqueness of mappings
  - 32H25 Picard-type theorems and generalizations (1 articles)
  - 32H30 Value distribution theory in higher dimensions (2 articles)
  - 32H35 Proper mappings, finiteness theorems (1 articles)
  - 32H40 Boundary regularity of mappings
  - 32H50 Iteration problems (1 articles)
  - 32H99 None of the above, but in this section (3 articles)
- 32Jxx Compact analytic spaces (3 articles)
  - 32Jxx Compact analytic spaces
  - 32J05 Compactification of analytic spaces
  - 32J10 Algebraic dependence theorems
  - 32J15 Compact surfaces
  - 32J17 Compact $3$-folds (1 articles)
  - 32J18 Compact $n$-folds
  - 32J25 Transcendental methods of algebraic geometry (1 articles)
  - 32J27 Compact Kähler manifolds: generalizations, classification (1 articles)
  - 32J81 Applications to physics
  - 32J99 None of the above, but in this section
- 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem) (5 articles)
  - 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)
  - 32K05 Banach analytic spaces (2 articles)
  - 32K07 Formal and graded complex spaces
  - 32K15 Differentiable functions on analytic spaces, differentiable spaces
  - 32K99 None of the above, but in this section (3 articles)
- 32Lxx Holomorphic fiber spaces (18 articles)
  - 32Lxx Holomorphic fiber spaces
  - 32L05 Holomorphic bundles and generalizations (3 articles)
  - 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results (4 articles)
  - 32L15 Bundle convexity
  - 32L20 Vanishing theorems (1 articles)
  - 32L25 Twistor theory, double fibrations (9 articles)
  - 32L81 Applications to physics (1 articles)
  - 32L99 None of the above, but in this section
- 32Mxx Complex spaces with a group of automorphisms (21 articles)
  - 32Mxx Complex spaces with a group of automorphisms
  - 32M05 Complex Lie groups, automorphism groups acting on complex spaces (6 articles)
  - 32M10 Homogeneous complex manifolds (7 articles)
  - 32M12 Almost homogeneous manifolds and spaces (1 articles)
  - 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (6 articles)
  - 32M17 Automorphism groups of $
  - 32M25 Complex vector fields
  - 32M99 None of the above, but in this section (1 articles)
- 32Nxx Automorphic functions
  - 32Nxx Automorphic functions
  - 32N05 General theory of automorphic functions of several complex variables
  - 32N10 Automorphic forms
  - 32N15 Automorphic functions in symmetric domains
  - 32N99 None of the above, but in this section
- 32P05 Non-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
- 32Qxx Complex manifolds (17 articles)
  - 32Qxx Complex manifolds
  - 32Q05 Negative curvature manifolds
  - 32Q10 Positive curvature manifolds
  - 32Q15 Kähler manifolds (5 articles)
  - 32Q20 Kähler-Einstein manifolds (3 articles)
  - 32Q25 Calabi-Yau theory
  - 32Q28 Stein manifolds
  - 32Q30 Uniformization
  - 32Q35 Complex manifolds as subdomains of Euclidean space
  - 32Q40 Embedding theorems (1 articles)
  - 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds (2 articles)
  - 32Q55 Topological aspects of complex manifolds
  - 32Q57 Classification theorems
  - 32Q60 Almost complex manifolds (4 articles)
  - 32Q65 Pseudoholomorphic curves
  - 32Q99 None of the above, but in this section (2 articles)
- 32Sxx Singularities (3 articles)
  - 32Sxx Singularities
  - 32S05 Local singularities
  - 32S10 Invariants of analytic local rings
  - 32S15 Equisingularity (topological and analytic)
  - 32S20 Global theory of singularities; cohomological properties
  - 32S22 Relations with arrangements of hyperplanes
  - 32S25 Surface and hypersurface singularities
  - 32S30 Deformations of singularities; vanishing cycles (1 articles)
  - 32S35 Mixed Hodge theory of singular varieties
  - 32S40 Monodromy; relations with differential equations and $D$-modules
  - 32S45 Modifications; resolution of singularities
  - 32S50 Topological aspects: Lefschetz theorems, topological classification, invariants (1 articles)
  - 32S55 Milnor fibration; relations with knot theory
  - 32S60 Stratifications; constructible sheaves; intersection cohomology
  - 32S65 Singularities of holomorphic vector fields and foliations (1 articles)
  - 32S70 Other operations on singularities
  - 32S99 None of the above, but in this section
- 32Txx Pseudoconvex domains (4 articles)
  - 32Txx Pseudoconvex domains
  - 32T05 Domains of holomorphy
  - 32T15 Strongly pseudoconvex domains
  - 32T20 Worm domains
  - 32T25 Finite type domains (1 articles)
  - 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries
  - 32T35 Exhaustion functions
  - 32T40 Peak functions (1 articles)
  - 32T99 None of the above, but in this section (2 articles)
- 32Uxx Pluripotential theory (4 articles)
  - 32Uxx Pluripotential theory
  - 32U05 Plurisubharmonic functions and generalizations (1 articles)
  - 32U10 Plurisubharmonic exhaustion functions
  - 32U15 General pluripotential theory (1 articles)
  - 32U20 Capacity theory and generalizations
  - 32U25 Lelong numbers
  - 32U30 Removable sets (1 articles)
  - 32U35 Pluricomplex Green functions
  - 32U40 Currents (1 articles)
  - 32U99 None of the above, but in this section
- 32Vxx CR manifolds (22 articles)
  - 32Vxx CR manifolds (3 articles)
  - 32V05 CR structures, CR operators, and generalizations (7 articles)
  - 32V10 CR functions
  - 32V15 CR manifolds as boundaries of domains (1 articles)
  - 32V20 Analysis on CR manifolds
  - 32V25 Extension of functions and other analytic objects from CR manifolds
  - 32V30 Embeddings of CR manifolds
  - 32V35 Finite type conditions on CR manifolds (3 articles)
  - 32V40 Real submanifolds in complex manifolds (8 articles)
  - 32V99 None of the above, but in this section
- 32Wxx Differential operators in several variables (10 articles)
  - 32Wxx Differential operators in several variables
  - 32W05 $overlinepartial$ and $overlinepartial$-Neumann operators (10 articles)
  - 32W10 $overlinepartial_b$ and $overlinepartial_b$-Neumann operators
  - 32W20 Complex Monge-Ampère operators
  - 32W25 Pseudodifferential operators in several complex variables
  - 32W30 Heat kernels in several complex variables
  - 32W50 Other partial differential equations of complex analysis
  - 32W99 None of the above, but in this section
33 Special functions (265 articles)
- 33 Special functions
- 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 33-01 Instructional exposition (textbooks, tutorial papers, etc.) (8 articles)
- 33-02 Research exposition (monographs, survey articles)
- 33-03 Historical (must also be assigned at least one classification number from Section 01)
- 33-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 33-06 Proceedings, conferences, collections, etc.
- 33.0 (1940-1958) Special functions
- 33.00 (1959-1972) General
- 33.04 (1959-1972) Number-theoretic functions, special sequences
- 33.10 (1959-1972) Exponential and trigonometric functions
- 33.15 (1959-1972) Gamma and beta functions
- 33.17 (1959-1972) Error function, probability integral
- 33.19 (1959-1972) Elliptic functions and integrals
- 33.20 (1959-1972) Hypergeometric functions, generalizations
- 33.21 (1959-1972) $E$-functions, $G$-functions (1 articles)
- 33.25 (1959-1972) Cylindrical functions; Bessel functions
- 33.27 (1959-1972) Spherical functions; Legendre polynomials and functions, spherical harmonics, ultraspherical polynomials
- 33.28 (1959-1972) Lam\'e, Mathieu, spheroidal wave functions
- 33.30 (1959-1972) Wave functions
- 33.32 (1959-1972) Gegenbauer functions
- 33.40 (1959-1972) Laguerre, etc.)
- 33.45 (1959-1972) Other special functions
- 33.50 (1959-1972) Special functions and Lie groups
- 33.99 (1959-1972) None of the above, but in this section
- 33Bxx Elementary classical functions (61 articles)
  - 33Bxx Elementary classical functions
  - 33B10 Exponential and trigonometric functions (26 articles)
  - 33B15 Gamma, beta and polygamma functions (28 articles)
  - 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (2 articles)
  - 33B30 Higher logarithm functions
  - 33B99 None of the above, but in this section (5 articles)
- 33Cxx Hypergeometric functions (98 articles)
  - 33Cxx Hypergeometric functions
  - 33C05 Classical hypergeometric functions, $_2F_1$ (7 articles)
  - 33C10 Bessel and Airy functions, cylinder functions, $_0F_1$ (23 articles)
  - 33C15 Confluent hypergeometric functions, Whittaker functions, $_1F_1$ (2 articles)
  - 33C20 Generalized hypergeometric series, $_pF_q$ (5 articles)
  - 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (34 articles)
  - 33C47 Other special orthogonal polynomials and functions (1 articles)
  - 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (2 articles)
  - 33C52 Orthogonal polynomials and functions associated with root systems
  - 33C55 Spherical harmonics (7 articles)
  - 33C60 Hypergeometric integrals and functions defined by them ($E$, $G$ and $ (2 articles)
  - 33C65 Appell, Horn and Lauricella functions (1 articles)
  - 33C67 Hypergeometric functions associated with root systems
  - 33C70 Other hypergeometric functions and integrals in several variables
  - 33C75 Elliptic integrals as hypergeometric functions
  - 33C80 Connections with groups and algebras, and related topics (6 articles)
  - 33C90 Applications (6 articles)
  - 33C99 None of the above, but in this section (2 articles)
- 33Dxx Basic hypergeometric functions (24 articles)
  - 33Dxx Basic hypergeometric functions
  - 33D05 $q$-gamma functions, $q$-beta functions and integrals (2 articles)
  - 33D15 Basic hypergeometric functions in one variable, $ (8 articles)
  - 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (4 articles)
  - 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable (1 articles)
  - 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
  - 33D60 Basic hypergeometric integrals and functions defined by them (3 articles)
  - 33D65 Bibasic functions and multiple bases
  - 33D67 Basic hypergeometric functions associated with root systems
  - 33D70 Other basic hypergeometric functions and integrals in several variables (2 articles)
  - 33D80 Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics (1 articles)
  - 33D90 Applications (1 articles)
  - 33D99 None of the above, but in this section (2 articles)
- 33Exx Other special functions (68 articles)
  - 33Exx Other special functions
  - 33E05 Elliptic functions and integrals (34 articles)
  - 33E10 Lamé, Mathieu, and spheroidal wave functions (1 articles)
  - 33E12 Mittag-Leffler functions and generalizations (1 articles)
  - 33E15 Other wave functions
  - 33E17 Painlevé-type functions
  - 33E20 Other functions defined by series and integrals (14 articles)
  - 33E30 Other functions coming from differential, difference and integral equations (6 articles)
  - 33E50 Special functions in characteristic $p$ (gamma functions, etc.) (2 articles)
  - 33E99 None of the above, but in this section (10 articles)
- 33Fxx Computational aspects (4 articles)
  - 33Fxx Computational aspects
  - 33F05 Numerical approximation (4 articles)
  - 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.)
  - 33F99 None of the above, but in this section
34 Ordinary differential equations (4462 articles)
- 34 Ordinary differential equations
- 34-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (14 articles)
- 34-01 Instructional exposition (textbooks, tutorial papers, etc.) (28 articles)
- 34-02 Research exposition (monographs, survey articles) (7 articles)
- 34-03 Historical (must also be assigned at least one classification number from Section 01) (8 articles)
- 34-04 Explicit machine computation and programs (not the theory of computation or programming) (9 articles)
- 34-06 Proceedings, conferences, collections, etc. (5 articles)
- 34.0 (1940-1958) Ordinary differential equations
- 34.00 (1959-1972) General (25 articles)
- 34.02 (1959-1972) Solutions in closed form; integration by quadratures; reduction of differential equations
- 34.04 (1959-1972) General existence and uniqueness theorems; continuous dependence of solution on parameter, initial and boundary conditions (10 articles)
- 34.06 (1959-1972) Differential equations in the complex domain (2 articles)
- 34.10 (1959-1972) Analytical theory: series, transformations, transforms, operational calculus, etc. (8 articles)
- 34.20 (1959-1972) Linear equations and systems, general (10 articles)
- 34.30 (1959-1972) behavior of eigenfunctions, distribution of eigenvalues (5 articles)
- 34.36 (1959-1972) Nonlinear and multipoint boundary value problems (1 articles)
- 34.40 (1959-1972) Qualitative theory, general (8 articles)
- 34.41 (1959-1972) Limit cycles, singular points
- 34.42 (1959-1972) Zeros, growth, oscillation and comparison of solutions (13 articles)
- 34.45 (1959-1972) Nonlinear oscillations, periodic and almost periodic solutions, integral manifolds, averaging method (8 articles)
- 34.50 (1959-1972) Asymptotic expansions, asymptotic behavior of solutions, turning points (6 articles)
- 34.51 (1959-1972) Stability (4 articles)
- 34.53 (1959-1972) Perturbations (2 articles)
- 34.54 (1959-1972) Singular perturbations; small parameter with highest derivative
- 34.60 (1959-1972) Equations and systems with randomness (See 60.75 for stochastic differential equations) (1 articles)
- 34.65 (1959-1972) Dynamical systems, systems on manifolds (9 articles)
- 34.70 (1959-1972) Differential equations of infinite order
- 34.75 (1959-1972) Functional differential equations, differential-difference equations, equations with retarded argument
- 34.85 (1959-1972) Optimal control problems (2 articles)
- 34.90 (1959-1972) Differential inequalities
- 34.95 (1959-1972) Differential equations in Banach and other abstract spaces (1 articles)
- 34.99 (1959-1972) None of the above, but in this section (1 articles)
- 34Axx General theory (828 articles)
  - 34Axx General theory (1 articles)
  - 34A05 Explicit solutions and reductions (32 articles)
  - 34A09 Implicit equations, differential-algebraic equations (11 articles)
  - 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions (92 articles)
  - 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc. (93 articles)
  - 34A26 Geometric methods in differential equations (14 articles)
  - 34A30 Linear equations and systems, general (197 articles)
  - 34A34 Nonlinear equations and systems, general (145 articles)
  - 34A35 Differential equations of infinite order (2 articles)
  - 34A36 Discontinuous equations (6 articles)
  - 34A37 Differential equations with impulses (30 articles)
  - 34A40 Differential inequalities (26 articles)
  - 34A45 Theoretical approximation of solutions (31 articles)
  - 34A55 Inverse problems (10 articles)
  - 34A60 Differential inclusions (105 articles)
  - 34A99 None of the above, but in this section (33 articles)
- 34Bxx Boundary value problems (706 articles)
  - 34Bxx Boundary value problems (1 articles)
  - 34B05 Linear boundary value problems (67 articles)
  - 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameter
  - 34B08 Multi-parameter boundary value problems (6 articles)
  - 34B09 Boundary value problems with an indefinite weight (4 articles)
  - 34B10 Multipoint boundary value problems (117 articles)
  - 34B15 Nonlinear boundary value problems (319 articles)
  - 34B16 Singular nonlinear boundary value problems (31 articles)
  - 34B18 Positive solutions of nonlinear boundary value problems (45 articles)
  - 34B20 Weyl theory and its generalizations (5 articles)
  - 34B24 Sturm-Liouville theory (21 articles)
  - 34B27 Green functions (24 articles)
  - 34B30 Special equations (Mathieu, Hill, Bessel, etc.) (10 articles)
  - 34B37 Boundary value problems with impulses (13 articles)
  - 34B40 Boundary value problems on infinite intervals (20 articles)
  - 34B45 Boundary value problems on graphs and networks (1 articles)
  - 34B60 Applications (6 articles)
  - 34B99 None of the above, but in this section (16 articles)
- 34Cxx Qualitative theory (1225 articles)
  - 34Cxx Qualitative theory (1 articles)
  - 34C05 Location of integral curves, singular points, limit cycles (41 articles)
  - 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) (7 articles)
  - 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
  - 34C10 Oscillation theory, zeros, disconjugacy and comparison theory (494 articles)
  - 34C11 Growth, boundedness, comparison of solutions (123 articles)
  - 34C12 Monotone systems (4 articles)
  - 34C14 Symmetries, invariants (8 articles)
  - 34C15 Nonlinear oscillations, coupled oscillators (83 articles)
  - 34C20 Transformation and reduction of equations and systems, normal forms (105 articles)
  - 34C23 Bifurcation (30 articles)
  - 34C25 Periodic solutions (195 articles)
  - 34C26 Relaxation oscillations (2 articles)
  - 34C27 Almost periodic solutions (20 articles)
  - 34C28 Complex behavior, chaotic systems (10 articles)
  - 34C29 Averaging method (7 articles)
  - 34C30 Manifolds of solutions (18 articles)
  - 34C37 Homoclinic and heteroclinic solutions (11 articles)
  - 34C40 Equations and systems on manifolds (5 articles)
  - 34C41 Equivalence, asymptotic equivalence (5 articles)
  - 34C45 Method of integral manifolds (2 articles)
  - 34C55 Hysteresis (11 articles)
  - 34C60 Applications (7 articles)
  - 34C99 None of the above, but in this section (36 articles)
- 34Dxx Stability theory (262 articles)
  - 34Dxx Stability theory (2 articles)
  - 34D05 Asymptotic properties (109 articles)
  - 34D08 Characteristic and Lyapunov exponents (3 articles)
  - 34D09 Dichotomy, trichotomy (4 articles)
  - 34D10 Perturbations (19 articles)
  - 34D15 Singular perturbations (5 articles)
  - 34D20 Lyapunov stability (73 articles)
  - 34D23 Global stability (8 articles)
  - 34D30 Structural stability and analogous concepts (5 articles)
  - 34D35 Stability of manifolds of solutions (7 articles)
  - 34D40 Ultimate boundedness (8 articles)
  - 34D45 Attractors (8 articles)
  - 34D99 None of the above, but in this section (11 articles)
- 34Exx Asymptotic theory (110 articles)
  - 34Exx Asymptotic theory
  - 34E05 Asymptotic expansions (54 articles)
  - 34E10 Perturbations, asymptotics (12 articles)
  - 34E13 Multiple scale methods (1 articles)
  - 34E15 Singular perturbations, general theory (22 articles)
  - 34E18 Methods of nonstandard analysis
  - 34E20 Singular perturbations, turning point theory, WKB methods (12 articles)
  - 34E99 None of the above, but in this section (9 articles)
- 34F05 Equations and systems with randomness (27 articles)
- 34Gxx Differential equations in abstract spaces (228 articles)
  - 34Gxx Differential equations in abstract spaces (1 articles)
  - 34G10 Linear equations (44 articles)
  - 34G20 Nonlinear equations (136 articles)
  - 34G25 Evolution inclusions (23 articles)
  - 34G99 None of the above, but in this section (24 articles)
- 34H05 Control problems (39 articles)
- 34Kxx Functional-differential and differential-difference equations (741 articles)
  - 34Kxx Functional-differential and differential-difference equations
  - 34K05 General theory (68 articles)
  - 34K06 Linear functional-differential equations (36 articles)
  - 34K07 Theoretical approximation of solutions (4 articles)
  - 34K10 Boundary value problems (46 articles)
  - 34K11 Oscillation theory (95 articles)
  - 34K12 Growth, boundedness, comparison of solutions (17 articles)
  - 34K13 Periodic solutions (24 articles)
  - 34K14 Almost periodic solutions (6 articles)
  - 34K17 Transformation and reduction of equations and systems, normal forms (5 articles)
  - 34K18 Bifurcation theory (5 articles)
  - 34K19 Invariant manifolds
  - 34K20 Stability theory (65 articles)
  - 34K23 Complex (chaotic) behavior of solutions (1 articles)
  - 34K25 Asymptotic theory (92 articles)
  - 34K26 Singular perturbations (1 articles)
  - 34K28 Numerical approximation of solutions (5 articles)
  - 34K29 Inverse problems
  - 34K30 Equations in abstract spaces (39 articles)
  - 34K35 Control problems (25 articles)
  - 34K40 Neutral equations (88 articles)
  - 34K45 Equations with impulses (15 articles)
  - 34K50 Stochastic delay equations (6 articles)
  - 34K60 Applications (5 articles)
  - 34K99 None of the above, but in this section (93 articles)
- 34Lxx Ordinary differential operators (65 articles)
  - 34Lxx Ordinary differential operators
  - 34L05 General spectral theory (11 articles)
  - 34L10 Eigenfunction expansions, completeness of eigenfunctions (6 articles)
  - 34L15 Estimation of eigenvalues, upper and lower bounds (7 articles)
  - 34L16 Numerical approximation of eigenvalues and of other parts of the spectrum (1 articles)
  - 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions (1 articles)
  - 34L25 Scattering theory
  - 34L30 Nonlinear ordinary differential operators (9 articles)
  - 34L40 Particular operators (Dirac, one-dimensional Schrödinger, etc.) (8 articles)
  - 34L99 None of the above, but in this section (22 articles)
- 34Mxx Differential equations in the complex domain (44 articles)
  - 34Mxx Differential equations in the complex domain
  - 34M05 Entire and meromorphic solutions (3 articles)
  - 34M10 Oscillation, growth of solutions (8 articles)
  - 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) (2 articles)
  - 34M20 Nonanalytic aspects
  - 34M25 Formal solutions, transform techniques
  - 34M30 Asymptotics, summation methods
  - 34M35 Singularities, monodromy, local behavior of solutions, normal forms (2 articles)
  - 34M37 Resurgence phenomena
  - 34M40 Stokes phenomena and connection problems (linear and nonlinear)
  - 34M45 Differential equations on complex manifolds (1 articles)
  - 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
  - 34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
  - 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) (1 articles)
  - 34M99 None of the above, but in this section (27 articles)
35 Partial differential equations (3963 articles)
- 35 Partial differential equations
- 35-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (5 articles)
- 35-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 35-02 Research exposition (monographs, survey articles) (6 articles)
- 35-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 35-04 Explicit machine computation and programs (not the theory of computation or programming) (3 articles)
- 35-06 Proceedings, conferences, collections, etc. (9 articles)
- 35.0 (1940-1958) Partial differential equations
- 35.00 (1959-1972) General (11 articles)
- 35.01 (1959-1972) Existence and uniqueness theorems, general
- 35.02 (1959-1972) Successive approximations
- 35.03 (1959-1972) Cauchy-Kowalewski theorems, series solutions
- 35.04 (1959-1972) Variational methods, a priori estimates
- 35.05 (1959-1972) Analytic methods; singularities
- 35.06 (1959-1972) Other special methods
- 35.07 (1959-1972) Dependence of solutions on initial and boundary data, parameters (1 articles)
- 35.09 (1959-1972) Geometric theory, characteristics, transformations
- 35.10 (1959-1972) Qualitative theory, general (2 articles)
- 35.11 (1959-1972) Comparison theorems; oscillation, zeros and growth of solutions
- 35.12 (1959-1972) Periodic solutions (6 articles)
- 35.13 (1959-1972) Perturbations
- 35.14 (1959-1972) Singular perturbations, almost periodic solutions (2 articles)
- 35.15 (1959-1972) Stability and control, boundedness (1 articles)
- 35.16 (1959-1972) Asymptotic behavior of solutions
- 35.19 (1959-1972) Differential inequalities; a priori estimates
- 35.20 (1959-1972) Generalized solutions
- 35.21 (1959-1972) Embedding theorems, Sobolev spaces
- 35.23 (1959-1972) Pseudodifferential operators
- 35.24 (1959-1972) Regularity of generalized solutions (1 articles)
- 35.30 (1959-1972) Linear equations and systems, first order
- 35.31 (1959-1972) Linear equations and systems, higher order
- 35.35 (1959-1972) Nonlinear equations and systems, first order
- 35.36 (1959-1972) Nonlinear equations and systems, higher order (2 articles)
- 35.37 (1959-1972) Cauchy problems
- 35.38 (1959-1972) Discontinuous coefficients or data
- 35.39 (1959-1972) Equations and systems with constant coefficients (1 articles)
- 35.42 (1959-1972) Second order elliptic equations (3 articles)
- 35.43 (1959-1972) Higher order elliptic equations
- 35.44 (1959-1972) Elliptic systems (linear or nonlinear)
- 35.45 (1959-1972) Boundary value problems for elliptic equations (5 articles)
- 35.46 (1959-1972) Boundary value problems for elliptic systems
- 35.47 (1959-1972) Quasilinear elliptic equations and systems
- 35.48 (1959-1972) Hypoelliptic equations and systems
- 35.52 (1959-1972) Second order hyperbolic equations
- 35.53 (1959-1972) Hyperbolic systems, hyperbolic equations of higher order (1 articles)
- 35.55 (1959-1972) Boundary value problems for hyperbolic equations and systems (1 articles)
- 35.57 (1959-1972) Quasilinear hyperbolic equations and systems
- 35.62 (1959-1972) Second order parabolic equations (5 articles)
- 35.63 (1959-1972) Parabolic systems, parabolic equations of higher order
- 35.65 (1959-1972) Boundary value problems for parabolic equations and systems (3 articles)
- 35.70 (1959-1972) Equations and systems of mixed type (boundary value problems, etc.)
- 35.75 (1959-1972) Laplace's equation, reduced wave equation, Poisson's equation
- 35.76 (1959-1972) Wave equation (3 articles)
- 35.77 (1959-1972) Schr"odinger equation
- 35.78 (1959-1972) Heat equation (1 articles)
- 35.79 (1959-1972) Other special equations and problems (1 articles)
- 35.80 (1959-1972) Eigenvalue problems, spectral theory, eigenfunction expansions (1 articles)
- 35.88 (1959-1972) Difference-partial differential equations; equations with time lag
- 35.95 (1959-1972) Operator equations, general
- 35.96 (1959-1972) Equations on manifolds
- 35.97 (1959-1972) Equations in function spaces
- 35.99 (1959-1972) None of the above, but in this section (5 articles)
- 35Axx General theory (215 articles)
  - 35Axx General theory
  - 35A05 General existence and uniqueness theorems (60 articles)
  - 35A07 Local existence and uniqueness theorems (7 articles)
  - 35A08 Fundamental solutions (5 articles)
  - 35A10 Cauchy-Kovalevskaya theorems (4 articles)
  - 35A15 Variational methods (34 articles)
  - 35A17 Parametrices
  - 35A18 Wave front sets (1 articles)
  - 35A20 Analytic methods, singularities (7 articles)
  - 35A21 Propagation of singularities (1 articles)
  - 35A22 Transform methods (e.g. integral transforms) (12 articles)
  - 35A25 Other special methods (10 articles)
  - 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE (4 articles)
  - 35A30 Geometric theory, characteristics, transformations (22 articles)
  - 35A35 Theoretical approximation to solutions (43 articles)
  - 35A99 None of the above, but in this section (5 articles)
- 35Bxx Qualitative properties of solutions (765 articles)
  - 35Bxx Qualitative properties of solutions (1 articles)
  - 35B05 General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems) (52 articles)
  - 35B10 Periodic solutions (80 articles)
  - 35B15 Almost periodic solutions (12 articles)
  - 35B20 Perturbations (12 articles)
  - 35B25 Singular perturbations (28 articles)
  - 35B27 Homogenization; partial differential equations in media with periodic structure (45 articles)
  - 35B30 Dependence of solutions of PDE on initial and boundary data, parameters (23 articles)
  - 35B32 Bifurcation (41 articles)
  - 35B33 Critical exponents (6 articles)
  - 35B34 Resonances (3 articles)
  - 35B35 Stability, boundedness (62 articles)
  - 35B37 PDE in connection with control problems (9 articles)
  - 35B38 Critical points (9 articles)
  - 35B40 Asymptotic behavior of solutions (151 articles)
  - 35B41 Attractors (12 articles)
  - 35B42 Inertial manifolds (2 articles)
  - 35B45 A priori estimates (80 articles)
  - 35B50 Maximum principles (17 articles)
  - 35B60 Continuation and prolongation of solutions of PDE (10 articles)
  - 35B65 Smoothness and regularity of solutions of PDE (102 articles)
  - 35B99 None of the above, but in this section (8 articles)
- 35Cxx Representations of solutions (46 articles)
  - 35Cxx Representations of solutions
  - 35C05 Solutions in closed form (11 articles)
  - 35C10 Series solutions, expansion theorems (11 articles)
  - 35C15 Integral representations of solutions of PDE (13 articles)
  - 35C20 Asymptotic expansions (9 articles)
  - 35C99 None of the above, but in this section (2 articles)
- 35Dxx Generalized solutions of partial differential equations (163 articles)
  - 35Dxx Generalized solutions of partial differential equations
  - 35D05 Existence of generalized solutions (89 articles)
  - 35D10 Regularity of generalized solutions (67 articles)
  - 35D99 None of the above, but in this section (7 articles)
- 35Exx Equations and systems with constant coefficients (11 articles)
  - 35Exx Equations and systems with constant coefficients
  - 35E05 Fundamental solutions (1 articles)
  - 35E10 Convexity properties (1 articles)
  - 35E15 Initial value problems (4 articles)
  - 35E20 General theory (2 articles)
  - 35E99 None of the above, but in this section (3 articles)
- 35Fxx General first-order equations and systems (35 articles)
  - 35Fxx General first-order equations and systems
  - 35F05 General theory of linear first-order PDE (5 articles)
  - 35F10 Initial value problems for linear first-order PDE, linear evolution equations (1 articles)
  - 35F15 Boundary value problems for linear first-order PDE (4 articles)
  - 35F20 General theory of nonlinear first-order PDE (13 articles)
  - 35F25 Initial value problems for nonlinear first-order PDE, nonlinear evolution equations (5 articles)
  - 35F30 Boundary value problems for nonlinear first-order PDE (6 articles)
  - 35F99 None of the above, but in this section (1 articles)
- 35Gxx General higher-order equations and systems (87 articles)
  - 35Gxx General higher-order equations and systems
  - 35G05 General theory of linear higher-order PDE (14 articles)
  - 35G10 Initial value problems for linear higher-order PDE, linear evolution equations (24 articles)
  - 35G15 Boundary value problems for linear higher-order PDE (5 articles)
  - 35G20 General theory of nonlinear higher-order PDE (16 articles)
  - 35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations (10 articles)
  - 35G30 Boundary value problems for nonlinear higher-order PDE (15 articles)
  - 35G99 None of the above, but in this section (3 articles)
- 35Hxx Close-to-elliptic equations (5 articles)
  - 35Hxx Close-to-elliptic equations
  - 35H10 Hypoelliptic equations (1 articles)
  - 35H20 Subelliptic equations (3 articles)
  - 35H30 Quasi-elliptic equations (1 articles)
  - 35H99 None of the above, but in this section
- 35Jxx Partial differential equations of elliptic type (909 articles)
  - 35Jxx Partial differential equations of elliptic type (10 articles)
  - 35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (67 articles)
  - 35J10 Schrödinger operator (12 articles)
  - 35J15 General theory of second-order, elliptic equations (27 articles)
  - 35J20 Variational methods for second-order, elliptic equations (73 articles)
  - 35J25 Boundary value problems for second-order, elliptic equations (170 articles)
  - 35J30 General theory of higher-order, elliptic equations (15 articles)
  - 35J35 Variational methods for higher-order, elliptic equations (16 articles)
  - 35J40 Boundary value problems for higher-order, elliptic equations (42 articles)
  - 35J45 General theory of elliptic systems of PDE (19 articles)
  - 35J50 Variational methods for elliptic systems (18 articles)
  - 35J55 Boundary value problems for elliptic systems (27 articles)
  - 35J60 Nonlinear PDE of elliptic type (170 articles)
  - 35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE (136 articles)
  - 35J67 Boundary values of solutions to elliptic PDE (7 articles)
  - 35J70 Elliptic partial differential equations of degenerate type (57 articles)
  - 35J85 Unilateral problems and variational inequalities for elliptic PDE (36 articles)
  - 35J99 None of the above, but in this section (7 articles)
- 35Kxx Parabolic equations and systems (655 articles)
  - 35Kxx Parabolic equations and systems (11 articles)
  - 35K05 Heat equation (59 articles)
  - 35K10 General theory of second-order, parabolic equations (16 articles)
  - 35K15 Initial value problems for second-order, parabolic equations (32 articles)
  - 35K20 Boundary value problems for second-order, parabolic equations (72 articles)
  - 35K25 General theory of higher-order, parabolic equations (22 articles)
  - 35K30 Initial value problems for higher-order, parabolic equations (5 articles)
  - 35K35 Boundary value problems for higher-order, parabolic equations (13 articles)
  - 35K40 General theory of parabolic systems of PDE (20 articles)
  - 35K45 Initial value problems for parabolic systems (12 articles)
  - 35K50 Boundary value problems for parabolic systems (20 articles)
  - 35K55 Nonlinear PDE of parabolic type (145 articles)
  - 35K57 Reaction-diffusion equations (71 articles)
  - 35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE (65 articles)
  - 35K65 Parabolic partial differential equations of degenerate type (47 articles)
  - 35K70 Ultraparabolic, pseudoparabolic PDE, etc. (3 articles)
  - 35K85 Unilateral problems and variational inequalities for parabolic PDE (16 articles)
  - 35K90 Abstract parabolic evolution equations (12 articles)
  - 35K99 None of the above, but in this section (14 articles)
- 35Lxx Partial differential equations of hyperbolic type (278 articles)
  - 35Lxx Partial differential equations of hyperbolic type (2 articles)
  - 35L05 Wave equation (25 articles)
  - 35L10 General theory of second-order, hyperbolic equations (12 articles)
  - 35L15 Initial value problems for second-order, hyperbolic equations (16 articles)
  - 35L20 Boundary value problems for second-order, hyperbolic equations (33 articles)
  - 35L25 General theory of higher-order, hyperbolic equations (2 articles)
  - 35L30 Initial value problems for higher-order, hyperbolic equations (1 articles)
  - 35L35 Boundary value problems for higher-order, hyperbolic equations (5 articles)
  - 35L40 General theory of hyperbolic systems of first-order PDE (5 articles)
  - 35L45 Initial value problems for hyperbolic systems of first-order PDE (6 articles)
  - 35L50 Boundary value problems for hyperbolic systems of first-order PDE (12 articles)
  - 35L55 Hyperbolic systems of higher-order PDE (3 articles)
  - 35L60 Nonlinear first-order PDE of hyperbolic type (30 articles)
  - 35L65 Conservation laws (25 articles)
  - 35L67 Shocks and singularities (11 articles)
  - 35L70 Nonlinear second-order PDE of hyperbolic type (60 articles)
  - 35L75 Nonlinear hyperbolic PDE of higher ($gtr 2$) order (7 articles)
  - 35L80 Hyperbolic PDE of degenerate type (6 articles)
  - 35L82 Pseudohyperbolic equations
  - 35L85 Unilateral problems; variational inequalities for hyperbolic PDE (6 articles)
  - 35L90 Abstract hyperbolic evolution equations (3 articles)
  - 35L99 None of the above, but in this section (8 articles)
- 35Mxx Partial differential equations of special type (mixed, composite, etc.) (14 articles)
  - 35Mxx Partial differential equations of special type (mixed, composite, etc.)
  - 35M10 PDE of mixed type (7 articles)
  - 35M20 PDE of composite type (3 articles)
  - 35M99 None of the above, but in this section (4 articles)
- 35Nxx Overdetermined systems (8 articles)
  - 35Nxx Overdetermined systems
  - 35N05 Overdetermined systems with constant coefficients (1 articles)
  - 35N10 Overdetermined systems with variable coefficients (general) (4 articles)
  - 35N15 $overlinepartial$-Neumann problem and generalizations; formal complexes (2 articles)
  - 35N99 None of the above, but in this section (1 articles)
- 35Pxx Spectral theory and eigenvalue problems for partial differential operators (97 articles)
  - 35Pxx Spectral theory and eigenvalue problems for partial differential operators (1 articles)
  - 35P05 General spectral theory of PDE (19 articles)
  - 35P10 Completeness of eigenfunctions, eigenfunction expansions for PDO (7 articles)
  - 35P15 Estimation of eigenvalues, upper and lower bounds (25 articles)
  - 35P20 Asymptotic distribution of eigenvalues and eigenfunctions for PDO (8 articles)
  - 35P25 Scattering theory for PDE (5 articles)
  - 35P30 Nonlinear eigenvalue problems, nonlinear spectral theory for PDO (28 articles)
  - 35P99 None of the above, but in this section (4 articles)
- 35Qxx Equations of mathematical physics and other areas of application (392 articles)
  - 35Qxx Equations of mathematical physics and other areas of application (8 articles)
  - 35Q05 Euler-Poisson-Darboux equation and generalizations (3 articles)
  - 35Q15 Riemann-Hilbert problems (1 articles)
  - 35Q30 Stokes and Navier-Stokes equations (130 articles)
  - 35Q35 Other equations arising in fluid mechanics (109 articles)
  - 35Q40 Equations from quantum mechanics (13 articles)
  - 35Q51 Solitons (3 articles)
  - 35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (12 articles)
  - 35Q55 NLS-like (nonlinear Schrödinger) equations (11 articles)
  - 35Q58 Other completely integrable equations
  - 35Q60 Equations of electromagnetic theory and optics (26 articles)
  - 35Q72 Other equations from mechanics (26 articles)
  - 35Q75 PDE in relativity
  - 35Q80 Applications of PDE in areas other than physics (4 articles)
  - 35Q99 None of the above, but in this section (46 articles)
- 35Rxx Miscellaneous topics involving partial differential equations (189 articles)
  - 35Rxx Miscellaneous topics involving partial differential equations
  - 35R05 PDE with discontinuous coefficients or data (21 articles)
  - 35R10 Partial functional-differential or differential-difference equations, with or without deviating arguments (33 articles)
  - 35R12 Impulsive partial differential equations (3 articles)
  - 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) (6 articles)
  - 35R20 Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions) (16 articles)
  - 35R25 Improperly posed problems for PDE (1 articles)
  - 35R30 Inverse problems (undetermined coefficients, etc.) for PDE (37 articles)
  - 35R35 Free boundary problems for PDE (38 articles)
  - 35R45 Partial differential inequalities (7 articles)
  - 35R50 Partial differential equations of infinite order
  - 35R60 Partial differential equations with randomness (17 articles)
  - 35R70 PDE with multivalued right-hand sides (8 articles)
  - 35R99 None of the above, but in this section (2 articles)
- 35Sxx Pseudodifferential operators and other generalizations of partial differential operators (13 articles)
  - 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
  - 35S05 General theory of PsDO (4 articles)
  - 35S10 Initial value problems for PsDO
  - 35S15 Boundary value problems for PsDO (4 articles)
  - 35S30 Fourier integral operators (3 articles)
  - 35S35 Topological aspects: intersection cohomology, stratified sets, etc.
  - 35S50 Paradifferential operators (1 articles)
  - 35S99 None of the above, but in this section (1 articles)
36 (1940-1958) Differential equations, operational calculus
- 36 (1940-1958) Differential equations, operational calculus
- 36.0 (1940-1958) Differential equations
- 36.1 (1940-1958) Differential equations, operational calculus
37 Dynamical systems and ergodic theory (445 articles)
- 37 Dynamical systems and ergodic theory
- 37-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 37-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 37-02 Research exposition (monographs, survey articles)
- 37-03 Historical (must also be assigned at least one classification number from Section 01)
- 37-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 37-06 Proceedings, conferences, collections, etc. (2 articles)
- 37Axx Ergodic theory (27 articles)
 - 37Axx Ergodic theory
 - 37A05 Measure-preserving transformations (3 articles)
 - 37A10 One-parameter continuous families of measure-preserving transformations
 - 37A15 General groups of measure-preserving transformations (1 articles)
 - 37A17 Homogeneous flows
 - 37A20 Orbit equivalence, cocycles, ergodic equivalence relations
 - 37A25 Ergodicity, mixing, rates of mixing (4 articles)
 - 37A30 Ergodic theorems, spectral theory, Markov operators (5 articles)
 - 37A35 Entropy and other invariants, isomorphism, classification (4 articles)
 - 37A40 Nonsingular (and infinite-measure preserving) transformations (1 articles)
 - 37A45 Relations with number theory and harmonic analysis (2 articles)
 - 37A50 Relations with probability theory and stochastic processes (2 articles)
 - 37A55 Relations with the theory of $C^*$-algebras
 - 37A60 Dynamical systems in statistical mechanics (1 articles)
 - 37A99 None of the above, but in this section (4 articles)
- 37Bxx Topological dynamics (82 articles)
 - 37Bxx Topological dynamics
 - 37B05 Transformations and group actions with special properties (minimality, distality, proximality, etc.) (14 articles)
 - 37B10 Symbolic dynamics (9 articles)
 - 37B15 Cellular automata
 - 37B20 Notions of recurrence (9 articles)
 - 37B25 Lyapunov functions and stability; attractors, repellers (13 articles)
 - 37B30 Index theory, Morse-Conley indices (4 articles)
 - 37B35 Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
 - 37B40 Topological entropy (9 articles)
 - 37B45 Continua theory in dynamics
 - 37B50 Multi-dimensional shifts of finite type, tiling dynamics
 - 37B55 Nonautonomous dynamical systems (6 articles)
 - 37B99 None of the above, but in this section (18 articles)
- 37Cxx Smooth dynamical systems: general theory (58 articles)
 - 37Cxx Smooth dynamical systems: general theory (2 articles)
 - 37C05 Smooth mappings and diffeomorphisms (2 articles)
 - 37C10 Vector fields, flows, ordinary differential equations (11 articles)
 - 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classification (1 articles)
 - 37C20 Generic properties, structural stability (1 articles)
 - 37C25 Fixed points, periodic points, fixed-point index theory (7 articles)
 - 37C27 Periodic orbits of vector fields and flows (1 articles)
 - 37C29 Homoclinic and heteroclinic orbits (6 articles)
 - 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems (1 articles)
 - 37C35 Orbit growth
 - 37C40 Smooth ergodic theory, invariant measures (1 articles)
 - 37C45 Dimension theory of dynamical systems (4 articles)
 - 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) (1 articles)
 - 37C55 Periodic and quasiperiodic flows and diffeomorphisms
 - 37C60 Nonautonomous smooth dynamical systems (1 articles)
 - 37C65 Monotone flows
 - 37C70 Attractors and repellers, topological structure (9 articles)
 - 37C75 Stability theory (6 articles)
 - 37C80 Symmetries, equivariant dynamical systems (3 articles)
 - 37C85 Dynamics of group actions other than Z and R, and foliations
 - 37C99 None of the above, but in this section (1 articles)
- 37Dxx Dynamical systems with hyperbolic behavior (42 articles)
 - 37Dxx Dynamical systems with hyperbolic behavior
 - 37D05 Hyperbolic orbits and sets
 - 37D10 Invariant manifold theory (2 articles)
 - 37D15 Morse-Smale systems (1 articles)
 - 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (1 articles)
 - 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
 - 37D30 Partially hyperbolic systems and dominated splittings
 - 37D35 Thermodynamic formalism, variational principles, equilibrium states (1 articles)
 - 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (1 articles)
 - 37D45 Strange attractors, chaotic dynamics (31 articles)
 - 37D50 Hyperbolic systems with singularities (billiards, etc.) (1 articles)
 - 37D99 None of the above, but in this section (4 articles)
- 37Exx Low-dimensional dynamical systems (29 articles)
 - 37Exx Low-dimensional dynamical systems
 - 37E05 Maps of the interval (piecewise continuous, continuous, smooth) (4 articles)
 - 37E10 Maps of the circle (8 articles)
 - 37E15 Combinatorial dynamics (types of periodic orbits) (2 articles)
 - 37E20 Universality, renormalization
 - 37E25 Maps of trees and graphs (2 articles)
 - 37E30 Homeomorphisms and diffeomorphisms of planes and surfaces
 - 37E35 Flows on surfaces
 - 37E40 Twist maps
 - 37E45 Rotation numbers and vectors (1 articles)
 - 37E99 None of the above, but in this section (12 articles)
- 37Fxx Complex dynamical systems (5 articles)
 - 37Fxx Complex dynamical systems (1 articles)
 - 37F05 Relations and correspondences
 - 37F10 Polynomials; rational maps; entire and meromorphic functions (1 articles)
 - 37F15 Expanding maps; hyperbolicity; structural stability
 - 37F20 Combinatorics and topology
 - 37F25 Renormalization
 - 37F30 Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
 - 37F35 Conformal densities and Hausdorff dimension
 - 37F40 Geometric limits
 - 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (1 articles)
 - 37F50 Small divisors, rotation domains and linearization; Fatou and Julia sets (1 articles)
 - 37F75 Holomorphic foliations and vector fields
 - 37F99 None of the above, but in this section (1 articles)
- 37Gxx Local and nonlocal bifurcation theory (31 articles)
 - 37Gxx Local and nonlocal bifurcation theory
 - 37G05 Normal forms (1 articles)
 - 37G10 Bifurcations of singular points (1 articles)
 - 37G15 Bifurcations of limit cycles and periodic orbits (8 articles)
 - 37G20 Hyperbolic singular points with homoclinic trajectories
 - 37G25 Bifurcations connected with nontransversal intersection
 - 37G30 Infinite nonwandering sets arising in bifurcations
 - 37G35 Attractors and their bifurcations
 - 37G40 Symmetries, equivariant bifurcation theory (1 articles)
 - 37G99 None of the above, but in this section (20 articles)
- 37Hxx Random dynamical systems (3 articles)
 - 37Hxx Random dynamical systems
 - 37H05 Foundations, general theory of cocycles, algebraic ergodic theory (1 articles)
 - 37H10 Generation, random and stochastic difference and differential equations (2 articles)
 - 37H15 Multiplicative ergodic theory, Lyapunov exponents
 - 37H20 Bifurcation theory
 - 37H99 None of the above, but in this section
- 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems (68 articles)
 - 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems (2 articles)
 - 37J05 General theory, relations with symplectic geometry and topology (5 articles)
 - 37J10 Symplectic mappings, fixed points
 - 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (3 articles)
 - 37J20 Bifurcation problems (1 articles)
 - 37J25 Stability problems
 - 37J30 Obstructions to integrability (nonintegrability criteria) (1 articles)
 - 37J35 Completely integrable systems, topological structure of phase space, integration methods (4 articles)
 - 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion (7 articles)
 - 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (6 articles)
 - 37J50 Action-minimizing orbits and measures
 - 37J55 Contact systems
 - 37J60 Nonholonomic dynamical systems (5 articles)
 - 37J99 None of the above, but in this section (34 articles)
- 37Kxx Infinite-dimensional Hamiltonian systems (11 articles)
 - 37Kxx Infinite-dimensional Hamiltonian systems
 - 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (2 articles)
 - 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) (2 articles)
 - 37K15 Integration of completely integrable systems by inverse spectral and scattering methods (2 articles)
 - 37K20 Relations with algebraic geometry, complex analysis, special functions
 - 37K25 Relations with differential geometry
 - 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structures
 - 37K35 Lie-Bäcklund and other transformations
 - 37K40 Soliton theory, asymptotic behavior of solutions (1 articles)
 - 37K45 Stability problems
 - 37K50 Bifurcation problems (1 articles)
 - 37K55 Perturbations, KAM for infinite-dimensional systems
 - 37K60 Lattice dynamics (1 articles)
 - 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (2 articles)
 - 37K99 None of the above, but in this section
- 37Lxx Infinite-dimensional dissipative dynamical systems (33 articles)
 - 37Lxx Infinite-dimensional dissipative dynamical systems
 - 37L05 General theory, nonlinear semigroups, evolution equations (5 articles)
 - 37L10 Normal forms, center manifold theory, bifurcation theory (3 articles)
 - 37L15 Stability problems (2 articles)
 - 37L20 Symmetries (1 articles)
 - 37L25 Inertial manifolds and other invariant attracting sets (2 articles)
 - 37L30 Attractors and their dimensions, Lyapunov exponents (9 articles)
 - 37L40 Invariant measures (4 articles)
 - 37L45 Hyperbolicity; Lyapunov functions (1 articles)
 - 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
 - 37L55 Infinite-dimensional random dynamical systems; stochastic equations (3 articles)
 - 37L60 Lattice dynamics (1 articles)
 - 37L65 Special approximation methods (nonlinear Galerkin, etc.) (1 articles)
 - 37L99 None of the above, but in this section (1 articles)
- 37Mxx Approximation methods and numerical treatment of dynamical systems (13 articles)
 - 37Mxx Approximation methods and numerical treatment of dynamical systems (1 articles)
 - 37M05 Simulation (2 articles)
 - 37M10 Time series analysis (5 articles)
 - 37M15 Symplectic integrators
 - 37M20 Computational methods for bifurcation problems (2 articles)
 - 37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy) (1 articles)
 - 37M99 None of the above, but in this section (2 articles)
- 37Nxx Applications (39 articles)
 - 37Nxx Applications
 - 37N05 Dynamical systems in classical and celestial mechanics (1 articles)
 - 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology (4 articles)
 - 37N15 Dynamical systems in solid mechanics (1 articles)
 - 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (1 articles)
 - 37N25 Dynamical systems in biology (10 articles)
 - 37N30 Dynamical systems in numerical analysis (1 articles)
 - 37N35 Dynamical systems in control (11 articles)
 - 37N40 Dynamical systems in optimization and economics (7 articles)
 - 37N99 None of the above, but in this section (3 articles)
39 Difference and functional equations (427 articles)
- 39 Difference and functional equations
- 39-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 39-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 39-02 Research exposition (monographs, survey articles) (1 articles)
- 39-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 39-04 Explicit machine computation and programs (not the theory of computation or programming)
- 39-06 Proceedings, conferences, collections, etc.
- 39.0 (1940-1958) Difference equations, functional equations
- 39.00 (1959-1972) General (2 articles)
- 39.1 (1940-1958) Functional equations and operational calculus
- 39.10 (1959-1972) Finite differences, general
- 39.2 (1940-1958) Special functional equations
- 39.20 (1959-1972) Difference equations
- 39.25 (1959-1972) Discrete analogues of topics in analysis (1 articles)
- 39.30 (1959-1972) Functional equations, general
- 39.31 (1959-1972) Classical functional equations
- 39.33 (1959-1972) Linear and multilinear functional equations
- 39.35 (1959-1972) Functional equations in several variables, systems
- 39.37 (1959-1972) Matrix functional equations
- 39.38 (1959-1972) Functional equations on abstract structures
- 39.99 (1959-1972) None of the above, but in this section
- 39Axx Difference equations (271 articles)
  - 39Axx Difference equations (1 articles)
  - 39A05 General (11 articles)
  - 39A10 Difference equations, additive (113 articles)
  - 39A11 Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc. (53 articles)
  - 39A12 Discrete version of topics in analysis (57 articles)
  - 39A13 Difference equations, scaling ($q$-differences) (11 articles)
  - 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness type (8 articles)
  - 39A70 Difference operators (10 articles)
  - 39A99 None of the above, but in this section (7 articles)
- 39Bxx Functional equations and inequalities (146 articles)
  - 39Bxx Functional equations and inequalities
  - 39B05 General (12 articles)
  - 39B12 Iteration theory, iterative and composite equations (21 articles)
  - 39B22 Equations for real functions (26 articles)
  - 39B32 Equations for complex functions (9 articles)
  - 39B42 Matrix and operator equations (3 articles)
  - 39B52 Equations for functions with more general domains and/or ranges (14 articles)
  - 39B55 Orthogonal additivity and other conditional equations
  - 39B62 Functional inequalities, including subadditivity, convexity, etc. (13 articles)
  - 39B72 Systems of functional equations and inequalities (11 articles)
  - 39B82 Stability, separation, extension, and related topics (12 articles)
  - 39B99 None of the above, but in this section (25 articles)
40 Sequences, series, summability (282 articles)
- 40 Sequences, series, summability
- 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 40-01 Instructional exposition (textbooks, tutorial papers, etc.) (2 articles)
- 40-02 Research exposition (monographs, survey articles)
- 40-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 40-04 Explicit machine computation and programs (not the theory of computation or programming)
- 40-06 Proceedings, conferences, collections, etc.
- 40.0 (1940-1958) Sequences, series, summability
- 40.00 (1959-1972) General (6 articles)
- 40.10 (1959-1972) Series and sequences of numbers, general
- 40.11 (1959-1972) Infinite products
- 40.12 (1959-1972) Continued fractions (1 articles)
- 40.13 (1959-1972) Convergence and divergence (3 articles)
- 40.15 (1959-1972) Multiple series and sequences
- 40.20 (1959-1972) Sequences and series of functions, convergence
- 40.30 (1959-1972) Summability, general methods
- 40.31 (1959-1972) Summability, matrix methods
- 40.32 (1959-1972) Ces`aro summability
- 40.33 (1959-1972) Abel, Poisson summability
- 40.35 (1959-1972) Summability of double series
- 40.40 (1959-1972) Convergence and summability of integrals
- 40.42 (1959-1972) Tauberian theorems
- 40.46 (1959-1972) Functional-analytic methods in summability theory (1 articles)
- 40.50 (1959-1972) Summability in topological groups, linear spaces, etc.
- 40.99 (1959-1972) None of the above, but in this section
- 40Axx Convergence and divergence of infinite limiting processes (120 articles)
  - 40Axx Convergence and divergence of infinite limiting processes
  - 40A05 Convergence and divergence of series and sequences (85 articles)
  - 40A10 Convergence and divergence of integrals (2 articles)
  - 40A15 Convergence and divergence of continued fractions (3 articles)
  - 40A20 Convergence and divergence of infinite products (1 articles)
  - 40A25 Approximation to limiting values (summation of series, etc.) (8 articles)
  - 40A30 Convergence and divergence of series and sequences of functions (17 articles)
  - 40A99 None of the above, but in this section (4 articles)
- 40B05 Multiple sequences and series (3 articles)
- 40Cxx General summability methods (43 articles)
  - 40Cxx General summability methods
  - 40C05 Matrix methods (29 articles)
  - 40C10 Integral methods (3 articles)
  - 40C15 Function-theoretic methods (including power series methods and semicontinuous methods) (5 articles)
  - 40C99 None of the above, but in this section (6 articles)
- 40Dxx Direct theorems on summability (24 articles)
  - 40Dxx Direct theorems on summability
  - 40D05 General theorems (6 articles)
  - 40D09 Structure of summability fields (1 articles)
  - 40D10 Tauberian constants and oscillation limits
  - 40D15 Convergence factors and summability factors (2 articles)
  - 40D20 Summability and bounded fields of methods (3 articles)
  - 40D25 Inclusion and equivalence theorems (11 articles)
  - 40D99 None of the above, but in this section (1 articles)
- 40Exx Inversion theorems (10 articles)
  - 40Exx Inversion theorems
  - 40E05 Tauberian theorems, general (9 articles)
  - 40E10 Growth estimates (1 articles)
  - 40E15 Lacunary inversion theorems
  - 40E20 Tauberian constants
  - 40E99 None of the above, but in this section
- 40F05 Absolute and strong summability (14 articles)
- 40Gxx Special methods of summability (25 articles)
  - 40Gxx Special methods of summability (1 articles)
  - 40G05 Cesàro, Euler, Nörlund and Hausdorff methods (13 articles)
  - 40G10 Abel, Borel and power series methods (3 articles)
  - 40G99 None of the above, but in this section (8 articles)
- 40H05 Functional analytic methods in summability (16 articles)
- 40J05 Summability in abstract structures (11 articles)
41 Approximations and expansions (354 articles)
- 41 Approximations and expansions
- 41-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 41-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 41-02 Research exposition (monographs, survey articles)
- 41-03 Historical (must also be assigned at least one classification number from Section 01)
- 41-04 Explicit machine computation and programs (not the theory of computation or programming)
- 41-06 Proceedings, conferences, collections, etc.
- 41.00 (1959-1972) General (4 articles)
- 41.1 (1940-1958) Polynomials, polynomial approximation
- 41.10 (1959-1972) Interpolation
- 41.15 (1959-1972) Polynomial approximation
- 41.17 (1959-1972) Approximation by rational functions
- 41.30 (1959-1972) Approximation by other special function classes (1 articles)
- 41.35 (1959-1972) Approximation by operators (in particular, by integral operators)
- 41.40 (1959-1972) Best approximation
- 41.41 (1959-1972) Degree of approximation, rate of convergence
- 41.44 (1959-1972) Approximate quadratures
- 41.50 (1959-1972) Asymptotic expansions
- 41.55 (1959-1972) Constructive theory of functions
- 41.60 (1959-1972) Abstract approximation theory, approximation in normed linear spaces and other abstract spaces (1 articles)
- 41.99 (1959-1972) None of the above, but in this section
- 41A05 Interpolation (39 articles)
- 41A10 Approximation by polynomials (28 articles)
- 41A15 Spline approximation (42 articles)
- 41A17 Inequalities in approximation (Bernstein, Jackson, Nikolcprime skiui-type inequalities) (5 articles)
- 41A20 Approximation by rational functions (5 articles)
- 41A21 Padé approximation
- 41A25 Rate of convergence, degree of approximation (23 articles)
- 41A27 Inverse theorems
- 41A28 Simultaneous approximation (3 articles)
- 41A29 Approximation with constraints (5 articles)
- 41A30 Approximation by other special function classes (22 articles)
- 41A35 Approximation by operators (in particular, by integral operators) (15 articles)
- 41A36 Approximation by positive operators (24 articles)
- 41A40 Saturation
- 41A44 Best constants
- 41A45 Approximation by arbitrary linear expressions (6 articles)
- 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy (4 articles)
- 41A50 Best approximation, Chebyshev systems (27 articles)
- 41A52 Uniqueness of best approximation (3 articles)
- 41A55 Approximate quadratures (12 articles)
- 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) (6 articles)
- 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (8 articles)
- 41A63 Multidimensional problems (should also be assigned at least one other classification number in this section) (16 articles)
- 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (45 articles)
- 41A80 Remainders in approximation formulas (3 articles)
- 41A99 Miscellaneous topics (3 articles)
42 Fourier analysis (411 articles)
- 42 Fourier analysis
- 42-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 42-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 42-02 Research exposition (monographs, survey articles)
- 42-03 Historical (must also be assigned at least one classification number from Section 01)
- 42-04 Explicit machine computation and programs (not the theory of computation or programming)
- 42-06 Proceedings, conferences, collections, etc.
- 42.00 (1959-1972) General (6 articles)
- 42.05 (1959-1972) Trigonometric polynomials (1 articles)
- 42.06 (1959-1972) Best approximation by trigonometric polynomials
- 42.08 (1959-1972) Trigonometric interpolation
- 42.1 (1940-1958) Interpolation, approximation, orthogonal functions
- 42.10 (1959-1972) Fourier coefficients
- 42.11 (1959-1972) Convergence of Fourier series
- 42.12 (1959-1972) Absolute convergence of Fourier series
- 42.15 (1959-1972) Orthogonal functions and polynomials, general (2 articles)
- 42.16 (1959-1972) Expansions in orthogonal functions and polynomials (1 articles)
- 42.17 (1959-1972) Completeness of sets of orthogonal functions
- 42.18 (1959-1972) Completeness, closure, spectral synthesis
- 42.2 (1940-1958) Trigonometric series and integrals
- 42.20 (1959-1972) Summability of Fourier and generalized Fourier expansions (1 articles)
- 42.25 (1959-1972) Fourier transform (1 articles)
- 42.26 (1959-1972) Other Fourier-type transforms
- 42.27 (1959-1972) Trigonometric moment problems
- 42.3 (1940-1958) Fourier series and generalizations, theory of approximation
- 42.30 (1959-1972) Almost periodic functions
- 42.35 (1959-1972) Positive definite functions
- 42.4 (1940-1958) Fourier series, integral transforms
- 42.40 (1959-1972) Multiple Fourier series and integrals
- 42.50 (1959-1972) Abstract harmonic analysis (Fourier analysis on LCA groups) (1 articles)
- 42.51 (1959-1972) Characters, duality
- 42.52 (1959-1972) Fourier-Stieltjes transform
- 42.53 (1959-1972) Abstract almost periodic functions
- 42.54 (1959-1972) Positive definite functions on LCA groups
- 42.55 (1959-1972) Convolution, factorization
- 42.56 (1959-1972) Measure algebras, group algebras (2 articles)
- 42.58 (1959-1972) Ideals, spectral synthesis
- 42.99 (1959-1972) None of the above, but in this section (1 articles)
- 42Axx Fourier analysis in one variable (129 articles)
  - 42Axx Fourier analysis in one variable
  - 42A05 Trigonometric polynomials, inequalities, extremal problems (5 articles)
  - 42A10 Trigonometric approximation (8 articles)
  - 42A15 Trigonometric interpolation (3 articles)
  - 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series (21 articles)
  - 42A20 Convergence and absolute convergence of Fourier and trigonometric series (20 articles)
  - 42A24 Summability and absolute summability of Fourier and trigonometric series (5 articles)
  - 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (8 articles)
  - 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (19 articles)
  - 42A45 Multipliers (1 articles)
  - 42A50 Conjugate functions, conjugate series, singular integrals (6 articles)
  - 42A55 Lacunary series of trigonometric and other functions; Riesz products
  - 42A61 Probabilistic methods (1 articles)
  - 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization (2 articles)
  - 42A65 Completeness of sets of functions
  - 42A70 Trigonometric moment problems (1 articles)
  - 42A75 Classical almost periodic functions, mean periodic functions (21 articles)
  - 42A82 Positive definite functions (2 articles)
  - 42A85 Convolution, factorization (2 articles)
  - 42A99 None of the above, but in this section (4 articles)
- 42Bxx Fourier analysis in several variables (210 articles)
  - 42Bxx Fourier analysis in several variables
  - 42B05 Fourier series and coefficients (6 articles)
  - 42B08 Summability (2 articles)
  - 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (9 articles)
  - 42B15 Multipliers (15 articles)
  - 42B20 Singular integrals (Calderón-Zygmund, etc.) (35 articles)
  - 42B25 Maximal functions, Littlewood-Paley theory (74 articles)
  - 42B30 $H^p$-spaces (21 articles)
  - 42B35 Function spaces arising in harmonic analysis (41 articles)
  - 42B99 None of the above, but in this section (7 articles)
- 42Cxx Nontrigonometric Fourier analysis (56 articles)
  - 42Cxx Nontrigonometric Fourier analysis
  - 42C05 Orthogonal functions and polynomials, general theory (8 articles)
  - 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (10 articles)
  - 42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions (17 articles)
  - 42C20 Rearrangements and other transformations of Fourier and other orthogonal series (4 articles)
  - 42C25 Uniqueness and localization for orthogonal series
  - 42C30 Completeness of sets of functions (1 articles)
  - 42C40 Wavelets (15 articles)
  - 42C99 None of the above, but in this section (1 articles)
43 Abstract harmonic analysis (105 articles)
- 43 Abstract harmonic analysis
- 43-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 43-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 43-02 Research exposition (monographs, survey articles) (2 articles)
- 43-03 Historical (must also be assigned at least one classification number from Section 01)
- 43-04 Explicit machine computation and programs (not the theory of computation or programming)
- 43-06 Proceedings, conferences, collections, etc.
- 43A05 Measures on groups and semigroups, etc. (9 articles)
- 43A07 Means on groups, semigroups, etc.; amenable groups (10 articles)
- 43A10 Measure algebras on groups, semigroups, etc. (4 articles)
- 43A15 $L^p$-spaces and other function spaces on groups, semigroups, etc. (11 articles)
- 43A17 Analysis on ordered groups, $ (1 articles)
- 43A20 $L^1$-algebras on groups, semigroups, etc. (9 articles)
- 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
- 43A25 Fourier and Fourier-Stieltjes transforms on locally compact abelian groups (6 articles)
- 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (1 articles)
- 43A32 Other transforms and operators of Fourier type (5 articles)
- 43A35 Positive definite functions on groups, semigroups, etc. (5 articles)
- 43A40 Character groups and dual objects (4 articles)
- 43A45 Spectral synthesis on groups, semigroups, etc.
- 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) (7 articles)
- 43A50 Convergence of Fourier series and of inverse transforms
- 43A55 Summability methods on groups, semigroups, etc.
- 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (11 articles)
- 43A62 Hypergroups (1 articles)
- 43A65 Representations of groups, semigroups, etc. (4 articles)
- 43A70 Analysis on specific locally compact abelian groups
- 43A75 Analysis on specific compact groups
- 43A77 Analysis on general compact groups
- 43A80 Analysis on other specific Lie groups (3 articles)
- 43A85 Analysis on homogeneous spaces (10 articles)
- 43A90 Spherical functions (1 articles)
- 43A95 Categorical methods
- 43A99 Miscellaneous topics (1 articles)
44 Integral transforms, operational calculus (102 articles)
- 44 Integral transforms, operational calculus
- 44-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 44-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 44-02 Research exposition (monographs, survey articles)
- 44-03 Historical (must also be assigned at least one classification number from Section 01)
- 44-04 Explicit machine computation and programs (not the theory of computation or programming)
- 44-06 Proceedings, conferences, collections, etc.
- 44.0 (1940-1958) Integral transforms, operational calculus
- 44.00 (1959-1972) General (2 articles)
- 44.10 (1959-1972) Laplace transform (1 articles)
- 44.25 (1959-1972) Convolution
- 44.28 (1959-1972) General transforms
- 44.30 (1959-1972) Special transforms. Legendre, Hilbert, etc.
- 44.32 (1959-1972) Multiple transforms
- 44.33 (1959-1972) Transforms of special functions
- 44.40 (1959-1972) Operational calculus (2 articles)
- 44.42 (1959-1972) Operational calculus in several variables
- 44.50 (1959-1972) Fractional integrals
- 44.60 (1959-1972) Moment problems
- 44.99 (1959-1972) None of the above, but in this section
- 44A05 General transforms (6 articles)
- 44A10 Laplace transform (28 articles)
- 44A12 Radon transform (4 articles)
- 44A15 Special transforms (Legendre, Hilbert, etc.) (26 articles)
- 44A20 Transforms of special functions (6 articles)
- 44A30 Multiple transforms (1 articles)
- 44A35 Convolution (9 articles)
- 44A40 Calculus of Mikusi\'nski and other operational calculi (2 articles)
- 44A45 Classical operational calculus (1 articles)
- 44A55 Discrete operational calculus (2 articles)
- 44A60 Moment problems (9 articles)
- 44A99 Miscellaneous topics (2 articles)
45 Integral equations (338 articles)
- 45 Integral equations
- 45-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (2 articles)
- 45-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 45-02 Research exposition (monographs, survey articles) (1 articles)
- 45-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 45-04 Explicit machine computation and programs (not the theory of computation or programming)
- 45-06 Proceedings, conferences, collections, etc.
- 45.0 (1940-1958) Integral and integro-differential equations, equations in infinitely many variables
- 45.00 (1959-1972) General (3 articles)
- 45.10 (1959-1972) Linear integral equations, general
- 45.11 (1959-1972) Fredholm equations
- 45.12 (1959-1972) Eigenvalue problems
- 45.13 (1959-1972) Volterra equations
- 45.15 (1959-1972) Singular equations
- 45.20 (1959-1972) Systems of linear equations
- 45.25 (1959-1972) Dual and triple integral equations, and generalizations
- 45.30 (1959-1972) Nonlinear integral equations
- 45.31 (1959-1972) Singular nonlinear equations
- 45.33 (1959-1972) Miscellaneous special kernels
- 45.40 (1959-1972) Integro-differential equations, ordinary (1 articles)
- 45.45 (1959-1972) Integro-partial differential equations
- 45.99 (1959-1972) None of the above, but in this section
- 45A05 Linear integral equations (8 articles)
- 45B05 Fredholm integral equations (13 articles)
- 45C05 Eigenvalue problems (6 articles)
- 45D05 Volterra integral equations (38 articles)
- 45Exx Singular integral equations (20 articles)
  - 45Exx Singular integral equations (1 articles)
  - 45E05 Integral equations with kernels of Cauchy type (10 articles)
  - 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (6 articles)
  - 45E99 None of the above, but in this section (3 articles)
- 45Fxx Systems of linear integral equations (4 articles)
  - 45Fxx Systems of linear integral equations
  - 45F05 Systems of nonsingular linear integral equations (2 articles)
  - 45F10 Dual, triple, etc., integral and series equations
  - 45F15 Systems of singular linear integral equations (2 articles)
  - 45F99 None of the above, but in this section
- 45Gxx Nonlinear integral equations (67 articles)
  - 45Gxx Nonlinear integral equations (2 articles)
  - 45G05 Singular nonlinear integral equations (6 articles)
  - 45G10 Other nonlinear integral equations (56 articles)
  - 45G15 Systems of nonlinear integral equations (3 articles)
- 45H05 Miscellaneous special kernels (10 articles)
- 45J05 Integro-ordinary differential equations (30 articles)
- 45K05 Integro-partial differential equations (47 articles)
- 45L05 Theoretical approximation of solutions (19 articles)
- 45Mxx Qualitative behavior (17 articles)
  - 45Mxx Qualitative behavior
  - 45M05 Asymptotics (4 articles)
  - 45M10 Stability theory (4 articles)
  - 45M15 Periodic solutions (3 articles)
  - 45M20 Positive solutions (3 articles)
  - 45M99 None of the above, but in this section (3 articles)
- 45N05 Abstract integral equations, integral equations in abstract spaces (36 articles)
- 45P05 Integral operators (14 articles)
- 45Q05 Inverse problems (1 articles)
- 45R05 Random integral equations
46 Functional analysis (2731 articles)
- 46 Functional analysis
- 46-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (7 articles)
- 46-01 Instructional exposition (textbooks, tutorial papers, etc.) (10 articles)
- 46-02 Research exposition (monographs, survey articles)
- 46-03 Historical (must also be assigned at least one classification number from Section 01) (8 articles)
- 46-04 Explicit machine computation and programs (not the theory of computation or programming)
- 46-06 Proceedings, conferences, collections, etc.
- 46.0 (1940-1958) Functional analysis
- 46.00 (1959-1972) General (14 articles)
- 46.01 (1959-1972) Topological linear spaces (12 articles)
- 46.06 (1959-1972) Ordered TLS; vector lattices (1 articles)
- 46.1 (1940-1958) Topological vector spaces
- 46.10 (1959-1972) Normed linear spaces, Banach spaces (8 articles)
- 46.15 (1959-1972) Inner product spaces, Hilbert spaces, spaces with an indefinite metric
- 46.2 (1940-1958) Banach spaces, Banach algebras, Hilbert space
- 46.20 (1959-1972) Other special spaces (2 articles)
- 46.25 (1959-1972) Spaces of continuous functions (5 articles)
- 46.3 (1940-1958) Differential and integral equations, functional analysis, ergodic theory
- 46.30 (1959-1972) Spaces of differentiable and analytic functions
- 46.35 (1959-1972) Spaces of measurable functions; $L^p$ spaces, Orlicz spaces
- 46.38 (1959-1972) Sobolev spaces, embedding theorems, interpolation spaces (6 articles)
- 46.40 (1959-1972) Distributions, generalized functions (7 articles)
- 46.45 (1959-1972) Derivatives and differentials in abstract spaces (3 articles)
- 46.50 (1959-1972) Topological algebras; normed rings and algebras, Banach algebras. general theory
- 46.55 (1959-1972) Commutative Banach algebras; function algebras (5 articles)
- 46.60 (1959-1972) Rings and algebras with an involution, $*$-algebras. general theory
- 46.65 (1959-1972) Rings and algebras of operators (with or without involution); $C^*$-algebras, von Neumann algebras (1 articles)
- 46.80 (1959-1972) Group algebras, convolution algebras
- 46.90 (1959-1972) Miscellaneous applications of functional analysis (1 articles)
- 46.99 (1959-1972) None of the above, but in this section
- 46Axx Topological linear spaces and related structures (465 articles)
 - 46Axx Topological linear spaces and related structures (15 articles)
 - 46A03 General theory of locally convex spaces (27 articles)
 - 46A04 Locally convex Fréchet spaces and (DF)-spaces (23 articles)
 - 46A08 Barrelled spaces, bornological spaces (14 articles)
 - 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (8 articles)
 - 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) (21 articles)
 - 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (21 articles)
 - 46A17 Bornologies and related structures; Mackey convergence, etc. (6 articles)
 - 46A19 Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $ (15 articles)
 - 46A20 Duality theory (21 articles)
 - 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators (14 articles)
 - 46A25 Reflexivity and semi-reflexivity (9 articles)
 - 46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) (25 articles)
 - 46A32 Spaces of linear operators; topological tensor products; approximation properties (18 articles)
 - 46A35 Summability and bases (3 articles)
 - 46A40 Ordered topological linear spaces, vector lattices (79 articles)
 - 46A45 Sequence spaces (including Köthe sequence spaces) (53 articles)
 - 46A50 Compactness in topological linear spaces; angelic spaces, etc. (8 articles)
 - 46A55 Convex sets in topological linear spaces; Choquet theory (46 articles)
 - 46A61 Graded Fréchet spaces and tame operators
 - 46A63 Topological invariants ((DN), ($Omega$), etc.)
 - 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) (5 articles)
 - 46A80 Modular spaces (7 articles)
 - 46A99 None of the above, but in this section (27 articles)
- 46Bxx Normed linear spaces and Banach spaces; Banach lattices (691 articles)
 - 46Bxx Normed linear spaces and Banach spaces; Banach lattices (34 articles)
 - 46B03 Isomorphic theory (including renorming) of Banach spaces (35 articles)
 - 46B04 Isometric theory of Banach spaces (13 articles)
 - 46B07 Local theory of Banach spaces (13 articles)
 - 46B08 Ultraproduct techniques in Banach space theory
 - 46B09 Probabilistic methods in Banach space theory (3 articles)
 - 46B10 Duality and reflexivity (54 articles)
 - 46B15 Summability and bases (25 articles)
 - 46B20 Geometry and structure of normed linear spaces (197 articles)
 - 46B22 Radon-Nikodym, Krein-Milman and related properties (26 articles)
 - 46B25 Classical Banach spaces in the general theory (57 articles)
 - 46B26 Nonseparable Banach spaces (17 articles)
 - 46B28 Spaces of operators; tensor products; approximation properties (43 articles)
 - 46B40 Ordered normed spaces (23 articles)
 - 46B42 Banach lattices (53 articles)
 - 46B45 Banach sequence spaces (29 articles)
 - 46B50 Compactness in Banach (or normed) spaces (9 articles)
 - 46B70 Interpolation between normed linear spaces (7 articles)
 - 46B99 None of the above, but in this section (53 articles)
- 46Cxx Inner product spaces and their generalizations, Hilbert spaces (59 articles)
 - 46Cxx Inner product spaces and their generalizations, Hilbert spaces (3 articles)
 - 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (23 articles)
 - 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) (2 articles)
 - 46C15 Characterizations of Hilbert spaces (6 articles)
 - 46C20 Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) (3 articles)
 - 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.) (4 articles)
 - 46C99 None of the above, but in this section (18 articles)
- 46Exx Linear function spaces and their duals (572 articles)
 - 46Exx Linear function spaces and their duals (8 articles)
 - 46E05 Lattices of continuous, differentiable or analytic functions (11 articles)
 - 46E10 Topological linear spaces of continuous, differentiable or analytic functions (27 articles)
 - 46E15 Banach spaces of continuous, differentiable or analytic functions (50 articles)
 - 46E20 Hilbert spaces of continuous, differentiable or analytic functions (3 articles)
 - 46E22 Hilbert spaces with reproducing kernels (= (10 articles)
 - 46E25 Rings and algebras of continuous, differentiable or analytic functions (18 articles)
 - 46E27 Spaces of measures (12 articles)
 - 46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (193 articles)
 - 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems (162 articles)
 - 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables (1 articles)
 - 46E40 Spaces of vector- and operator-valued functions (53 articles)
 - 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (3 articles)
 - 46E99 None of the above, but in this section (21 articles)
- 46Fxx Distributions, generalized functions, distribution spaces (118 articles)
 - 46Fxx Distributions, generalized functions, distribution spaces (2 articles)
 - 46F05 Topological linear spaces of test functions, distributions and ultradistributions (22 articles)
 - 46F10 Operations with distributions (38 articles)
 - 46F12 Integral transforms in distribution spaces (22 articles)
 - 46F15 Hyperfunctions, analytic functionals (4 articles)
 - 46F20 Distributions and ultradistributions as boundary values of analytic functions (3 articles)
 - 46F25 Distributions on infinite-dimensional spaces (2 articles)
 - 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (15 articles)
 - 46F99 None of the above, but in this section (10 articles)
- 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) (248 articles)
 - 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) (3 articles)
 - 46G05 Derivatives (74 articles)
 - 46G10 Vector-valued measures and integration (121 articles)
 - 46G12 Measures and integration on abstract linear spaces (17 articles)
 - 46G15 Functional analytic lifting theory (2 articles)
 - 46G20 Infinite-dimensional holomorphy (17 articles)
 - 46G25 (Spaces of) multilinear mappings, polynomials (9 articles)
 - 46G99 None of the above, but in this section (5 articles)
- 46Hxx Topological algebras, normed rings and algebras, Banach algebras (105 articles)
 - 46Hxx Topological algebras, normed rings and algebras, Banach algebras (2 articles)
 - 46H05 General theory of topological algebras (41 articles)
 - 46H10 Ideals and subalgebras (11 articles)
 - 46H15 Representations of topological algebras (2 articles)
 - 46H20 Structure, classification of topological algebras (14 articles)
 - 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-xx or 16-xx) (15 articles)
 - 46H30 Functional calculus in topological algebras (7 articles)
 - 46H35 Topological algebras of operators (1 articles)
 - 46H40 Automatic continuity (4 articles)
 - 46H70 Nonassociative topological algebras (3 articles)
 - 46H99 None of the above, but in this section (5 articles)
- 46Jxx Commutative Banach algebras and commutative topological algebras (64 articles)
 - 46Jxx Commutative Banach algebras and commutative topological algebras (2 articles)
 - 46J05 General theory of commutative topological algebras (5 articles)
 - 46J10 Banach algebras of continuous functions, function algebras (35 articles)
 - 46J15 Banach algebras of differentiable or analytic functions, $ (9 articles)
 - 46J20 Ideals, maximal ideals, boundaries (8 articles)
 - 46J25 Representations of commutative topological algebras
 - 46J30 Subalgebras
 - 46J40 Structure, classification of commutative topological algebras (1 articles)
 - 46J45 Radical Banach algebras
 - 46J99 None of the above, but in this section (4 articles)
- 46Kxx Topological (rings and) algebras with an involution (21 articles)
 - 46Kxx Topological (rings and) algebras with an involution
 - 46K05 General theory of topological algebras with involution (14 articles)
 - 46K10 Representations of topological algebras with involution (1 articles)
 - 46K15 Hilbert algebras (2 articles)
 - 46K50 Nonselfadjoint (sub)algebras in algebras with involution
 - 46K70 Nonassociative topological algebras with an involution (1 articles)
 - 46K99 None of the above, but in this section (3 articles)
- 46Lxx Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.) (112 articles)
 - 46Lxx Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.)
 - 46L05 General theory of $C^*$-algebras (27 articles)
 - 46L06 Tensor products of $C^*$-algebras
 - 46L07 Operator spaces and completely bounded maps (1 articles)
 - 46L08 $C^*$-modules (2 articles)
 - 46L09 Free products of $C^*$-algebras (1 articles)
 - 46L10 General theory of von Neumann algebras (7 articles)
 - 46L30 States (5 articles)
 - 46L35 Classifications of $C^*$-algebras, factors (1 articles)
 - 46L37 Subfactors and their classification
 - 46L40 Automorphisms (2 articles)
 - 46L45 Decomposition theory for $C^*$-algebras (1 articles)
 - 46L51 Noncommutative measure and integration (12 articles)
 - 46L52 Noncommutative function spaces (1 articles)
 - 46L53 Noncommutative probability and statistics (9 articles)
 - 46L54 Free probability and free operator algebras (9 articles)
 - 46L55 Noncommutative dynamical systems
 - 46L57 Derivations, dissipations and positive semigroups in $C^*$-algebras (1 articles)
 - 46L60 Applications of selfadjoint operator algebras to physics (2 articles)
 - 46L65 Quantizations, deformations (1 articles)
 - 46L70 Nonassociative selfadjoint operator algebras (5 articles)
 - 46L80 $K$-theory and operator algebras (including cyclic theory) (3 articles)
 - 46L85 Noncommutative topology (6 articles)
 - 46L87 Noncommutative differential geometry (5 articles)
 - 46L89 Other ``noncommutative'' mathematics based on $C^*$-algebra theory (3 articles)
 - 46L99 None of the above, but in this section (8 articles)
- 46Mxx Methods of category theory in functional analysis (81 articles)
 - 46Mxx Methods of category theory in functional analysis
 - 46M05 Tensor products (23 articles)
 - 46M07 Ultraproducts
 - 46M10 Projective and injective objects (6 articles)
 - 46M15 Categories, functors (15 articles)
 - 46M18 Homological methods (exact sequences, right inverses, lifting, etc.) (2 articles)
 - 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) (6 articles)
 - 46M35 Abstract interpolation of topological vector spaces (14 articles)
 - 46M40 Inductive and projective limits (11 articles)
 - 46M99 None of the above, but in this section (4 articles)
- 46Nxx Miscellaneous applications of functional analysis (64 articles)
 - 46Nxx Miscellaneous applications of functional analysis (1 articles)
 - 46N10 Applications in optimization, convex analysis, mathematical programming, economics (27 articles)
 - 46N20 Applications to differential and integral equations (10 articles)
 - 46N30 Applications in probability theory and statistics (4 articles)
 - 46N40 Applications in numerical analysis (6 articles)
 - 46N50 Applications in quantum physics (8 articles)
 - 46N55 Applications in statistical physics
 - 46N60 Applications in biology and other sciences
 - 46N99 None of the above, but in this section (8 articles)
- 46Sxx Other (nonclassical) types of functional analysis (24 articles)
 - 46Sxx Other (nonclassical) types of functional analysis
 - 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis (13 articles)
 - 46S20 Nonstandard functional analysis (4 articles)
 - 46S30 Constructive functional analysis
 - 46S40 Fuzzy functional analysis (4 articles)
 - 46S50 Functional analysis in probabilistic metric linear spaces (1 articles)
 - 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
 - 46S99 None of the above, but in this section (2 articles)
- 46Txx Nonlinear functional analysis (17 articles)
 - 46Txx Nonlinear functional analysis
 - 46T05 Infinite-dimensional manifolds (2 articles)
 - 46T10 Manifolds of mappings (1 articles)
 - 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (1 articles)
 - 46T20 Continuous and differentiable maps (7 articles)
 - 46T25 Holomorphic maps (2 articles)
 - 46T30 Distributions and generalized functions on nonlinear spaces (2 articles)
 - 46T99 None of the above, but in this section (2 articles)
47 Operator theory (2326 articles)
- 47 Operator theory
- 47-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (5 articles)
- 47-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 47-02 Research exposition (monographs, survey articles) (2 articles)
- 47-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 47-04 Explicit machine computation and programs (not the theory of computation or programming)
- 47-06 Proceedings, conferences, collections, etc. (1 articles)
- 47.00 (1959-1972) General (1 articles)
- 47.10 (1959-1972) Single linear operators, general theory (8 articles)
- 47.20 (1959-1972) Operators in ordered spaces (4 articles)
- 47.25 (1959-1972) Operators in function spaces and other special spaces (2 articles)
- 47.30 (1959-1972) Spectral theory, functional calculus (3 articles)
- 47.35 (1959-1972) Reducibility, invariant subspaces (2 articles)
- 47.40 (1959-1972) Structure, classification, canonical forms
- 47.45 (1959-1972) Compact (completely continuous) operators
- 47.48 (1959-1972) Perturbation theory
- 47.50 (1959-1972) Semigroups and groups of operators (2 articles)
- 47.55 (1959-1972) Other systems of operators
- 47.60 (1959-1972) Ordinary differential operators (2 articles)
- 47.65 (1959-1972) Partial differential operators
- 47.69 (1959-1972) Difference operators
- 47.70 (1959-1972) Integral and integro-differential operators (1 articles)
- 47.80 (1959-1972) Nonlinear operators, general theory (4 articles)
- 47.85 (1959-1972) Fixed-point theorems (1 articles)
- 47.90 (1959-1972) Miscellaneous applications (1 articles)
- 47.99 (1959-1972) None of the above, but in this section
- 47Axx General theory of linear operators (420 articles)
 - 47Axx General theory of linear operators (12 articles)
 - 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (30 articles)
 - 47A06 Linear relations (multivalued linear operators) (2 articles)
 - 47A07 Forms (bilinear, sesquilinear, multilinear) (2 articles)
 - 47A10 Spectrum, resolvent (71 articles)
 - 47A11 Local spectral properties (15 articles)
 - 47A12 Numerical range, numerical radius (9 articles)
 - 47A13 Several-variable operator theory (spectral, Fredholm, etc.) (4 articles)
 - 47A15 Invariant subspaces (19 articles)
 - 47A16 Cyclic and hypercyclic vectors (10 articles)
 - 47A20 Dilations, extensions, compressions (17 articles)
 - 47A25 Spectral sets (4 articles)
 - 47A30 Norms (inequalities, more than one norm, etc.) (21 articles)
 - 47A35 Ergodic theory (26 articles)
 - 47A40 Scattering theory (4 articles)
 - 47A45 Canonical models for contractions and nonselfadjoint operators (10 articles)
 - 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
 - 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (1 articles)
 - 47A50 Equations and inequalities involving linear operators, with vector unknowns (20 articles)
 - 47A52 Ill-posed problems, regularization (1 articles)
 - 47A53 (Semi-) Fredholm operators; index theories (31 articles)
 - 47A55 Perturbation theory (22 articles)
 - 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) (2 articles)
 - 47A57 Operator methods in interpolation, moment and extension problems (2 articles)
 - 47A58 Operator approximation theory (3 articles)
 - 47A60 Functional calculus (15 articles)
 - 47A62 Equations involving linear operators, with operator unknowns (2 articles)
 - 47A63 Operator inequalities (7 articles)
 - 47A64 Operator means, shorted operators, etc. (1 articles)
 - 47A65 Structure theory (8 articles)
 - 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
 - 47A67 Representation theory (2 articles)
 - 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) (6 articles)
 - 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces (14 articles)
 - 47A75 Eigenvalue problems (12 articles)
 - 47A80 Tensor products of operators (1 articles)
 - 47A99 None of the above, but in this section (14 articles)
- 47Bxx Special classes of linear operators (472 articles)
 - 47Bxx Special classes of linear operators (12 articles)
 - 47B06 Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (21 articles)
 - 47B07 Operators defined by compactness properties (16 articles)
 - 47B10 Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) (44 articles)
 - 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) (25 articles)
 - 47B20 Subnormal operators, hyponormal operators, etc. (14 articles)
 - 47B25 Symmetric and selfadjoint operators (unbounded) (17 articles)
 - 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (3 articles)
 - 47B33 Composition operators (16 articles)
 - 47B34 Kernel operators (2 articles)
 - 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators (36 articles)
 - 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations (2 articles)
 - 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (30 articles)
 - 47B38 Operators on function spaces (general) (98 articles)
 - 47B39 Difference operators (4 articles)
 - 47B40 Spectral operators, decomposable operators, well-bounded operators, etc. (13 articles)
 - 47B44 Accretive operators, dissipative operators, etc. (3 articles)
 - 47B47 Commutators, derivations, elementary operators, etc. (23 articles)
 - 47B48 Operators on Banach algebras (8 articles)
 - 47B49 Transformers (= operators on spaces of operators) (2 articles)
 - 47B50 Operators on spaces with an indefinite metric (3 articles)
 - 47B60 Operators on ordered spaces (32 articles)
 - 47B65 Positive operators and order-bounded operators (25 articles)
 - 47B80 Random operators (1 articles)
 - 47B99 None of the above, but in this section (22 articles)
- 47Cxx Individual linear operators as elements of algebraic systems (8 articles)
 - 47Cxx Individual linear operators as elements of algebraic systems
 - 47C05 Operators in algebras (4 articles)
 - 47C10 Operators in $^*$-algebras (1 articles)
 - 47C15 Operators in $C^*$- or von Neumann algebras (2 articles)
 - 47C99 None of the above, but in this section (1 articles)
- 47Dxx Groups and semigroups of linear operators, their generalizations and applications (87 articles)
 - 47Dxx Groups and semigroups of linear operators, their generalizations and applications (6 articles)
 - 47D03 Groups and semigroups of linear operators (20 articles)
 - 47D06 One-parameter semigroups and linear evolution equations (42 articles)
 - 47D07 Markov semigroups and applications to diffusion processes (5 articles)
 - 47D08 Schrödinger and Feynman-Kac semigroups
 - 47D09 Operator sine and cosine functions and higher-order Cauchy problems (3 articles)
 - 47D60 $C$-semigroups
 - 47D62 Integrated semigroups (1 articles)
 - 47D99 None of the above, but in this section (10 articles)
- 47E05 Ordinary differential operators (33 articles)
- 47F05 Partial differential operators (33 articles)
- 47Gxx Integral, integro-differential, and pseudodifferential operators (58 articles)
 - 47Gxx Integral, integro-differential, and pseudodifferential operators (6 articles)
 - 47G10 Integral operators (37 articles)
 - 47G20 Integro-differential operators (7 articles)
 - 47G30 Pseudodifferential operators (8 articles)
 - 47G99 None of the above, but in this section
- 47Hxx Nonlinear operators and their properties (670 articles)
 - 47Hxx Nonlinear operators and their properties (31 articles)
 - 47H04 Set-valued operators (36 articles)
 - 47H05 Monotone operators (with respect to duality) (56 articles)
 - 47H06 Accretive operators, dissipative operators, etc. (16 articles)
 - 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (25 articles)
 - 47H09 Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.) (84 articles)
 - 47H10 Fixed-point theorems (276 articles)
 - 47H11 Degree theory (22 articles)
 - 47H14 Perturbations of nonlinear operators (1 articles)
 - 47H20 Semigroups of nonlinear operators (17 articles)
 - 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.) (35 articles)
 - 47H40 Random operators (8 articles)
 - 47H50 Potential operators
 - 47H60 Multilinear and polynomial operators (3 articles)
 - 47H99 None of the above, but in this section (60 articles)
- 47Jxx Equations and inequalities involving nonlinear operators (272 articles)
 - 47Jxx Equations and inequalities involving nonlinear operators
 - 47J05 Equations involving nonlinear operators (general) (116 articles)
 - 47J06 Nonlinear ill-posed problems (2 articles)
 - 47J07 Abstract inverse mapping and implicit function theorems (2 articles)
 - 47J10 Nonlinear eigenvalue problems (17 articles)
 - 47J15 Abstract bifurcation theory (9 articles)
 - 47J20 Variational and other types of inequalities involving nonlinear operators (general) (23 articles)
 - 47J25 Methods for solving nonlinear operator equations (general) (58 articles)
 - 47J30 Variational methods (21 articles)
 - 47J35 Nonlinear evolution equations (11 articles)
 - 47J40 Equations with hysteresis operators (12 articles)
 - 47J99 None of the above, but in this section (1 articles)
- 47Lxx Linear spaces and algebras of operators (71 articles)
 - 47Lxx Linear spaces and algebras of operators (1 articles)
 - 47L05 Linear spaces of operators (16 articles)
 - 47L07 Convex sets and cones of operators (2 articles)
 - 47L10 Algebras of operators on Banach spaces and other topological linear spaces (10 articles)
 - 47L15 Operator algebras with symbol structure
 - 47L20 Operator ideals (18 articles)
 - 47L25 Operator spaces (= matricially normed spaces) (1 articles)
 - 47L30 Abstract operator algebras on Hilbert spaces (8 articles)
 - 47L35 Nest algebras, CSL algebras (5 articles)
 - 47L40 Limit algebras, subalgebras of $C^*$-algebras
 - 47L45 Dual algebras; weakly closed singly generated operator algebras (2 articles)
 - 47L50 Dual spaces of operator algebras
 - 47L55 Representations of (nonselfadjoint) operator algebras
 - 47L60 Algebras of unbounded operators; partial algebras of operators (1 articles)
 - 47L65 Crossed product algebras (analytic crossed products)
 - 47L70 Nonassociative nonselfadjoint operator algebras
 - 47L75 Other nonselfadjoint operator algebras (1 articles)
 - 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (2 articles)
 - 47L90 Applications of operator algebras to physics (2 articles)
 - 47L99 None of the above, but in this section (2 articles)
- 47Nxx Miscellaneous applications of operator theory (148 articles)
 - 47Nxx Miscellaneous applications of operator theory
 - 47N10 Applications in optimization, convex analysis, mathematical programming, economics (12 articles)
 - 47N20 Applications to differential and integral equations (126 articles)
 - 47N30 Applications in probability theory and statistics (2 articles)
 - 47N40 Applications in numerical analysis
 - 47N50 Applications in quantum physics (2 articles)
 - 47N55 Applications in statistical physics
 - 47N60 Applications in biology and other sciences
 - 47N70 Applications in systems theory, circuits, etc. (5 articles)
 - 47N99 None of the above, but in this section (1 articles)
- 47Sxx Other (nonclassical) types of operator theory (12 articles)
 - 47Sxx Other (nonclassical) types of operator theory
 - 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory (5 articles)
 - 47S20 Nonstandard operator theory
 - 47S30 Constructive operator theory
 - 47S40 Fuzzy operator theory (5 articles)
 - 47S50 Operator theory in probabilistic metric linear spaces (2 articles)
 - 47S99 None of the above, but in this section
48 (1940-1958) Geometry
- 48 (1940-1958) Geometry
- 48.0 (1940-1958) Geometry
49 Calculus of variations and optimal control; optimization (919 articles)
- 49 Calculus of variations and optimal control; optimization
- 49-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (2 articles)
- 49-01 Instructional exposition (textbooks, tutorial papers, etc.) (6 articles)
- 49-02 Research exposition (monographs, survey articles) (7 articles)
- 49-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 49-04 Explicit machine computation and programs (not the theory of computation or programming)
- 49-06 Proceedings, conferences, collections, etc.
- 49.0 (1940-1958) Calculus of variations
- 49.00 (1959-1972) General (3 articles)
- 49.10 (1959-1972) Calculus of variations
- 49.20 (1959-1972) Optimal control
- 49Jxx Existence theories (408 articles)
  - 49Jxx Existence theories
  - 49J05 Free problems in one independent variable (1 articles)
  - 49J10 Free problems in two or more independent variables (12 articles)
  - 49J15 Optimal control problems involving ordinary differential equations (22 articles)
  - 49J20 Optimal control problems involving partial differential equations (59 articles)
  - 49J22 Optimal control problems involving integral equations (1 articles)
  - 49J24 Optimal control problems involving differential inclusions (16 articles)
  - 49J25 Optimal control problems involving equations with retarded arguments (2 articles)
  - 49J27 Problems in abstract spaces (22 articles)
  - 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (8 articles)
  - 49J35 Minimax problems (10 articles)
  - 49J40 Variational methods including variational inequalities (124 articles)
  - 49J45 Methods involving semicontinuity and convergence; relaxation (40 articles)
  - 49J50 Fréchet and Gateaux differentiability (17 articles)
  - 49J52 Nonsmooth analysis (43 articles)
  - 49J53 Set-valued and variational analysis (13 articles)
  - 49J55 Problems involving randomness (1 articles)
  - 49J99 None of the above, but in this section (17 articles)
- 49Kxx Necessary conditions and sufficient conditions for optimality (146 articles)
  - 49Kxx Necessary conditions and sufficient conditions for optimality (1 articles)
  - 49K05 Free problems in one independent variable (4 articles)
  - 49K10 Free problems in two or more independent variables (11 articles)
  - 49K15 Problems involving ordinary differential equations (30 articles)
  - 49K20 Problems involving partial differential equations (23 articles)
  - 49K22 Problems involving integral equations (1 articles)
  - 49K24 Problems involving differential inclusions (2 articles)
  - 49K25 Problems involving equations with retarded arguments (4 articles)
  - 49K27 Problems in abstract spaces (13 articles)
  - 49K30 Optimal solutions belonging to restricted classes (4 articles)
  - 49K35 Minimax problems (11 articles)
  - 49K40 Sensitivity, stability, well-posedness (17 articles)
  - 49K45 Problems involving randomness (9 articles)
  - 49K99 None of the above, but in this section (16 articles)
- 49Lxx Hamilton-Jacobi theories, including dynamic programming (27 articles)
  - 49Lxx Hamilton-Jacobi theories, including dynamic programming
  - 49L20 Dynamic programming method (13 articles)
  - 49L25 Viscosity solutions (2 articles)
  - 49L99 None of the above, but in this section (12 articles)
- 49Mxx Methods of successive approximations (109 articles)
  - 49Mxx Methods of successive approximations (3 articles)
  - 49M05 Methods based on necessary conditions (6 articles)
  - 49M15 Methods of Newton-Raphson, Galerkin and Ritz types (25 articles)
  - 49M20 Methods of relaxation type (3 articles)
  - 49M25 Discrete approximations (15 articles)
  - 49M27 Decomposition methods (6 articles)
  - 49M29 Methods involving duality (4 articles)
  - 49M30 Other methods, not based on necessary conditions (penalty function, etc.) (19 articles)
  - 49M37 Methods of nonlinear programming type (20 articles)
  - 49M99 None of the above, but in this section (8 articles)
- 49Nxx Miscellaneous topics (105 articles)
  - 49Nxx Miscellaneous topics
  - 49N05 Linear optimal control problems (3 articles)
  - 49N10 Linear-quadratic problems (28 articles)
  - 49N15 Duality theory (15 articles)
  - 49N20 Periodic optimization (3 articles)
  - 49N25 Impulsive optimal control problems (1 articles)
  - 49N30 Problems with incomplete information (1 articles)
  - 49N35 Optimal feedback synthesis (7 articles)
  - 49N45 Inverse problems (12 articles)
  - 49N60 Regularity of solutions (24 articles)
  - 49N70 Differential games (4 articles)
  - 49N75 Pursuit and evasion games (2 articles)
  - 49N90 Applications of optimal control and differential games (2 articles)
  - 49N99 None of the above, but in this section (3 articles)
- 49Qxx Manifolds (67 articles)
  - 49Qxx Manifolds
  - 49Q05 Minimal surfaces (7 articles)
  - 49Q10 Optimization of shapes other than minimal surfaces (25 articles)
  - 49Q12 Sensitivity analysis (4 articles)
  - 49Q15 Geometric measure and integration theory, integral and normal currents (9 articles)
  - 49Q20 Variational problems in a geometric measure-theoretic setting (17 articles)
  - 49Q99 None of the above, but in this section (5 articles)
- 49R50 Variational methods for eigenvalues of operators [See also 47A75] (15 articles)
- 49S05 Variational principles of physics (22 articles)
50 (1940-1979) Geometry (38 articles)
- 50 (1940-1979) Geometry
- 50-00 (1973-1979) Difficult to classify at the second level (must be assigned at least one other classification number in this section) (7 articles)
- 50-01 (1973-1979) Elementary exposition (collegiate level)
- 50-02 (1973-1979) Advanced exposition (research surveys, etc.)
- 50-03 (1973-1979) Historical (1 articles)
- 50-04 (1973-1979) Explicit machine computation and programs (not the theory of computation or programming)
- 50-06 (1973-1979) Collections of papers; proceedings of conferences
- 50.0 (1940-1958) Geometries, Euclidean and other
- 50.00 (1959-1972) General (6 articles)
- 50.05 (1959-1972) Foundations
- 50.10 (1959-1972) Euclidean (1 articles)
- 50.14 (1959-1972) Constructions (2 articles)
- 50.20 (1959-1972) Affine geometry, general (1 articles)
- 50.25 (1959-1972) Transformations (2 articles)
- 50.30 (1959-1972) Projective geometry, general (3 articles)
- 50.35 (1959-1972) Transformations (3 articles)
- 50.38 (1959-1972) Second-order loci
- 50.40 (1959-1972) Non-Euclidean geometry (i.e. hyperbolic or elliptic) (2 articles)
- 50.48 (1959-1972) Special geometries (1 articles)
- 50.60 (1959-1972) Finite geometries (1 articles)
- 50.70 (1959-1972) Projective planes (2 articles)
- 50.90 (1959-1972) Regular figures, divisions of space (6 articles)
- 50.99 (1959-1972) None of the above, but in this section
51 Geometry (528 articles)
- 51 Geometry
- 51-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 51-01 Instructional exposition (textbooks, tutorial papers, etc.) (13 articles)
- 51-02 Research exposition (monographs, survey articles) (5 articles)
- 51-03 Historical (must also be assigned at least one classification number from Section 01) (24 articles)
- 51-04 Explicit machine computation and programs (not the theory of computation or programming) (4 articles)
- 51-06 Proceedings, conferences, collections, etc. (1 articles)
- 51Axx Linear incidence geometry (87 articles)
  - 51Axx Linear incidence geometry (4 articles)
  - 51A05 General theory and projective geometries (5 articles)
  - 51A10 Homomorphism, automorphism and dualities (6 articles)
  - 51A15 Structures with parallelism (9 articles)
  - 51A20 Configuration theorems (8 articles)
  - 51A25 Algebraization (21 articles)
  - 51A30 Desarguesian and Pappian geometries (5 articles)
  - 51A35 Non-Desarguesian affine and projective planes (8 articles)
  - 51A40 Translation planes and spreads (5 articles)
  - 51A45 Incidence structures imbeddable into projective geometries (10 articles)
  - 51A50 Polar geometry, symplectic spaces, orthogonal spaces (1 articles)
  - 51A99 None of the above, but in this section (5 articles)
- 51Bxx Nonlinear incidence geometry (16 articles)
  - 51Bxx Nonlinear incidence geometry
  - 51B05 General theory (2 articles)
  - 51B10 Möbius geometries (5 articles)
  - 51B15 Laguerre geometries (4 articles)
  - 51B20 Minkowski geometries (1 articles)
  - 51B25 Lie geometries (1 articles)
  - 51B99 None of the above, but in this section (3 articles)
- 51C05 Ring geometry (Hjelmslev, Barbilian, etc.) (18 articles)
- 51Dxx Geometric closure systems (11 articles)
  - 51Dxx Geometric closure systems (4 articles)
  - 51D05 Abstract (Maeda) geometries
  - 51D10 Abstract geometries with exchange axiom
  - 51D15 Abstract geometries with parallelism (1 articles)
  - 51D20 Combinatorial geometries
  - 51D25 Lattices of subspaces
  - 51D30 Continuous geometries and related topics (1 articles)
  - 51D99 None of the above, but in this section (5 articles)
- 51Exx Finite geometry and special incidence structures (37 articles)
  - 51Exx Finite geometry and special incidence structures
  - 51E05 General block designs (1 articles)
  - 51E10 Steiner systems
  - 51E12 Generalized quadrangles, generalized polygons
  - 51E14 Finite partial geometries (general), nets, partial spreads (2 articles)
  - 51E15 Affine and projective planes (6 articles)
  - 51E20 Combinatorial structures in finite projective spaces (12 articles)
  - 51E21 Blocking sets, ovals, $k$-arcs
  - 51E22 Linear codes and caps in Galois spaces
  - 51E23 Spreads and packing problems
  - 51E24 Buildings and the geometry of diagrams
  - 51E25 Other finite nonlinear geometries (2 articles)
  - 51E26 Other finite linear geometries
  - 51E30 Other finite incidence structures (10 articles)
  - 51E99 None of the above, but in this section (4 articles)
- 51Fxx Metric geometry (14 articles)
  - 51Fxx Metric geometry
  - 51F05 Absolute planes
  - 51F10 Absolute spaces
  - 51F15 Reflection groups, reflection geometries (1 articles)
  - 51F20 Congruence and orthogonality (4 articles)
  - 51F25 Orthogonal and unitary groups (1 articles)
  - 51F99 None of the above, but in this section (8 articles)
- 51G05 Ordered geometries (ordered incidence structures, etc.) (11 articles)
- 51Hxx Topological geometry (2 articles)
  - 51Hxx Topological geometry
  - 51H05 General theory (1 articles)
  - 51H10 Topological linear incidence structures
  - 51H15 Topological nonlinear incidence structures
  - 51H20 Topological geometries on manifolds (1 articles)
  - 51H25 Geometries with differentiable structure
  - 51H30 Geometries with algebraic manifold structure
  - 51H99 None of the above, but in this section
- 51Jxx Incidence groups (3 articles)
  - 51Jxx Incidence groups (1 articles)
  - 51J05 General theory
  - 51J10 Projective incidence groups
  - 51J15 Kinematic spaces (1 articles)
  - 51J20 Representation by near-fields and near-algebras (1 articles)
  - 51J99 None of the above, but in this section
- 51Kxx Distance geometry (8 articles)
  - 51Kxx Distance geometry
  - 51K05 General theory (2 articles)
  - 51K10 Synthetic differential geometry (4 articles)
  - 51K99 None of the above, but in this section (2 articles)
- 51Lxx Geometric order structures
  - 51Lxx Geometric order structures
  - 51L05 Geometry of orders of nondifferentiable curves
  - 51L10 Directly differentiable curves
  - 51L15 $n$-vertex theorems via direct methods
  - 51L20 Geometry of orders of surfaces
  - 51L99 None of the above, but in this section
- 51Mxx Real and complex geometry (104 articles)
  - 51Mxx Real and complex geometry (8 articles)
  - 51M04 Elementary problems in Euclidean geometries (21 articles)
  - 51M05 Euclidean geometries (general) and generalizations (9 articles)
  - 51M09 Elementary problems in hyperbolic and elliptic geometries (2 articles)
  - 51M10 Hyperbolic and elliptic geometries (general) and generalizations (12 articles)
  - 51M15 Geometric constructions (10 articles)
  - 51M16 Inequalities and extremum problems (4 articles)
  - 51M20 Polyhedra and polytopes; regular figures, division of spaces (24 articles)
  - 51M25 Length, area and volume (9 articles)
  - 51M30 Line geometries and their generalizations (2 articles)
  - 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
  - 51M99 None of the above, but in this section (3 articles)
- 51Nxx Analytic and descriptive geometry (163 articles)
  - 51Nxx Analytic and descriptive geometry (5 articles)
  - 51N05 Descriptive geometry (40 articles)
  - 51N10 Affine analytic geometry (18 articles)
  - 51N15 Projective analytic geometry (13 articles)
  - 51N20 Euclidean analytic geometry (58 articles)
  - 51N25 Analytic geometry with other transformation groups (8 articles)
  - 51N30 Geometry of classical groups (2 articles)
  - 51N35 Questions of classical algebraic geometry (15 articles)
  - 51N99 None of the above, but in this section (4 articles)
- 51P05 Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) (7 articles)
52 Convex and discrete geometry (316 articles)
- 52 Convex and discrete geometry
- 52-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (5 articles)
- 52-01 Instructional exposition (textbooks, tutorial papers, etc.) (2 articles)
- 52-02 Research exposition (monographs, survey articles) (3 articles)
- 52-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 52-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 52-06 Proceedings, conferences, collections, etc.
- 52.0 (1940-1958) Convex domains, extremal problems, integral geometry
- 52.00 (1959-1972) General (5 articles)
- 52.10 (1959-1972) Convex polyhedra (6 articles)
- 52.25 (1959-1972) Convex curves
- 52.30 (1959-1972) Convex regions
- 52.34 (1959-1972) Helly-type theorems
- 52.40 (1959-1972) Extremum problems and geometric inequalities (4 articles)
- 52.45 (1959-1972) Packing and covering (4 articles)
- 52.50 (1959-1972) Distance geometries (2 articles)
- 52.99 (1959-1972) None of the above, but in this section
- 52Axx General convexity (175 articles)
  - 52Axx General convexity (3 articles)
  - 52A01 Axiomatic and generalized convexity (15 articles)
  - 52A05 Convex sets without dimension restrictions (23 articles)
  - 52A07 Convex sets in topological vector spaces (17 articles)
  - 52A10 Convex sets in $2$ dimensions (including convex curves) (10 articles)
  - 52A15 Convex sets in $3$ dimensions (including convex surfaces) (4 articles)
  - 52A20 Convex sets in $n$ dimensions (including convex hypersurfaces) (37 articles)
  - 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.) (2 articles)
  - 52A22 Random convex sets and integral geometry (10 articles)
  - 52A27 Approximation by convex sets (2 articles)
  - 52A30 Variants of convex sets (star-shaped, ($m, n$)-convex, etc.) (4 articles)
  - 52A35 Helly-type theorems and geometric transversal theory (3 articles)
  - 52A37 Other problems of combinatorial convexity (8 articles)
  - 52A38 Length, area, volume (4 articles)
  - 52A39 Mixed volumes and related topics
  - 52A40 Inequalities and extremum problems (23 articles)
  - 52A41 Convex functions and convex programs (7 articles)
  - 52A55 Spherical and hyperbolic convexity (1 articles)
  - 52A99 None of the above, but in this section (2 articles)
- 52Bxx Polytopes and polyhedra (64 articles)
  - 52Bxx Polytopes and polyhedra (12 articles)
  - 52B05 Combinatorial properties (number of faces, shortest paths, etc.) (10 articles)
  - 52B10 Three-dimensional polytopes (11 articles)
  - 52B11 $n$-dimensional polytopes (4 articles)
  - 52B12 Special polytopes (linear programming, centrally symmetric, etc.) (7 articles)
  - 52B15 Symmetry properties of polytopes (2 articles)
  - 52B20 Lattice polytopes (including relations with commutative algebra and algebraic geometry) (2 articles)
  - 52B22 Shellability
  - 52B35 Gale and other diagrams
  - 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (1 articles)
  - 52B45 Dissections and valuations (Hilbert's third problem, etc.) (1 articles)
  - 52B55 Computational aspects related to convexity (6 articles)
  - 52B60 Isoperimetric problems for polytopes (1 articles)
  - 52B70 Polyhedral manifolds (3 articles)
  - 52B99 None of the above, but in this section (4 articles)
- 52Cxx Discrete geometry (42 articles)
  - 52Cxx Discrete geometry
  - 52C05 Lattices and convex bodies in $2$ dimensions (2 articles)
  - 52C07 Lattices and convex bodies in $n$ dimensions (2 articles)
  - 52C10 Erdös problems and related topics of discrete geometry (4 articles)
  - 52C15 Packing and covering in $2$ dimensions (6 articles)
  - 52C17 Packing and covering in $n$ dimensions (12 articles)
  - 52C20 Tilings in $2$ dimensions (6 articles)
  - 52C22 Tilings in $n$ dimensions (2 articles)
  - 52C23 Quasicrystals, aperiodic tilings
  - 52C25 Rigidity and flexibility of structures
  - 52C26 Circle packings and discrete conformal geometry (1 articles)
  - 52C30 Planar arrangements of lines and pseudolines
  - 52C35 Arrangements of points, flats, hyperplanes (2 articles)
  - 52C40 Oriented matroids (1 articles)
  - 52C45 Combinatorial complexity of geometric structures (1 articles)
  - 52C99 None of the above, but in this section (3 articles)
53 Differential geometry (2340 articles)
- 53 Differential geometry
- 53-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (10 articles)
- 53-01 Instructional exposition (textbooks, tutorial papers, etc.) (29 articles)
- 53-02 Research exposition (monographs, survey articles) (10 articles)
- 53-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 53-04 Explicit machine computation and programs (not the theory of computation or programming) (2 articles)
- 53-06 Proceedings, conferences, collections, etc. (3 articles)
- 53.0 (1940-1958) Differential geometry
- 53.00 (1959-1972) General (27 articles)
- 53.01 (1959-1972) Curves and surfaces in Euclidean spaces (21 articles)
- 53.04 (1959-1972) Minimal surfaces
- 53.1 (1940-1958) Riemannian geometry, connections
- 53.10 (1959-1972) Affine differential geometry (4 articles)
- 53.2 (1940-1958) Manifolds, connections
- 53.20 (1959-1972) Projective differential geometry (30 articles)
- 53.23 (1959-1972) Differential line geometry (16 articles)
- 53.25 (1959-1972) Conformal differential geometry
- 53.3 (1940-1958) Complex manifolds
- 53.30 (1959-1972) Non-Euclidean differential geometry
- 53.32 (1959-1972) Other special differential geometries (4 articles)
- 53.35 (1959-1972) Vector and tensor analysis
- 53.38 (1959-1972) Spinor analysis
- 53.40 (1959-1972) bundles (2 articles)
- 53.42 (1959-1972) Differential invariants (local theory), geometric objects (1 articles)
- 53.45 (1959-1972) fields, etc.
- 53.50 (1959-1972) Connections, general (7 articles)
- 53.52 (1959-1972) $G$-Structures (1 articles)
- 53.55 (1959-1972) Affine connections (5 articles)
- 53.60 (1959-1972) Projective connections (11 articles)
- 53.66 (1959-1972) Homogeneous manifolds (2 articles)
- 53.70 (1959-1972) Local Riemannian geometry (1 articles)
- 53.72 (1959-1972) Riemannian manifolds
- 53.73 (1959-1972) Symmetric spaces (1 articles)
- 53.74 (1959-1972) Submanifolds, isometric imbeddings (3 articles)
- 53.75 (1959-1972) Global surface theory (convex surfaces) (6 articles)
- 53.78 (1959-1972) Lorentz metrics and generalizations (1 articles)
- 53.80 (1959-1972) Hermitian and K"ahlerian structures
- 53.85 (1959-1972) Finsler spaces and generalizations (areal metrics) (1 articles)
- 53.90 (1959-1972) Integral geometry
- 53.95 (1959-1972) Direct methods ($G$-spaces of Busemann), geometric orders
- 53.99 (1959-1972) Other generalizations
- 53Axx Classical differential geometry (490 articles)
  - 53Axx Classical differential geometry (22 articles)
  - 53A04 Curves in Euclidean space (37 articles)
  - 53A05 Surfaces in Euclidean space (69 articles)
  - 53A07 Higher-dimensional and -codimensional surfaces in Euclidean $n$-space (13 articles)
  - 53A10 Minimal surfaces, surfaces with prescribed mean curvature (23 articles)
  - 53A15 Affine differential geometry (32 articles)
  - 53A17 Kinematics (35 articles)
  - 53A20 Projective differential geometry (65 articles)
  - 53A25 Differential line geometry (22 articles)
  - 53A30 Conformal differential geometry (25 articles)
  - 53A35 Non-Euclidean differential geometry (14 articles)
  - 53A40 Other special differential geometries (12 articles)
  - 53A45 Vector and tensor analysis (13 articles)
  - 53A55 Differential invariants (local theory), geometric objects (95 articles)
  - 53A60 Geometry of webs (12 articles)
  - 53A99 None of the above, but in this section (1 articles)
- 53Bxx Local differential geometry (300 articles)
  - 53Bxx Local differential geometry (2 articles)
  - 53B05 Linear and affine connections (49 articles)
  - 53B10 Projective connections (5 articles)
  - 53B15 Other connections (23 articles)
  - 53B20 Local Riemannian geometry (59 articles)
  - 53B21 Methods of Riemannian geometry (18 articles)
  - 53B25 Local submanifolds (36 articles)
  - 53B30 Lorentz metrics, indefinite metrics (53 articles)
  - 53B35 Hermitian and Kählerian structures (26 articles)
  - 53B40 Finsler spaces and generalizations (areal metrics) (17 articles)
  - 53B50 Applications to physics (9 articles)
  - 53B99 None of the above, but in this section (3 articles)
- 53Cxx Global differential geometry (1220 articles)
  - 53Cxx Global differential geometry (11 articles)
  - 53C05 Connections, general theory (143 articles)
  - 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) (21 articles)
  - 53C10 $G$-structures (49 articles)
  - 53C12 Foliations (differential geometric aspects) (20 articles)
  - 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) (132 articles)
  - 53C17 Sub-Riemannian geometry (5 articles)
  - 53C20 Global Riemannian geometry, including pinching (87 articles)
  - 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions (44 articles)
  - 53C22 Geodesics (32 articles)
  - 53C23 Global topological methods (à la Gromov) (4 articles)
  - 53C24 Rigidity results (9 articles)
  - 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) (102 articles)
  - 53C26 Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry (12 articles)
  - 53C27 Spin and Spin$^c$ geometry (23 articles)
  - 53C28 Twistor methods (7 articles)
  - 53C29 Issues of holonomy (10 articles)
  - 53C30 Homogeneous manifolds (88 articles)
  - 53C35 Symmetric spaces (44 articles)
  - 53C38 Calibrations and calibrated geometries
  - 53C40 Global submanifolds (82 articles)
  - 53C42 Immersions (minimal, prescribed curvature, tight, etc.) (59 articles)
  - 53C43 Differential geometric aspects of harmonic maps (16 articles)
  - 53C44 Geometric evolution equations (mean curvature flow) (13 articles)
  - 53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov) (26 articles)
  - 53C50 Lorentz manifolds, manifolds with indefinite metrics (48 articles)
  - 53C55 Hermitian and Kählerian manifolds (33 articles)
  - 53C56 Other complex differential geometry (7 articles)
  - 53C60 Finsler spaces and generalizations (areal metrics) (28 articles)
  - 53C65 Integral geometry (19 articles)
  - 53C70 Direct methods ($G$-spaces of Busemann, etc.) (4 articles)
  - 53C75 Geometric orders, order geometry (4 articles)
  - 53C80 Applications to physics (36 articles)
  - 53C99 None of the above, but in this section (2 articles)
- 53Dxx Symplectic geometry, contact geometry (114 articles)
  - 53Dxx Symplectic geometry, contact geometry (1 articles)
  - 53D05 Symplectic manifolds, general (26 articles)
  - 53D10 Contact manifolds, general (17 articles)
  - 53D12 Lagrangian submanifolds; Maslov index (4 articles)
  - 53D15 Almost contact and almost symplectic manifolds (14 articles)
  - 53D17 Poisson manifolds (22 articles)
  - 53D20 Momentum maps; symplectic reduction (1 articles)
  - 53D22 Canonical transformations
  - 53D25 Geodesic flows (4 articles)
  - 53D30 Symplectic structures of moduli spaces (1 articles)
  - 53D35 Global theory of symplectic and contact manifolds (5 articles)
  - 53D40 Floer homology and cohomology, symplectic aspects
  - 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (3 articles)
  - 53D50 Geometric quantization (10 articles)
  - 53D55 Deformation quantization, star products (4 articles)
  - 53D99 None of the above, but in this section (2 articles)
- 53Z05 Applications to physics (16 articles)
54 General topology (4885 articles)
- 54 General topology
- 54-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (5 articles)
- 54-01 Instructional exposition (textbooks, tutorial papers, etc.) (9 articles)
- 54-02 Research exposition (monographs, survey articles) (8 articles)
- 54-03 Historical (must also be assigned at least one classification number from Section 01) (4 articles)
- 54-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 54-06 Proceedings, conferences, collections, etc. (1 articles)
- 54.0 (1940-1958) General topology
- 54.00 (1959-1972) General (21 articles)
- 54.10 (1959-1972) Axiomatics, generalizations of topological spaces, syntopogenous spaces (8 articles)
- 54.20 (1959-1972) Topological spaces, general (21 articles)
- 54.22 (1959-1972) Convergence notions (7 articles)
- 54.23 (1959-1972) Separation axioms, $T_i$-spaces (1 articles)
- 54.25 (1959-1972) General constructs (products, quotients, limits, etc.) (6 articles)
- 54.28 (1959-1972) Function spaces (2 articles)
- 54.30 (1959-1972) Uniform structures, proximity spaces (14 articles)
- 54.35 (1959-1972) Metric spaces, metrizability (8 articles)
- 54.38 (1959-1972) Moore spaces
- 54.40 (1959-1972) Countability conditions, separability, Lindel"of spaces (2 articles)
- 54.50 (1959-1972) Paracompact spaces (4 articles)
- 54.52 (1959-1972) Compactness, local compactness, generalizations (3 articles)
- 54.53 (1959-1972) Compactifications, other extensions (5 articles)
- 54.55 (1959-1972) Connectedness, continua (9 articles)
- 54.56 (1959-1972) Ordered topological spaces (2 articles)
- 54.60 (1959-1972) Mappings (12 articles)
- 54.65 (1959-1972) Set-valued mappings
- 54.70 (1959-1972) Dimension theory (8 articles)
- 54.75 (1959-1972) Topology of $E_2$, 2-manifolds (1 articles)
- 54.78 (1959-1972) Topology of $E_n$, $n$-manifolds $(ngeq 2)$ (2 articles)
- 54.80 (1959-1972) Transformation groups and semigroups (11 articles)
- 54.82 (1959-1972) Topological dynamics (7 articles)
- 54.85 (1959-1972) Fixed-point theorems, coincidence theorems, etc. (3 articles)
- 54.99 (1959-1972) None of the above, but in this section (3 articles)
- 54Axx Generalities (702 articles)
  - 54Axx Generalities (13 articles)
  - 54A05 Topological spaces and generalizations (closure spaces, etc.) (114 articles)
  - 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (57 articles)
  - 54A15 Syntopogeneous structures (3 articles)
  - 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) (133 articles)
  - 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) (222 articles)
  - 54A35 Consistency and independence results (78 articles)
  - 54A40 Fuzzy topology (55 articles)
  - 54A99 None of the above, but in this section (27 articles)
- 54Bxx Basic constructions (417 articles)
  - 54Bxx Basic constructions (5 articles)
  - 54B05 Subspaces (34 articles)
  - 54B10 Product spaces (144 articles)
  - 54B15 Quotient spaces, decompositions (29 articles)
  - 54B17 Adjunction spaces and similar constructions (4 articles)
  - 54B20 Hyperspaces (60 articles)
  - 54B30 Categorical methods (97 articles)
  - 54B35 Spectra (18 articles)
  - 54B40 Presheaves and sheaves (7 articles)
  - 54B99 None of the above, but in this section (19 articles)
- 54Cxx Maps and general types of spaces defined by maps (946 articles)
  - 54Cxx Maps and general types of spaces defined by maps (5 articles)
  - 54C05 Continuous maps (79 articles)
  - 54C08 Weak and generalized continuity (67 articles)
  - 54C10 Special maps on topological spaces (open, closed, perfect, etc.) (156 articles)
  - 54C15 Retraction (13 articles)
  - 54C20 Extension of maps (55 articles)
  - 54C25 Embedding (35 articles)
  - 54C30 Real-valued functions (85 articles)
  - 54C35 Function spaces (125 articles)
  - 54C40 Algebraic properties of function spaces (46 articles)
  - 54C45 $C$- and $C^*$-embedding (19 articles)
  - 54C50 Special sets defined by functions (47 articles)
  - 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (19 articles)
  - 54C56 Shape theory (16 articles)
  - 54C60 Set-valued maps (106 articles)
  - 54C65 Selections (36 articles)
  - 54C70 Entropy (12 articles)
  - 54C99 None of the above, but in this section (25 articles)
- 54Dxx Fairly general properties (1037 articles)
  - 54Dxx Fairly general properties (8 articles)
  - 54D05 Connected and locally connected spaces (general aspects) (44 articles)
  - 54D10 Lower separation axioms ($T_0$--$T_3$, etc.) (63 articles)
  - 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (91 articles)
  - 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) (195 articles)
  - 54D25 ``$P$-minimal'' and ``$P$-closed'' spaces (17 articles)
  - 54D30 Compactness (173 articles)
  - 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) (131 articles)
  - 54D40 Remainders (42 articles)
  - 54D45 Local compactness, $sigma$-compactness (24 articles)
  - 54D50 $k$-spaces (13 articles)
  - 54D55 Sequential spaces (100 articles)
  - 54D60 Realcompactness and realcompactification (33 articles)
  - 54D65 Separability (16 articles)
  - 54D70 Base properties (12 articles)
  - 54D80 Special constructions of spaces (spaces of ultrafilters, etc.) (31 articles)
  - 54D99 None of the above, but in this section (44 articles)
- 54Exx Spaces with richer structures (606 articles)
  - 54Exx Spaces with richer structures (10 articles)
  - 54E05 Proximity structures and generalizations (24 articles)
  - 54E15 Uniform structures and generalizations (198 articles)
  - 54E17 Nearness spaces (8 articles)
  - 54E18 $p$-spaces, $M$-spaces, $sigma$-spaces, etc. (14 articles)
  - 54E20 Stratifiable spaces, cosmic spaces, etc. (20 articles)
  - 54E25 Semimetric spaces (8 articles)
  - 54E30 Moore spaces (11 articles)
  - 54E35 Metric spaces, metrizability (105 articles)
  - 54E40 Special maps on metric spaces (38 articles)
  - 54E45 Compact (locally compact) metric spaces (27 articles)
  - 54E50 Complete metric spaces (35 articles)
  - 54E52 Baire category, Baire spaces (42 articles)
  - 54E55 Bitopologies (17 articles)
  - 54E70 Probabilistic metric spaces (7 articles)
  - 54E99 None of the above, but in this section (42 articles)
- 54Fxx Special properties (281 articles)
  - 54Fxx Special properties
  - 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (87 articles)
  - 54F15 Continua and generalizations (51 articles)
  - 54F35 Higher-dimensional local connectedness (1 articles)
  - 54F45 Dimension theory (61 articles)
  - 54F50 Spaces of dimension $leq 1$; curves, dendrites (35 articles)
  - 54F55 Unicoherence, multicoherence (3 articles)
  - 54F65 Topological characterizations of particular spaces (22 articles)
  - 54F99 None of the above, but in this section (21 articles)
- 54Gxx Peculiar spaces (179 articles)
  - 54Gxx Peculiar spaces (3 articles)
  - 54G05 Extremally disconnected spaces, $F$-spaces, etc. (39 articles)
  - 54G10 $P$-spaces (22 articles)
  - 54G12 Scattered spaces (12 articles)
  - 54G15 Pathological spaces (17 articles)
  - 54G20 Counterexamples (69 articles)
  - 54G99 None of the above, but in this section (17 articles)
- 54Hxx Connections with other structures, applications (510 articles)
  - 54Hxx Connections with other structures, applications (20 articles)
  - 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (89 articles)
  - 54H10 Topological representations of algebraic systems (25 articles)
  - 54H11 Topological groups (70 articles)
  - 54H12 Topological lattices, etc. (11 articles)
  - 54H13 Topological fields, rings, etc. (12 articles)
  - 54H15 Transformation groups and semigroups (32 articles)
  - 54H20 Topological dynamics (67 articles)
  - 54H25 Fixed-point and coincidence theorems (151 articles)
  - 54H99 None of the above, but in this section (33 articles)
- 54J05 Nonstandard topology (19 articles)
55 Algebraic topology (330 articles)
- 55 Algebraic topology
- 55-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (8 articles)
- 55-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 55-02 Research exposition (monographs, survey articles) (2 articles)
- 55-03 Historical (must also be assigned at least one classification number from Section 01)
- 55-04 Explicit machine computation and programs (not the theory of computation or programming)
- 55-06 Proceedings, conferences, collections, etc.
- 55.0 (1940-1958) Algebraic topology
- 55.00 (1959-1972) General (2 articles)
- 55.10 (1959-1972) Graphs, map-coloring (5 articles)
- 55.20 (1959-1972) Knots, links (1 articles)
- 55.25 (1959-1972) Cell-complexes, simplicial complexes (1 articles)
- 55.30 (1959-1972) Homology and cohomology theories; $K$-theory (4 articles)
- 55.32 (1959-1972) Sheaves
- 55.34 (1959-1972) Cohomology operations, Steenrod algebra
- 55.36 (1959-1972) Periodic transformations, fixed points, coincidences (Smith theory) (3 articles)
- 55.38 (1959-1972) Dimension theory (1 articles)
- 55.40 (1959-1972) Homotopy theory, general (1 articles)
- 55.42 (1959-1972) Algebra of mappings (including cohomotopy groups)
- 55.45 (1959-1972) Computation of homotopy groups
- 55.50 (1959-1972) Fiber spaces
- 55.52 (1959-1972) Spectral sequences
- 55.60 (1959-1972) Manifolds
- 55.66 (1959-1972) Generalized manifolds, local homology (1 articles)
- 55.68 (1959-1972) Homotopy manifolds
- 55.70 (1959-1972) Imbedding, immersion
- 55.99 (1959-1972) None of the above, but in this section
- 55Mxx Classical topics (59 articles)
  - 55Mxx Classical topics (4 articles)
  - 55M05 Duality (5 articles)
  - 55M10 Dimension theory (5 articles)
  - 55M15 Absolute neighborhood retracts (4 articles)
  - 55M20 Fixed points and coincidences (25 articles)
  - 55M25 Degree, winding number (12 articles)
  - 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space (3 articles)
  - 55M35 Finite groups of transformations (including Smith theory)
  - 55M99 None of the above, but in this section (1 articles)
- 55Nxx Homology and cohomology theories (52 articles)
  - 55Nxx Homology and cohomology theories (2 articles)
  - 55N05 Cech types (18 articles)
  - 55N07 Steenrod-Sitnikov homologies
  - 55N10 Singular theory (2 articles)
  - 55N15 $K$-theory (6 articles)
  - 55N20 Generalized (extraordinary) homology and cohomology theories (1 articles)
  - 55N22 Bordism and cobordism theories, formal group laws
  - 55N25 Homology with local coefficients, equivariant cohomology (2 articles)
  - 55N30 Sheaf cohomology (4 articles)
  - 55N33 Intersection homology and cohomology (1 articles)
  - 55N34 Elliptic cohomology
  - 55N35 Other homology theories (9 articles)
  - 55N40 Axioms for homology theory and uniqueness theorems (1 articles)
  - 55N45 Products and intersections
  - 55N91 Equivariant homology and cohomology (5 articles)
  - 55N99 None of the above, but in this section (1 articles)
- 55Pxx Homotopy theory (54 articles)
  - 55Pxx Homotopy theory
  - 55P05 Homotopy extension properties, cofibrations (1 articles)
  - 55P10 Homotopy equivalences (4 articles)
  - 55P15 Classification of homotopy type (4 articles)
  - 55P20 Eilenberg-Mac Lane spaces
  - 55P25 Spanier-Whitehead duality
  - 55P30 Eckmann-Hilton duality
  - 55P35 Loop spaces (4 articles)
  - 55P40 Suspensions
  - 55P42 Stable homotopy theory, spectra (3 articles)
  - 55P43 Spectra with additional structure ($E_infty$, $A_infty$, ring spectra, etc.)
  - 55P45 $
  - 55P47 Infinite loop spaces (1 articles)
  - 55P48 Loop space machines, operads (10 articles)
  - 55P55 Shape theory (6 articles)
  - 55P57 Proper homotopy theory
  - 55P60 Localization and completion (1 articles)
  - 55P62 Rational homotopy theory (12 articles)
  - 55P65 Homotopy functors (1 articles)
  - 55P91 Equivariant homotopy theory (1 articles)
  - 55P92 Relations between equivariant and nonequivariant homotopy theory
  - 55P99 None of the above, but in this section (6 articles)
- 55Qxx Homotopy groups (11 articles)
  - 55Qxx Homotopy groups
  - 55Q05 Homotopy groups, general; sets of homotopy classes (3 articles)
  - 55Q07 Shape groups (1 articles)
  - 55Q10 Stable homotopy groups
  - 55Q15 Whitehead products and generalizations (2 articles)
  - 55Q20 Homotopy groups of wedges, joins, and simple spaces
  - 55Q25 Hopf invariants (1 articles)
  - 55Q35 Operations in homotopy groups
  - 55Q40 Homotopy groups of spheres
  - 55Q45 Stable homotopy of spheres
  - 55Q50 $J$-morphism
  - 55Q51 $v_n$-periodicity
  - 55Q52 Homotopy groups of special spaces (2 articles)
  - 55Q55 Cohomotopy groups
  - 55Q70 Homotopy groups of special types (2 articles)
  - 55Q91 Equivariant homotopy groups
  - 55Q99 None of the above, but in this section
- 55Rxx Fiber spaces and bundles (87 articles)
  - 55Rxx Fiber spaces and bundles
  - 55R05 Fiber spaces (8 articles)
  - 55R10 Fiber bundles (25 articles)
  - 55R12 Transfer
  - 55R15 Classification (3 articles)
  - 55R20 Spectral sequences and homology of fiber spaces (3 articles)
  - 55R25 Sphere bundles and vector bundles (17 articles)
  - 55R35 Classifying spaces of groups and $ (1 articles)
  - 55R37 Maps between classifying spaces
  - 55R40 Homology of classifying spaces, characteristic classes (11 articles)
  - 55R45 Homology and homotopy of $B (1 articles)
  - 55R50 Stable classes of vector space bundles, $K$-theory (3 articles)
  - 55R55 Fiberings with singularities
  - 55R60 Microbundles and block bundles
  - 55R65 Generalizations of fiber spaces and bundles (9 articles)
  - 55R70 Fibrewise topology
  - 55R80 Discriminantal varieties, configuration spaces (2 articles)
  - 55R91 Equivariant fiber spaces and bundles (2 articles)
  - 55R99 None of the above, but in this section (2 articles)
- 55Sxx Operations and obstructions (15 articles)
  - 55Sxx Operations and obstructions
  - 55S05 Primary cohomology operations (1 articles)
  - 55S10 Steenrod algebra (1 articles)
  - 55S12 Dyer-Lashof operations
  - 55S15 Symmetric products, cyclic products
  - 55S20 Secondary and higher cohomology operations
  - 55S25 $K$-theory operations and generalized cohomology operations (1 articles)
  - 55S30 Massey products (1 articles)
  - 55S35 Obstruction theory (3 articles)
  - 55S36 Extension and compression of mappings
  - 55S37 Classification of mappings (2 articles)
  - 55S40 Sectioning fiber spaces and bundles (3 articles)
  - 55S45 Postnikov systems, $k$-invariants
  - 55S91 Equivariant operations and obstructions (1 articles)
  - 55S99 None of the above, but in this section (2 articles)
- 55Txx Spectral sequences (6 articles)
  - 55Txx Spectral sequences
  - 55T05 General (1 articles)
  - 55T10 Serre spectral sequences (3 articles)
  - 55T15 Adams spectral sequences
  - 55T20 Eilenberg-Moore spectral sequences
  - 55T25 Generalized cohomology
  - 55T99 None of the above, but in this section (2 articles)
- 55Uxx Applied homological algebra and category theory (17 articles)
  - 55Uxx Applied homological algebra and category theory
  - 55U05 Abstract complexes (1 articles)
  - 55U10 Simplicial sets and complexes (2 articles)
  - 55U15 Chain complexes (6 articles)
  - 55U20 Universal coefficient theorems, Bockstein operator
  - 55U25 Homology of a product, Künneth formula
  - 55U30 Duality
  - 55U35 Abstract and axiomatic homotopy theory (5 articles)
  - 55U40 Topological categories, foundations of homotopy theory (2 articles)
  - 55U99 None of the above, but in this section (1 articles)
56 (1940-1958) Topology
- 56 (1940-1958) Topology
- 56.0 (1940-1958) Topology
57 Manifolds and cell complexes (337 articles)
- 57 Manifolds and cell complexes
- 57-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 57-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 57-02 Research exposition (monographs, survey articles) (1 articles)
- 57-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 57-04 Explicit machine computation and programs (not the theory of computation or programming)
- 57-06 Proceedings, conferences, collections, etc.
- 57.00 (1959-1972) General
- 57.01 (1959-1972) Topological manifolds, combinatorial manifolds
- 57.05 (1959-1972) Geometric topology (1 articles)
- 57.10 (1959-1972) Differentiable structures, cobordism
- 57.20 (1959-1972) Differentiable mappings, imbeddings, immersions, diffeomorphisms (2 articles)
- 57.30 (1959-1972) Fiber bundles, vector bundles (1 articles)
- 57.31 (1959-1972) Topology of differentiable manifolds
- 57.32 (1959-1972) Characteristic classes
- 57.34 (1959-1972) Topology of vector and tensor fields
- 57.36 (1959-1972) Foliations (1 articles)
- 57.40 (1959-1972) Topology of Lie groups
- 57.45 (1959-1972) Topology of homogeneous spaces
- 57.47 (1959-1972) Transformation groups
- 57.48 (1959-1972) Differentiable dynamical systems (2 articles)
- 57.50 (1959-1972) Analysis on differentiable manifolds (1 articles)
- 57.55 (1959-1972) Infinite-dimensional manifolds (1 articles)
- 57.60 (1959-1972) Complex manifolds
- 57.70 (1959-1972) Infinite Lie groups, deformations (2 articles)
- 57.99 (1959-1972) None of the above, but in this section
- 57Mxx Low-dimensional topology (43 articles)
 - 57Mxx Low-dimensional topology
 - 57M05 Fundamental group, presentations, free differential calculus (2 articles)
 - 57M07 Topological methods in group theory (5 articles)
 - 57M10 Covering spaces (3 articles)
 - 57M12 Special coverings, e.g. branched (1 articles)
 - 57M15 Relations with graph theory (8 articles)
 - 57M20 Two-dimensional complexes (5 articles)
 - 57M25 Knots and links in $S^3$ (11 articles)
 - 57M27 Invariants of knots and 3-manifolds (1 articles)
 - 57M30 Wild knots and surfaces, etc., wild embeddings
 - 57M35 Dehn's lemma, sphere theorem, loop theorem, asphericity (1 articles)
 - 57M40 Characterizations of $E^3$ and $S^3$ (Poincaré conjecture)
 - 57M50 Geometric structures on low-dimensional manifolds (1 articles)
 - 57M60 Group actions in low dimensions (3 articles)
 - 57M99 None of the above, but in this section (2 articles)
- 57Nxx Topological manifolds (74 articles)
 - 57Nxx Topological manifolds (3 articles)
 - 57N05 Topology of $E^2$, $2$-manifolds (6 articles)
 - 57N10 Topology of general $3$-manifolds (3 articles)
 - 57N12 Topology of $E^3$ and $S^3$
 - 57N13 Topology of $E^4$, $4$-manifolds (3 articles)
 - 57N15 Topology of $E^n$, $n$-manifolds ($4 < n < infty$) (6 articles)
 - 57N16 Geometric structures on manifolds (1 articles)
 - 57N17 Topology of topological vector spaces (6 articles)
 - 57N20 Topology of infinite-dimensional manifolds (17 articles)
 - 57N25 Shapes (1 articles)
 - 57N30 Engulfing
 - 57N35 Embeddings and immersions (4 articles)
 - 57N37 Isotopy and pseudo-isotopy
 - 57N40 Neighborhoods of submanifolds
 - 57N45 Flatness and tameness (1 articles)
 - 57N50 $S^ (4 articles)
 - 57N55 Microbundles and block bundles (1 articles)
 - 57N60 Cellularity
 - 57N65 Algebraic topology of manifolds (10 articles)
 - 57N70 Cobordism and concordance (1 articles)
 - 57N75 General position and transversality (2 articles)
 - 57N80 Stratifications
 - 57N99 None of the above, but in this section (5 articles)
- 57Pxx Generalized manifolds (2 articles)
 - 57Pxx Generalized manifolds
 - 57P05 Local properties of generalized manifolds
 - 57P10 Poincaré duality spaces
 - 57P99 None of the above, but in this section (2 articles)
- 57Qxx PL-topology (16 articles)
 - 57Qxx PL-topology
 - 57Q05 General topology of complexes (7 articles)
 - 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (1 articles)
 - 57Q12 Wall finiteness obstruction for CW-complexes
 - 57Q15 Triangulating manifolds (1 articles)
 - 57Q20 Cobordism
 - 57Q25 Comparison of PL-structures: classification, Hauptvermutung (2 articles)
 - 57Q30 Engulfing
 - 57Q35 Embeddings and immersions (2 articles)
 - 57Q37 Isotopy
 - 57Q40 Regular neighborhoods
 - 57Q45 Knots and links (in high dimensions) (2 articles)
 - 57Q50 Microbundles and block bundles
 - 57Q55 Approximations (1 articles)
 - 57Q60 Cobordism and concordance
 - 57Q65 General position and transversality
 - 57Q91 Equivariant PL-topology
 - 57Q99 None of the above, but in this section
- 57Rxx Differential topology (143 articles)
 - 57Rxx Differential topology
 - 57R05 Triangulating
 - 57R10 Smoothing (2 articles)
 - 57R12 Smooth approximations (1 articles)
 - 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (6 articles)
 - 57R17 Symplectic and contact topology (5 articles)
 - 57R19 Algebraic topology on manifolds (11 articles)
 - 57R20 Characteristic classes and numbers (28 articles)
 - 57R22 Topology of vector bundles and fiber bundles (13 articles)
 - 57R25 Vector fields, frame fields (18 articles)
 - 57R27 Controllability of vector fields on $C^infty$ and real-analytic manifolds
 - 57R30 Foliations; geometric theory (20 articles)
 - 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology (2 articles)
 - 57R35 Differentiable mappings (3 articles)
 - 57R40 Embeddings (2 articles)
 - 57R42 Immersions (4 articles)
 - 57R45 Singularities of differentiable mappings (3 articles)
 - 57R50 Diffeomorphisms (2 articles)
 - 57R52 Isotopy (1 articles)
 - 57R55 Differentiable structures (1 articles)
 - 57R56 Topological quantum field theories (1 articles)
 - 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants (2 articles)
 - 57R58 Floer homology
 - 57R60 Homotopy spheres, Poincaré conjecture (2 articles)
 - 57R65 Surgery and handlebodies (3 articles)
 - 57R67 Surgery obstructions, Wall groups (2 articles)
 - 57R70 Critical points and critical submanifolds (5 articles)
 - 57R75 O- and SO-cobordism
 - 57R77 Complex cobordism (U- and SU-cobordism)
 - 57R80 $h$- and $s$-cobordism (1 articles)
 - 57R85 Equivariant cobordism
 - 57R90 Other types of cobordism (1 articles)
 - 57R91 Equivariant algebraic topology of manifolds
 - 57R95 Realizing cycles by submanifolds
 - 57R99 None of the above, but in this section (4 articles)
- 57Sxx Topological transformation groups (23 articles)
 - 57Sxx Topological transformation groups
 - 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms (5 articles)
 - 57S10 Compact groups of homeomorphisms (2 articles)
 - 57S15 Compact Lie groups of differentiable transformations (3 articles)
 - 57S17 Finite transformation groups (2 articles)
 - 57S20 Noncompact Lie groups of transformations (3 articles)
 - 57S25 Groups acting on specific manifolds (4 articles)
 - 57S30 Discontinuous groups of transformations (2 articles)
 - 57S99 None of the above, but in this section (2 articles)
- 57Txx Homology and homotopy of topological groups and related structures (20 articles)
 - 57Txx Homology and homotopy of topological groups and related structures
 - 57T05 Hopf algebras (3 articles)
 - 57T10 Homology and cohomology of Lie groups (4 articles)
 - 57T15 Homology and cohomology of homogeneous spaces of Lie groups (8 articles)
 - 57T20 Homotopy groups of topological groups and homogeneous spaces (2 articles)
 - 57T25 Homology and cohomology of $
 - 57T30 Bar and cobar constructions
 - 57T35 Applications of Eilenberg-Moore spectral sequences
 - 57T99 None of the above, but in this section (3 articles)
58 Global analysis, analysis on manifolds (1063 articles)
- 58 Global analysis, analysis on manifolds
- 58-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 58-01 Instructional exposition (textbooks, tutorial papers, etc.) (2 articles)
- 58-02 Research exposition (monographs, survey articles) (1 articles)
- 58-03 Historical (must also be assigned at least one classification number from Section 01)
- 58-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 58-06 Proceedings, conferences, collections, etc.
- 58Axx General theory of differentiable manifolds (493 articles)
  - 58Axx General theory of differentiable manifolds (6 articles)
  - 58A03 Topos-theoretic approach to differentiable manifolds (2 articles)
  - 58A05 Differentiable manifolds, foundations (34 articles)
  - 58A07 Real-analytic and Nash manifolds
  - 58A10 Differential forms (45 articles)
  - 58A12 de Rham theory (16 articles)
  - 58A14 Hodge theory (4 articles)
  - 58A15 Exterior differential systems (Cartan theory) (16 articles)
  - 58A17 Pfaffian systems (14 articles)
  - 58A20 Jets (215 articles)
  - 58A25 Currents (3 articles)
  - 58A30 Vector distributions (subbundles of the tangent bundles) (21 articles)
  - 58A32 Natural bundles (79 articles)
  - 58A35 Stratified sets (2 articles)
  - 58A40 Differential spaces (11 articles)
  - 58A50 Supermanifolds and graded manifolds (15 articles)
  - 58A99 None of the above, but in this section (10 articles)
- 58Bxx Infinite-dimensional manifolds (46 articles)
  - 58Bxx Infinite-dimensional manifolds
  - 58B05 Homotopy and topological questions (6 articles)
  - 58B10 Differentiability questions (8 articles)
  - 58B12 Questions of holomorphy
  - 58B15 Fredholm structures (4 articles)
  - 58B20 Riemannian, Finsler and other geometric structures (12 articles)
  - 58B25 Group structures and generalizations on infinite-dimensional manifolds (7 articles)
  - 58B32 Geometry of quantum groups (1 articles)
  - 58B34 Noncommutative geometry (à la Connes) (3 articles)
  - 58B99 None of the above, but in this section (5 articles)
- 58Cxx Calculus on manifolds; nonlinear operators (134 articles)
  - 58Cxx Calculus on manifolds; nonlinear operators (1 articles)
  - 58C05 Real-valued functions (8 articles)
  - 58C06 Set valued and function-space valued mappings (5 articles)
  - 58C07 Continuity properties of mappings (4 articles)
  - 58C10 Holomorphic maps (2 articles)
  - 58C15 Implicit function theorems; global Newton methods (18 articles)
  - 58C20 Differentiation theory (Gateaux, Fréchet, etc.) (40 articles)
  - 58C25 Differentiable maps (19 articles)
  - 58C30 Fixed point theorems on manifolds (10 articles)
  - 58C35 Integration on manifolds; measures on manifolds (6 articles)
  - 58C40 Spectral theory; eigenvalue problems (9 articles)
  - 58C50 Analysis on supermanifolds or graded manifolds (4 articles)
  - 58C99 None of the above, but in this section (8 articles)
- 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx) (38 articles)
  - 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
  - 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds (9 articles)
  - 58D07 Groups and semigroups of nonlinear operators
  - 58D10 Spaces of imbeddings and immersions (2 articles)
  - 58D15 Manifolds of mappings (8 articles)
  - 58D17 Manifolds of metrics (esp. Riemannian)
  - 58D19 Group actions and symmetry properties (1 articles)
  - 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps
  - 58D25 Equations in function spaces; evolution equations (8 articles)
  - 58D27 Moduli problems for differential geometric structures (2 articles)
  - 58D29 Moduli problems for topological structures (1 articles)
  - 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.) (5 articles)
  - 58D99 None of the above, but in this section (2 articles)
- 58Exx Variational problems in infinite-dimensional spaces (174 articles)
  - 58Exx Variational problems in infinite-dimensional spaces (1 articles)
  - 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.) (35 articles)
  - 58E07 Abstract bifurcation theory (15 articles)
  - 58E09 Group-invariant bifurcation theory (1 articles)
  - 58E10 Applications to the theory of geodesics (problems in one independent variable) (3 articles)
  - 58E11 Critical metrics
  - 58E12 Applications to minimal surfaces (problems in two independent variables) (5 articles)
  - 58E15 Application to extremal problems in several variables; Yang-Mills functionals (12 articles)
  - 58E17 Pareto optimality, etc., applications to economics
  - 58E20 Harmonic maps (20 articles)
  - 58E25 Applications to control theory (4 articles)
  - 58E30 Variational principles (48 articles)
  - 58E35 Variational inequalities (global problems) (13 articles)
  - 58E40 Group actions (1 articles)
  - 58E50 Applications (8 articles)
  - 58E99 None of the above, but in this section (8 articles)
- 58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds (37 articles)
  - 58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
  - 58H05 Pseudogroups and differentiable groupoids (24 articles)
  - 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (7 articles)
  - 58H15 Deformations of structures (1 articles)
  - 58H99 None of the above, but in this section (5 articles)
- 58Jxx Partial differential equations on manifolds; differential operators (118 articles)
  - 58Jxx Partial differential equations on manifolds; differential operators (5 articles)
  - 58J05 Elliptic equations on manifolds, general theory (9 articles)
  - 58J10 Differential complexes (17 articles)
  - 58J15 Relations with hyperfunctions
  - 58J20 Index theory and related fixed point theorems (6 articles)
  - 58J22 Exotic index theories
  - 58J26 Elliptic genera
  - 58J28 Eta-invariants, Chern-Simons invariants (1 articles)
  - 58J30 Spectral flows
  - 58J32 Boundary value problems on manifolds (4 articles)
  - 58J35 Heat and other parabolic equation methods (10 articles)
  - 58J37 Perturbations; asymptotics (1 articles)
  - 58J40 Pseudodifferential and Fourier integral operators on manifolds (2 articles)
  - 58J42 Noncommutative global analysis, noncommutative residues
  - 58J45 Hyperbolic equations (3 articles)
  - 58J47 Propagation of singularities; initial value problems (2 articles)
  - 58J50 Spectral problems; spectral geometry; scattering theory (17 articles)
  - 58J52 Determinants and determinant bundles, analytic torsion (2 articles)
  - 58J53 Isospectrality
  - 58J55 Bifurcation (1 articles)
  - 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.) (12 articles)
  - 58J65 Diffusion processes and stochastic analysis on manifolds (4 articles)
  - 58J70 Invariance and symmetry properties (14 articles)
  - 58J72 Correspondences and other transformation methods (e.g. Lie-Bäcklund) (2 articles)
  - 58J90 Applications (1 articles)
  - 58J99 None of the above, but in this section (5 articles)
- 58Kxx Theory of singularities and catastrophe theory (14 articles)
  - 58Kxx Theory of singularities and catastrophe theory
  - 58K05 Critical points of functions and mappings (1 articles)
  - 58K10 Monodromy
  - 58K15 Topological properties of mappings
  - 58K20 Algebraic and analytic properties of mappings (1 articles)
  - 58K25 Stability (1 articles)
  - 58K30 Global theory
  - 58K35 Catastrophe theory (3 articles)
  - 58K40 Classification; finite determinacy of map germs
  - 58K45 Singularities of vector fields, topological aspects
  - 58K50 Normal forms
  - 58K55 Asymptotic behavior
  - 58K60 Deformation of singularities
  - 58K65 Topological invariants (3 articles)
  - 58K70 Symmetries, equivariance
  - 58K99 None of the above, but in this section (5 articles)
- 58Z05 Applications to physics (5 articles)
60 Probability theory and stochastic processes (1411 articles)
- 60 Probability theory and stochastic processes
- 60-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (6 articles)
- 60-01 Instructional exposition (textbooks, tutorial papers, etc.) (5 articles)
- 60-02 Research exposition (monographs, survey articles) (1 articles)
- 60-03 Historical (must also be assigned at least one classification number from Section 01) (15 articles)
- 60-04 Explicit machine computation and programs (not the theory of computation or programming)
- 60-06 Proceedings, conferences, collections, etc. (1 articles)
- 60-08 Computational methods (not classified at a more specific level) [See also 65C50] (3 articles)
- 60.0 (1940-1958) Probability
- 60.00 (1959-1972) General (14 articles)
- 60.02 (1959-1972) Axioms, foundations
- 60.05 (1959-1972) Probabilistic measure theory
- 60.08 (1959-1972) Probability in topological groups, other structures
- 60.1 (1940-1958) Applications of the theory of probability, economics
- 60.10 (1959-1972) Combinatorial probability
- 60.15 (1959-1972) Geometric probability
- 60.20 (1959-1972) Distributions, characteristic functions (2 articles)
- 60.30 (1959-1972) Limit theorems
- 60.40 (1959-1972) Stochastic processes, general theory (5 articles)
- 60.50 (1959-1972) Stationary processes
- 60.60 (1959-1972) Markov processes, general (2 articles)
- 60.62 (1959-1972) Hunt processes, diffusion processes, Brownian motion, probabilistic potential theory (3 articles)
- 60.65 (1959-1972) Markov chains (4 articles)
- 60.66 (1959-1972) Random walks
- 60.67 (1959-1972) Branching processes; Galton-Watson, birth-and-death processes (3 articles)
- 60.69 (1959-1972) Other special processes
- 60.70 (1959-1972) Renewal theory
- 60.75 (1959-1972) Stochastic differential and integral equations (9 articles)
- 60.80 (1959-1972) Queueing, congestion, allocation, storage (2 articles)
- 60.90 (1959-1972) Other applications
- 60.99 (1959-1972) None of the above, but in this section
- 60Axx Foundations of probability theory (88 articles)
  - 60Axx Foundations of probability theory
  - 60A05 Axioms; other general questions (30 articles)
  - 60A10 Probabilistic measure theory (34 articles)
  - 60A99 None of the above, but in this section (24 articles)
- 60Bxx Probability theory on algebraic and topological structures (112 articles)
  - 60Bxx Probability theory on algebraic and topological structures (3 articles)
  - 60B05 Probability measures on topological spaces (30 articles)
  - 60B10 Convergence of probability measures (29 articles)
  - 60B11 Probability theory on linear topological spaces (8 articles)
  - 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) (15 articles)
  - 60B15 Probability measures on groups, Fourier transforms, factorization (9 articles)
  - 60B99 None of the above, but in this section (18 articles)
- 60C05 Combinatorial probability (22 articles)
- 60D05 Geometric probability, stochastic geometry, random sets (43 articles)
- 60Exx Distribution theory (150 articles)
  - 60Exx Distribution theory (1 articles)
  - 60E05 Distributions: general theory (81 articles)
  - 60E07 Infinitely divisible distributions; stable distributions (6 articles)
  - 60E10 Characteristic functions; other transforms (11 articles)
  - 60E15 Inequalities; stochastic orderings (31 articles)
  - 60E99 None of the above, but in this section (20 articles)
- 60Fxx Limit theorems (167 articles)
  - 60Fxx Limit theorems (3 articles)
  - 60F05 Central limit and other weak theorems (58 articles)
  - 60F10 Large deviations (5 articles)
  - 60F15 Strong theorems (52 articles)
  - 60F17 Functional limit theorems; invariance principles (12 articles)
  - 60F20 Zero-one laws (4 articles)
  - 60F25 $L^p$-limit theorems (13 articles)
  - 60F99 None of the above, but in this section (20 articles)
- 60Gxx Stochastic processes (336 articles)
  - 60Gxx Stochastic processes (3 articles)
  - 60G05 Foundations of stochastic processes (5 articles)
  - 60G07 General theory of processes (4 articles)
  - 60G09 Exchangeability (5 articles)
  - 60G10 Stationary processes (55 articles)
  - 60G12 General second-order processes (8 articles)
  - 60G15 Gaussian processes (16 articles)
  - 60G17 Sample path properties (3 articles)
  - 60G18 Self-similar processes (3 articles)
  - 60G20 Generalized stochastic processes (6 articles)
  - 60G25 Prediction theory (16 articles)
  - 60G30 Continuity and singularity of induced measures (3 articles)
  - 60G35 Applications (signal detection, filtering, etc.) (41 articles)
  - 60G40 Stopping times; optimal stopping problems; gambling theory (19 articles)
  - 60G42 Martingales with discrete parameter (16 articles)
  - 60G44 Martingales with continuous parameter (11 articles)
  - 60G46 Martingales and classical analysis (5 articles)
  - 60G48 Generalizations of martingales (6 articles)
  - 60G50 Sums of independent random variables; random walks (18 articles)
  - 60G51 Processes with independent increments (3 articles)
  - 60G52 Stable processes (1 articles)
  - 60G55 Point processes (35 articles)
  - 60G57 Random measures (10 articles)
  - 60G60 Random fields (17 articles)
  - 60G70 Extreme value theory; extremal processes (14 articles)
  - 60G99 None of the above, but in this section (13 articles)
- 60Hxx Stochastic analysis (169 articles)
  - 60Hxx Stochastic analysis
  - 60H05 Stochastic integrals (25 articles)
  - 60H07 Stochastic calculus of variations and the Malliavin calculus (5 articles)
  - 60H10 Stochastic ordinary differential equations (60 articles)
  - 60H15 Stochastic partial differential equations (34 articles)
  - 60H20 Stochastic integral equations (5 articles)
  - 60H25 Random operators and equations (12 articles)
  - 60H30 Applications of stochastic analysis (to PDE, etc.) (16 articles)
  - 60H35 Computational methods for stochastic equations (5 articles)
  - 60H40 White noise theory (2 articles)
  - 60H99 None of the above, but in this section (5 articles)
- 60Jxx Markov processes (157 articles)
  - 60Jxx Markov processes (3 articles)
  - 60J05 Markov processes with discrete parameter (17 articles)
  - 60J10 Markov chains with discrete parameter (30 articles)
  - 60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.) (13 articles)
  - 60J22 Computational methods in Markov chains (3 articles)
  - 60J25 Markov processes with continuous parameter (5 articles)
  - 60J27 Markov chains with continuous parameter (15 articles)
  - 60J35 Transition functions, generators and resolvents (8 articles)
  - 60J40 Right processes (1 articles)
  - 60J45 Probabilistic potential theory (5 articles)
  - 60J50 Boundary theory (3 articles)
  - 60J55 Local time and additive functionals (2 articles)
  - 60J57 Multiplicative functionals
  - 60J60 Diffusion processes (13 articles)
  - 60J65 Brownian motion (12 articles)
  - 60J70 Applications of diffusion theory (population genetics, absorption problems, etc.) (2 articles)
  - 60J75 Jump processes (5 articles)
  - 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) (5 articles)
  - 60J85 Applications of branching processes
  - 60J99 None of the above, but in this section (15 articles)
- 60Kxx Special processes (92 articles)
  - 60Kxx Special processes
  - 60K05 Renewal theory (5 articles)
  - 60K10 Applications (reliability, demand theory, etc.) (19 articles)
  - 60K15 Markov renewal processes, semi-Markov processes (2 articles)
  - 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.) (9 articles)
  - 60K25 Queueing theory (21 articles)
  - 60K30 Applications (congestion, allocation, storage, traffic, etc.) (7 articles)
  - 60K35 Interacting random processes; statistical mechanics type models; percolation theory (14 articles)
  - 60K37 Processes in random environments (1 articles)
  - 60K40 Other physical applications of random processes (3 articles)
  - 60K99 None of the above, but in this section (11 articles)
62 Statistics (2450 articles)
- 62 Statistics
- 62-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (19 articles)
- 62-01 Instructional exposition (textbooks, tutorial papers, etc.) (7 articles)
- 62-02 Research exposition (monographs, survey articles) (3 articles)
- 62-03 Historical (must also be assigned at least one classification number from Section 01) (7 articles)
- 62-04 Explicit machine computation and programs (not the theory of computation or programming) (8 articles)
- 62-06 Proceedings, conferences, collections, etc. (2 articles)
- 62-07 Data analysis (5 articles)
- 62-09 Graphical methods (6 articles)
- 62.0 (1940-1958) Statistics
- 62.00 (1959-1972) General (3 articles)
- 62.05 (1959-1972) Foundations: axiomatics, sufficiency, invariance, other general considerations (2 articles)
- 62.1 (1940-1958) Actuarial mathematics
- 62.10 (1959-1972) Distribution theory
- 62.15 (1959-1972) Asymptotic theory (1 articles)
- 62.16 (1959-1972) Exact and asymptotic efficiency
- 62.20 (1959-1972) Estimation: parametric case (1 articles)
- 62.25 (1959-1972) Hypothesis testing; parametric case (1 articles)
- 62.30 (1959-1972) Decision theory (6 articles)
- 62.31 (1959-1972) Ranking and selection
- 62.35 (1959-1972) Bayesian inference
- 62.40 (1959-1972) Multivariate analysis
- 62.41 (1959-1972) Classification and discrimination
- 62.45 (1959-1972) Sequential methods (2 articles)
- 62.50 (1959-1972) Information-theoretic methods (3 articles)
- 62.55 (1959-1972) Linear statistical inference, regression analysis (1 articles)
- 62.56 (1959-1972) Analysis of variance; hierarchical models
- 62.60 (1959-1972) Design and analysis of experiments, general
- 62.61 (1959-1972) Construction of designs
- 62.62 (1959-1972) Optimal designs
- 62.63 (1959-1972) Factorial designs
- 62.64 (1959-1972) Paired and multiple comparisons
- 62.70 (1959-1972) Nonparametric methods
- 62.71 (1959-1972) Goodness-of-fit tests
- 62.75 (1959-1972) Order statistics
- 62.80 (1959-1972) Engineering statistics; life testing and reliability, quality control (1 articles)
- 62.85 (1959-1972) Statistical analysis of stochastic processes; time series (4 articles)
- 62.90 (1959-1972) Sample surveys
- 62.95 (1959-1972) Count data, contingency tables
- 62.97 (1959-1972) Biometrics
- 62.99 (1959-1972) Other applications
- 62A01 Foundational and philosophical topics (13 articles)
- 62Bxx Sufficiency and information (115 articles)
  - 62Bxx Sufficiency and information
  - 62B05 Sufficient statistics and fields (13 articles)
  - 62B10 Information-theoretic topics (88 articles)
  - 62B15 Theory of statistical experiments (8 articles)
  - 62B99 None of the above, but in this section (6 articles)
- 62Cxx Decision theory (57 articles)
  - 62Cxx Decision theory
  - 62C05 General considerations (8 articles)
  - 62C07 Complete class results
  - 62C10 Bayesian problems; characterization of Bayes procedures (20 articles)
  - 62C12 Empirical decision procedures; empirical Bayes procedures (5 articles)
  - 62C15 Admissibility (6 articles)
  - 62C20 Minimax procedures (5 articles)
  - 62C25 Compound decision problems (2 articles)
  - 62C99 None of the above, but in this section (11 articles)
- 62D05 Sampling theory, sample surveys (20 articles)
- 62Exx Distribution theory (180 articles)
  - 62Exx Distribution theory (1 articles)
  - 62E10 Characterization and structure theory (43 articles)
  - 62E15 Exact distribution theory (35 articles)
  - 62E17 Approximations to distributions (nonasymptotic) (16 articles)
  - 62E20 Asymptotic distribution theory (77 articles)
  - 62E99 None of the above, but in this section (8 articles)
- 62Fxx Parametric inference (455 articles)
  - 62Fxx Parametric inference
  - 62F03 Hypothesis testing (49 articles)
  - 62F05 Asymptotic properties of tests (28 articles)
  - 62F07 Ranking and selection (6 articles)
  - 62F10 Point estimation (129 articles)
  - 62F12 Asymptotic properties of estimators (72 articles)
  - 62F15 Bayesian inference (53 articles)
  - 62F25 Tolerance and confidence regions (26 articles)
  - 62F30 Inference under constraints (21 articles)
  - 62F35 Robustness and adaptive procedures (53 articles)
  - 62F40 Bootstrap, jackknife and other resampling methods (9 articles)
  - 62F99 None of the above, but in this section (9 articles)
- 62Gxx Nonparametric inference (288 articles)
  - 62Gxx Nonparametric inference (2 articles)
  - 62G05 Estimation (67 articles)
  - 62G07 Density estimation (24 articles)
  - 62G08 Nonparametric regression (11 articles)
  - 62G09 Resampling methods (9 articles)
  - 62G10 Hypothesis testing (74 articles)
  - 62G15 Tolerance and confidence regions (5 articles)
  - 62G20 Asymptotic properties (44 articles)
  - 62G30 Order statistics; empirical distribution functions (24 articles)
  - 62G32 Statistics of extreme values; tail inference (9 articles)
  - 62G35 Robustness (12 articles)
  - 62G99 None of the above, but in this section (7 articles)
- 62Hxx Multivariate analysis (311 articles)
  - 62Hxx Multivariate analysis (1 articles)
  - 62H05 Characterization and structure theory (45 articles)
  - 62H10 Distribution of statistics (24 articles)
  - 62H11 Directional data; spatial statistics (1 articles)
  - 62H12 Estimation (89 articles)
  - 62H15 Hypothesis testing (27 articles)
  - 62H17 Contingency tables (10 articles)
  - 62H20 Measures of association (correlation, canonical correlation, etc.) (34 articles)
  - 62H25 Factor analysis and principal components; correspondence analysis (11 articles)
  - 62H30 Classification and discrimination; cluster analysis (41 articles)
  - 62H35 Image analysis (2 articles)
  - 62H99 None of the above, but in this section (26 articles)
- 62Jxx Linear inference, regression (318 articles)
  - 62Jxx Linear inference, regression
  - 62J02 General nonlinear regression (55 articles)
  - 62J05 Linear regression (185 articles)
  - 62J07 Ridge regression; shrinkage estimators (5 articles)
  - 62J10 Analysis of variance and covariance (39 articles)
  - 62J12 Generalized linear models (7 articles)
  - 62J15 Paired and multiple comparisons (2 articles)
  - 62J20 Diagnostics (6 articles)
  - 62J99 None of the above, but in this section (19 articles)
- 62Kxx Design of experiments (43 articles)
  - 62Kxx Design of experiments
  - 62K05 Optimal designs (25 articles)
  - 62K10 Block designs (4 articles)
  - 62K15 Factorial designs (3 articles)
  - 62K20 Response surface designs
  - 62K25 Robust parameter designs
  - 62K99 None of the above, but in this section (11 articles)
- 62Lxx Sequential methods (52 articles)
  - 62Lxx Sequential methods (1 articles)
  - 62L05 Sequential design (1 articles)
  - 62L10 Sequential analysis (13 articles)
  - 62L12 Sequential estimation (10 articles)
  - 62L15 Optimal stopping (7 articles)
  - 62L20 Stochastic approximation (15 articles)
  - 62L99 None of the above, but in this section (5 articles)
- 62Mxx Inference from stochastic processes (297 articles)
  - 62Mxx Inference from stochastic processes (1 articles)
  - 62M02 Markov processes: hypothesis testing (7 articles)
  - 62M05 Markov processes: estimation (14 articles)
  - 62M07 Non-Markovian processes: hypothesis testing (13 articles)
  - 62M09 Non-Markovian processes: estimation (27 articles)
  - 62M10 Time series, auto-correlation, regression, etc. (129 articles)
  - 62M15 Spectral analysis (17 articles)
  - 62M20 Prediction (41 articles)
  - 62M30 Spatial processes (14 articles)
  - 62M40 Random fields; image analysis (9 articles)
  - 62M45 Neural nets and related approaches (9 articles)
  - 62M99 None of the above, but in this section (16 articles)
- 62Nxx Survival analysis and censored data (74 articles)
  - 62Nxx Survival analysis and censored data
  - 62N01 Censored data models (10 articles)
  - 62N02 Estimation (10 articles)
  - 62N03 Testing (5 articles)
  - 62N05 Reliability and life testing (43 articles)
  - 62N99 None of the above, but in this section (6 articles)
- 62Pxx Applications (132 articles)
  - 62Pxx Applications (2 articles)
  - 62P05 Applications to actuarial sciences and financial mathematics (28 articles)
  - 62P10 Applications to biology and medical sciences (14 articles)
  - 62P12 Applications to environmental and related topics (5 articles)
  - 62P15 Applications to psychology (13 articles)
  - 62P20 Applications to economics (11 articles)
  - 62P25 Applications to social sciences (3 articles)
  - 62P30 Applications in engineering and industry (33 articles)
  - 62P35 Applications to physics (3 articles)
  - 62P99 None of the above, but in this section (20 articles)
- 62Q05 Statistical tables (13 articles)
65 Numerical analysis (2903 articles)
- 65 Numerical analysis
- 65-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (15 articles)
- 65-01 Instructional exposition (textbooks, tutorial papers, etc.) (5 articles)
- 65-02 Research exposition (monographs, survey articles) (5 articles)
- 65-03 Historical (must also be assigned at least one classification number from Section 01) (7 articles)
- 65-04 Explicit machine computation and programs (not the theory of computation or programming) (8 articles)
- 65-05 Experimental papers (1 articles)
- 65-06 Proceedings, conferences, collections, etc. (16 articles)
- 65.0 (1940-1958) Numerical analysis
- 65.00 (1959-1972) General (3 articles)
- 65.05 (1959-1972) Tables, construction of tables
- 65.1 (1940-1958) Tables
- 65.10 (1959-1972) General mathematical methods: iteration, acceleration of convergence, numerical experiments (8 articles)
- 65.15 (1959-1972) Monte Carlo methods (1 articles)
- 65.2 (1940-1958) Graphical methods, nomography
- 65.20 (1959-1972) Interpolation, smoothing, least squares, curve fitting, approximation of functions
- 65.25 (1959-1972) Computation of special functions, series, integrals
- 65.3 (1940-1958) Numerical methods
- 65.30 (1959-1972) Mathematical programming and optimization techniques (3 articles)
- 65.33 (1959-1972) Linear inequalities
- 65.35 (1959-1972) Linear equations, determinants, matrices
- 65.40 (1959-1972) Eigenvalues, eigenvectors (3 articles)
- 65.49 (1959-1972) Numerical methods for variational problems and optimal control
- 65.50 (1959-1972) Solution of algebraic and transcendental equations and systems (10 articles)
- 65.55 (1959-1972) Numerical differentiation and integration, quadrature, cubature, etc. (2 articles)
- 65.60 (1959-1972) Ordinary differential equations, general
- 65.61 (1959-1972) Initial value problems (1 articles)
- 65.62 (1959-1972) Boundary value problems
- 65.65 (1959-1972) Partial differential equations, general (2 articles)
- 65.66 (1959-1972) Elliptic equations (2 articles)
- 65.67 (1959-1972) Hyperbolic equations (1 articles)
- 65.68 (1959-1972) Parabolic equations (3 articles)
- 65.70 (1959-1972) Difference and functional equations (1 articles)
- 65.75 (1959-1972) Integral and integro-differential equations (1 articles)
- 65.80 (1959-1972) Error analysis (1 articles)
- 65.82 (1959-1972) Miscellaneous inequalities
- 65.85 (1959-1972) Graphical methods (13 articles)
- 65.90 (1959-1972) Harmonic analysis and synthesis
- 65.99 (1959-1972) None of the above, but in this section
- 65A05 Tables (5 articles)
- 65Bxx Acceleration of convergence (31 articles)
 - 65Bxx Acceleration of convergence
 - 65B05 Extrapolation to the limit, deferred corrections (17 articles)
 - 65B10 Summation of series (2 articles)
 - 65B15 Euler-Maclaurin formula (2 articles)
 - 65B99 None of the above, but in this section (10 articles)
- 65Cxx Probabilistic methods, simulation and stochastic differential equations (135 articles)
 - 65Cxx Probabilistic methods, simulation and stochastic differential equations
 - 65C05 Monte Carlo methods (26 articles)
 - 65C10 Random number generation (16 articles)
 - 65C20 Models, numerical methods (14 articles)
 - 65C30 Stochastic differential and integral equations (5 articles)
 - 65C35 Stochastic particle methods (1 articles)
 - 65C40 Computational Markov chains (12 articles)
 - 65C50 Other computational problems in probability (6 articles)
 - 65C60 Computational problems in statistics (36 articles)
 - 65C99 None of the above, but in this section (19 articles)
- 65Dxx Numerical approximation and computational geometry (262 articles)
 - 65Dxx Numerical approximation and computational geometry (2 articles)
 - 65D05 Interpolation (70 articles)
 - 65D07 Splines (37 articles)
 - 65D10 Smoothing, curve fitting (24 articles)
 - 65D15 Algorithms for functional approximation (26 articles)
 - 65D17 Computer aided design (modeling of curves and surfaces) (11 articles)
 - 65D18 Computer graphics and computational geometry (13 articles)
 - 65D20 Computation of special functions, construction of tables (13 articles)
 - 65D25 Numerical differentiation (10 articles)
 - 65D30 Numerical integration (34 articles)
 - 65D32 Quadrature and cubature formulas (13 articles)
 - 65D99 None of the above, but in this section (9 articles)
- 65E05 Numerical methods in complex analysis (potential theory, etc.) (10 articles)
- 65Fxx Numerical linear algebra (287 articles)
 - 65Fxx Numerical linear algebra (6 articles)
 - 65F05 Direct methods for linear systems and matrix inversion (25 articles)
 - 65F10 Iterative methods for linear systems (109 articles)
 - 65F15 Eigenvalues, eigenvectors (42 articles)
 - 65F18 Inverse eigenvalue problems (3 articles)
 - 65F20 Overdetermined systems, pseudoinverses (17 articles)
 - 65F22 Ill-posedness, regularization (4 articles)
 - 65F25 Orthogonalization (6 articles)
 - 65F30 Other matrix algorithms (37 articles)
 - 65F35 Matrix norms, conditioning, scaling (14 articles)
 - 65F40 Determinants
 - 65F50 Sparse matrices (17 articles)
 - 65F99 None of the above, but in this section (7 articles)
- 65Gxx Error analysis and interval analysis (43 articles)
 - 65Gxx Error analysis and interval analysis
 - 65G20 Algorithms with automatic result verification (3 articles)
 - 65G30 Interval and finite arithmetic (15 articles)
 - 65G40 General methods in interval analysis (5 articles)
 - 65G50 Roundoff error (9 articles)
 - 65G99 None of the above, but in this section (11 articles)
- 65Hxx Nonlinear algebraic or transcendental equations (91 articles)
 - 65Hxx Nonlinear algebraic or transcendental equations (1 articles)
 - 65H05 Single equations (25 articles)
 - 65H10 Systems of equations (57 articles)
 - 65H17 Eigenvalues, eigenvectors (5 articles)
 - 65H20 Global methods, including homotopy approaches (2 articles)
 - 65H99 None of the above, but in this section (1 articles)
- 65Jxx Numerical analysis in abstract spaces (146 articles)
 - 65Jxx Numerical analysis in abstract spaces (29 articles)
 - 65J05 General theory (32 articles)
 - 65J10 Equations with linear operators (do not use 65Fxx) (20 articles)
 - 65J15 Equations with nonlinear operators (do not use <A HREF="/msc/65Hxx.html">65Hxx</A>) (44 articles)
 - 65J20 Improperly posed problems; regularization (4 articles)
 - 65J22 Inverse problems (1 articles)
 - 65J99 None of the above, but in this section (16 articles)
- 65Kxx Mathematical programming, optimization and variational techniques (199 articles)
 - 65Kxx Mathematical programming, optimization and variational techniques (1 articles)
 - 65K05 Mathematical programming (89 articles)
 - 65K10 Optimization and variational techniques (103 articles)
 - 65K99 None of the above, but in this section (6 articles)
- 65Lxx Ordinary differential equations (257 articles)
 - 65Lxx Ordinary differential equations
 - 65L05 Initial value problems (76 articles)
 - 65L06 Multistep, Runge-Kutta and extrapolation methods (23 articles)
 - 65L07 Numerical investigation of stability of solutions (12 articles)
 - 65L08 Improperly posed problems
 - 65L09 Inverse problems (1 articles)
 - 65L10 Boundary value problems (49 articles)
 - 65L12 Finite difference methods (7 articles)
 - 65L15 Eigenvalue problems (16 articles)
 - 65L20 Stability and convergence of numerical methods (24 articles)
 - 65L50 Mesh generation and refinement (3 articles)
 - 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods (23 articles)
 - 65L70 Error bounds (8 articles)
 - 65L80 Methods for differential-algebraic equations (2 articles)
 - 65L99 None of the above, but in this section (13 articles)
- 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value problems (382 articles)
 - 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value problems (1 articles)
 - 65M06 Finite difference methods (37 articles)
 - 65M12 Stability and convergence of numerical methods (57 articles)
 - 65M15 Error bounds (48 articles)
 - 65M20 Method of lines (38 articles)
 - 65M25 Method of characteristics (8 articles)
 - 65M30 Improperly posed problems (4 articles)
 - 65M32 Inverse problems (10 articles)
 - 65M50 Mesh generation and refinement (12 articles)
 - 65M55 Multigrid methods; domain decomposition (14 articles)
 - 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (112 articles)
 - 65M70 Spectral, collocation and related methods (15 articles)
 - 65M99 None of the above, but in this section (26 articles)
- 65Nxx Partial differential equations, boundary value problems (725 articles)
 - 65Nxx Partial differential equations, boundary value problems (2 articles)
 - 65N06 Finite difference methods (14 articles)
 - 65N12 Stability and convergence of numerical methods (59 articles)
 - 65N15 Error bounds (105 articles)
 - 65N21 Inverse problems (7 articles)
 - 65N22 Solution of discretized equations (30 articles)
 - 65N25 Eigenvalue problems (30 articles)
 - 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (339 articles)
 - 65N35 Spectral, collocation and related methods (17 articles)
 - 65N38 Boundary element methods (10 articles)
 - 65N40 Method of lines (11 articles)
 - 65N45 Method of contraction of the boundary
 - 65N50 Mesh generation and refinement (35 articles)
 - 65N55 Multigrid methods; domain decomposition (37 articles)
 - 65N99 None of the above, but in this section (29 articles)
- 65Pxx Numerical problems in dynamical systems (10 articles)
 - 65Pxx Numerical problems in dynamical systems (1 articles)
 - 65P10 Hamiltonian systems including symplectic integrators
 - 65P20 Numerical chaos (2 articles)
 - 65P30 Bifurcation problems (5 articles)
 - 65P40 Nonlinear stabilities (1 articles)
 - 65P99 None of the above, but in this section (1 articles)
- 65Q05 Difference and functional equations, recurrence relations (15 articles)
- 65Rxx Integral equations, integral transforms (59 articles)
 - 65Rxx Integral equations, integral transforms (1 articles)
 - 65R10 Integral transforms (10 articles)
 - 65R20 Integral equations (46 articles)
 - 65R30 Improperly posed problems
 - 65R32 Inverse problems (1 articles)
 - 65R99 None of the above, but in this section (1 articles)
- 65S05 Graphical methods (16 articles)
- 65Txx Numerical methods in Fourier analysis (39 articles)
 - 65Txx Numerical methods in Fourier analysis
 - 65T40 Trigonometric approximation and interpolation (7 articles)
 - 65T50 Discrete and fast Fourier transforms (12 articles)
 - 65T60 Wavelets (18 articles)
 - 65T99 None of the above, but in this section (2 articles)
- 65Yxx Computer aspects of numerical algorithms (47 articles)
 - 65Yxx Computer aspects of numerical algorithms
 - 65Y05 Parallel computation (21 articles)
 - 65Y10 Algorithms for specific classes of architectures (3 articles)
 - 65Y15 Packaged methods (2 articles)
 - 65Y20 Complexity and performance of numerical algorithms (21 articles)
 - 65Y99 None of the above, but in this section
- 65Z05 Applications to physics (32 articles)
68 Computer science (1171 articles)
- 68 Computer science
- 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (9 articles)
- 68-01 Instructional exposition (textbooks, tutorial papers, etc.) (5 articles)
- 68-02 Research exposition (monographs, survey articles) (4 articles)
- 68-03 Historical (must also be assigned at least one classification number from Section 01) (8 articles)
- 68-04 Explicit machine computation and programs (not the theory of computation or programming) (2 articles)
- 68-06 Proceedings, conferences, collections, etc. (31 articles)
- 68.0 (1940-1958) Computing machines and modeling
- 68.00 (1959-1972) General (8 articles)
- 68Mxx Computer system organization (20 articles)
  - 68Mxx Computer system organization
  - 68M01 General (1 articles)
  - 68M07 Mathematical problems of computer architecture (1 articles)
  - 68M10 Network design and communication (10 articles)
  - 68M12 Network protocols (3 articles)
  - 68M14 Distributed systems
  - 68M15 Reliability, testing and fault tolerance (3 articles)
  - 68M20 Performance evaluation; queueing; scheduling (1 articles)
  - 68M99 None of the above, but in this section (1 articles)
- 68Nxx Software (51 articles)
  - 68Nxx Software (1 articles)
  - 68N01 General (11 articles)
  - 68N15 Programming languages (11 articles)
  - 68N17 Logic programming (4 articles)
  - 68N18 Functional programming and lambda calculus
  - 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.) (5 articles)
  - 68N20 Compilers and interpreters (9 articles)
  - 68N25 Operating systems (1 articles)
  - 68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) (2 articles)
  - 68N99 None of the above, but in this section (7 articles)
- 68Pxx Theory of data (64 articles)
  - 68Pxx Theory of data (1 articles)
  - 68P01 General
  - 68P05 Data structures (10 articles)
  - 68P10 Searching and sorting (10 articles)
  - 68P15 Database theory (8 articles)
  - 68P20 Information storage and retrieval (13 articles)
  - 68P25 Data encryption (3 articles)
  - 68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (3 articles)
  - 68P99 None of the above, but in this section (16 articles)
- 68Qxx Theory of computing (336 articles)
  - 68Qxx Theory of computing (1 articles)
  - 68Q01 General (1 articles)
  - 68Q05 Models of computation (Turing machines, etc.) (19 articles)
  - 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) (5 articles)
  - 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) (12 articles)
  - 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (5 articles)
  - 68Q19 Descriptive complexity and finite models
  - 68Q25 Analysis of algorithms and problem complexity (71 articles)
  - 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) (6 articles)
  - 68Q32 Computational learning theory (2 articles)
  - 68Q42 Grammars and rewriting systems (24 articles)
  - 68Q45 Formal languages and automata (135 articles)
  - 68Q55 Semantics (9 articles)
  - 68Q60 Specification and verification (program logics, model checking, etc.) (3 articles)
  - 68Q65 Abstract data types; algebraic specification (4 articles)
  - 68Q70 Algebraic theory of languages and automata (17 articles)
  - 68Q80 Cellular automata (4 articles)
  - 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) (8 articles)
  - 68Q99 None of the above, but in this section (10 articles)
- 68Rxx Discrete mathematics in relation to computer science (53 articles)
  - 68Rxx Discrete mathematics in relation to computer science (1 articles)
  - 68R01 General (1 articles)
  - 68R05 Combinatorics (2 articles)
  - 68R10 Graph theory (30 articles)
  - 68R15 Combinatorics on words (15 articles)
  - 68R99 None of the above, but in this section (4 articles)
- 68Txx Artificial intelligence (317 articles)
  - 68Txx Artificial intelligence (1 articles)
  - 68T01 General (5 articles)
  - 68T05 Learning and adaptive systems (43 articles)
  - 68T10 Pattern recognition, speech recognition (52 articles)
  - 68T15 Theorem proving (deduction, resolution, etc.) (34 articles)
  - 68T20 Problem solving (heuristics, search strategies, etc.) (19 articles)
  - 68T27 Logic in artificial intelligence (6 articles)
  - 68T30 Knowledge representation (38 articles)
  - 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.) (19 articles)
  - 68T37 Reasoning under uncertainty (60 articles)
  - 68T40 Robotics (8 articles)
  - 68T45 Machine vision and scene understanding (3 articles)
  - 68T50 Natural language processing (17 articles)
  - 68T99 None of the above, but in this section (12 articles)
- 68Uxx Computing methodologies and applications (203 articles)
  - 68Uxx Computing methodologies and applications (1 articles)
  - 68U01 General
  - 68U05 Computer graphics; computational geometry (11 articles)
  - 68U07 Computer-aided design (1 articles)
  - 68U10 Image processing (73 articles)
  - 68U15 Text processing; mathematical typography (55 articles)
  - 68U20 Simulation (23 articles)
  - 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.) (6 articles)
  - 68U99 None of the above, but in this section (33 articles)
- 68Wxx Algorithms (60 articles)
  - 68Wxx Algorithms (1 articles)
  - 68W01 General
  - 68W05 Nonnumerical algorithms (5 articles)
  - 68W10 Parallel algorithms (7 articles)
  - 68W15 Distributed algorithms (12 articles)
  - 68W20 Randomized algorithms (1 articles)
  - 68W25 Approximation algorithms (2 articles)
  - 68W30 Symbolic computation and algebraic computation (13 articles)
  - 68W35 VLSI algorithms
  - 68W40 Analysis of algorithms (1 articles)
  - 68W99 None of the above, but in this section (18 articles)
69 (1940-1972) General applied mathematics
- 69 (1940-1972) General applied mathematics
- 69.00 (1959-1979) General applied mathematics
70 Mechanics of particles and systems (281 articles)
- 70 Mechanics of particles and systems
- 70-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (6 articles)
- 70-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 70-02 Research exposition (monographs, survey articles) (2 articles)
- 70-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 70-04 Explicit machine computation and programs (not the theory of computation or programming)
- 70-05 Experimental work
- 70-06 Proceedings, conferences, collections, etc.
- 70-08 Computational methods (1 articles)
- 70.0 (1940-1958) Mechanics of particles and systems
- 70.00 (1959-1979) General (1 articles)
- 70.01 (1959-1979) History and biography
- 70.02 (1959-1979) Logic and foundations
- 70.04 (1959-1972) Set theory
- 70.05 (1959-1972) Combinatorics
- 70.06 (1959-1972) Order, lattices, ordered algebraic structures
- 70.08 (1959-1972) General mathematical systems
- 70.1 (1940-1958) Dynamics, celestial mechanics
- 70.10 (1959-1979) Number theory
- 70.12 (1959-1972) Field theory and polynomials
- 70.13 (1959-1972) Commutative rings and algebras
- 70.14 (1959-1972) Algebraic geometry
- 70.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 70.16 (1959-1979) Associative rings and algebras
- 70.17 (1959-1979) Nonassociative rings and algebras
- 70.18 (1959-1972) Category theory, homological algebra
- 70.20 (1959-1979) Group theory and generalizations
- 70.22 (1959-1979) Topological groups, Lie groups
- 70.26 (1959-1979) Real functions
- 70.28 (1959-1979) Measure and integration
- 70.30 (1959-1979) Functions of a complex variable
- 70.31 (1959-1979) Potential theory
- 70.32 (1959-1972) Several complex variables and analytic spaces
- 70.33 (1959-1979) Special functions
- 70.34 (1959-1979) Ordinary differential equations
- 70.35 (1959-1979) Partial differential equations
- 70.39 (1959-1979) Finite differences and functional equations
- 70.40 (1959-1979) Sequences, series, summability
- 70.41 (1959-1979) Approximations and expansions
- 70.42 (1959-1979) Fourier analysis
- 70.44 (1959-1972) Integral transforms, operational calculus
- 70.45 (1959-1979) Integral equations
- 70.46 (1959-1979) Functional analysis
- 70.47 (1959-1979) Operator theory
- 70.49 (1959-1979) Calculus of variations and optimal control
- 70.50 (1959-1979) Geometry
- 70.52 (1959-1972) Convex sets and geometric inequalities
- 70.53 (1959-1979) Differential geometry
- 70.54 (1959-1979) General topology
- 70.55 (1959-1972) Algebraic topology
- 70.57 (1959-1979) Manifolds and cell complexes
- 70.58 (1973-1979) Global analysis, analysis on manifolds
- 70.60 (1959-1979) Probability theory and stochastic processes
- 70.62 (1959-1979) Statistics
- 70.65 (1959-1979) Numerical analysis
- 70.90 (1959-1972) Economics, operations research, programming, games
- 70.93 (1959-1972) Systems, control
- 70.94 (1959-1972) Information and communication, circuits, automata
- 70.99 (1959-1972) None of the above, but in this section
- 70A05 Axiomatics, foundations (2 articles)
- 70Bxx Kinematics (22 articles)
  - 70Bxx Kinematics (1 articles)
  - 70B05 Kinematics of a particle
  - 70B10 Kinematics of a rigid body (6 articles)
  - 70B15 Mechanisms, robots (12 articles)
  - 70B99 None of the above, but in this section (3 articles)
- 70C20 Statics (3 articles)
- 70Exx Dynamics of a rigid body and of multibody systems (24 articles)
  - 70Exx Dynamics of a rigid body and of multibody systems (1 articles)
  - 70E05 Motion of the gyroscope (3 articles)
  - 70E15 Free motion of a rigid body (3 articles)
  - 70E17 Motion of a rigid body with a fixed point
  - 70E18 Motion of a rigid body in contact with a solid surface (1 articles)
  - 70E20 Perturbation methods for rigid body dynamics
  - 70E40 Integrable cases of motion
  - 70E45 Higher-dimensional generalizations
  - 70E50 Stability problems (1 articles)
  - 70E55 Dynamics of multibody systems (3 articles)
  - 70E60 Robot dynamics and control (11 articles)
  - 70E99 None of the above, but in this section (1 articles)
- 70Fxx Dynamics of a system of particles, including celestial mechanics (33 articles)
  - 70Fxx Dynamics of a system of particles, including celestial mechanics (1 articles)
  - 70F05 Two-body problems (2 articles)
  - 70F07 Three-body problems (1 articles)
  - 70F10 $n$-body problems (5 articles)
  - 70F15 Celestial mechanics (3 articles)
  - 70F16 Collisions in celestial mechanics, regularization (3 articles)
  - 70F17 Inverse problems (1 articles)
  - 70F20 Holonomic systems (2 articles)
  - 70F25 Nonholonomic systems (10 articles)
  - 70F35 Collision of rigid or pseudo-rigid bodies (1 articles)
  - 70F40 Problems with friction (1 articles)
  - 70F45 Infinite particle systems (1 articles)
  - 70F99 None of the above, but in this section (2 articles)
- 70Gxx General models, approaches, and methods (35 articles)
  - 70Gxx General models, approaches, and methods (1 articles)
  - 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space (3 articles)
  - 70G40 Topological and differential-topological methods
  - 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) (20 articles)
  - 70G55 Algebraic geometry methods (1 articles)
  - 70G60 Dynamical systems methods (2 articles)
  - 70G65 Symmetries, Lie-group and Lie-algebra methods (1 articles)
  - 70G70 Functional-analytic methods
  - 70G75 Variational methods (4 articles)
  - 70G99 None of the above, but in this section (3 articles)
- 70Hxx Hamiltonian and Lagrangian mechanics (70 articles)
  - 70Hxx Hamiltonian and Lagrangian mechanics (1 articles)
  - 70H03 Lagrange's equations (22 articles)
  - 70H05 Hamilton's equations (15 articles)
  - 70H06 Completely integrable systems and methods of integration (2 articles)
  - 70H07 Nonintegrable systems
  - 70H08 Nearly integrable Hamiltonian systems, KAM theory
  - 70H09 Perturbation theories
  - 70H11 Adiabatic invariants
  - 70H12 Periodic and almost periodic solutions (1 articles)
  - 70H14 Stability problems (1 articles)
  - 70H15 Canonical and symplectic transformations (2 articles)
  - 70H20 Hamilton-Jacobi equations (2 articles)
  - 70H25 Hamilton's principle (1 articles)
  - 70H30 Other variational principles (3 articles)
  - 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction (8 articles)
  - 70H40 Relativistic dynamics (2 articles)
  - 70H45 Constrained dynamics, Dirac's theory of constraints (5 articles)
  - 70H50 Higher-order theories (2 articles)
  - 70H99 None of the above, but in this section (3 articles)
- 70Jxx Linear vibration theory (1 articles)
  - 70Jxx Linear vibration theory
  - 70J10 Modal analysis
  - 70J25 Stability (1 articles)
  - 70J30 Free motions
  - 70J35 Forced motions
  - 70J40 Parametric resonances
  - 70J50 Systems arising from the discretization of structural vibration problems
  - 70J99 None of the above, but in this section
- 70Kxx Nonlinear dynamics (30 articles)
  - 70Kxx Nonlinear dynamics
  - 70K05 Phase plane analysis, limit cycles (3 articles)
  - 70K20 Stability (5 articles)
  - 70K25 Free motions
  - 70K28 Parametric resonances
  - 70K30 Nonlinear resonances (6 articles)
  - 70K40 Forced motions (5 articles)
  - 70K42 Equilibria and periodic trajectories (2 articles)
  - 70K43 Quasi-periodic motions and invariant tori
  - 70K44 Homoclinic and heteroclinic trajectories (1 articles)
  - 70K45 Normal forms
  - 70K50 Bifurcations and instability (3 articles)
  - 70K55 Transition to stochasticity (chaotic behavior) (2 articles)
  - 70K60 General perturbation schemes
  - 70K65 Averaging of perturbations
  - 70K70 Systems with slow and fast motions
  - 70K75 Nonlinear modes
  - 70K99 None of the above, but in this section (3 articles)
- 70L05 Random vibrations (3 articles)
- 70M20 Orbital mechanics (1 articles)
- 70P05 Variable mass, rockets
- 70Q05 Control of mechanical systems (20 articles)
- 70Sxx Classical field theories (25 articles)
  - 70Sxx Classical field theories (1 articles)
  - 70S05 Lagrangian formalism and Hamiltonian formalism (11 articles)
  - 70S10 Symmetries and conservation laws (10 articles)
  - 70S15 Yang-Mills and other gauge theories (2 articles)
  - 70S20 More general nonquantum field theories (1 articles)
  - 70S99 None of the above, but in this section
71 (1940-1958) Mechanics
- 71 (1940-1958) Mechanics
- 71.0 (1940-1958) Mechanics
73 (1940-1999) Mechanics of solids (28 articles)
- 73 (1940-1999) Mechanics of solids
- 73-00 (1985-1999) General reference works (handbooks, dictionaries, bibliographies, etc.) (12 articles)
- 73-01 (1980-1999) Instructional exposition (textbooks, tutorial papers, etc.)
- 73-02 (1980-1999) Research exposition (monographs, survey articles)
- 73-03 (1980-1999) Historical (must also be assigned at least one classification number from section 01)
- 73-04 (1980-1999) Explicit machine computation and programs (not the theory of computation or programming)
- 73-05 (1980-1999) Experimental papers
- 73-06 (1980-1999) Proceedings, conferences, collections, etc.
- 73-08 (1980-1990) Computational methods (4 articles)
- 73.00 (1959-1979) General (4 articles)
- 73.01 (1959-1979) History and biography
- 73.02 (1959-1979) Logic and foundations
- 73.04 (1959-1972) Set theory
- 73.05 (1959-1979) Combinatorics
- 73.06 (1959-1979) Order, lattices, ordered algebraic structures
- 73.08 (1959-1972) General mathematical systems
- 73.1 (1940-1958) Mechanics of continua
- 73.10 (1959-1972) Number theory
- 73.12 (1959-1972) Field theory and polynomials
- 73.13 (1959-1972) Commutative rings and algebras
- 73.14 (1959-1972) Algebraic geometry (1 articles)
- 73.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 73.16 (1959-1972) Associative rings and algebras
- 73.17 (1959-1979) Nonassociative rings and algebras
- 73.18 (1959-1972) Category theory, homological algebra
- 73.2 (1940-1958) Elasticity, viscoplasticity, plasticity
- 73.20 (1959-1979) Group theory and generalizations
- 73.22 (1959-1979) Topological groups, Lie groups
- 73.26 (1959-1979) Real functions
- 73.28 (1959-1979) Measure and integration
- 73.30 (1959-1979) Functions of a complex variable
- 73.31 (1959-1979) Potential theory
- 73.32 (1959-1979) Several complex variables and analytic spaces
- 73.33 (1959-1979) Special functions
- 73.34 (1959-1979) Ordinary differential equations
- 73.35 (1959-1979) Partial differential equations (1 articles)
- 73.39 (1959-1979) Finite differences and functional equations
- 73.40 (1959-1979) Sequences, series, summability
- 73.41 (1959-1979) Approximations and expansions
- 73.42 (1959-1979) Fourier analysis
- 73.43 (1973-1979) Abstract harmonic analysis
- 73.44 (1959-1979) Integral transforms, operational calculus (1 articles)
- 73.45 (1959-1979) Integral equations
- 73.46 (1959-1979) Functional analysis
- 73.47 (1959-1979) Operator theory
- 73.49 (1959-1979) Calculus of variations and optimal control (1 articles)
- 73.50 (1959-1972) Geometry
- 73.52 (1959-1972) Convex sets and geometric inequalities
- 73.53 (1959-1979) Differential geometry
- 73.54 (1959-1979) General topology
- 73.55 (1959-1979) Algebraic topology
- 73.57 (1959-1979) Manifolds and cell complexes
- 73.58 (1973-1979) Global analysis, analysis on manifolds
- 73.60 (1959-1979) Probability theory and stochastic processes
- 73.62 (1959-1979) Statistics
- 73.65 (1959-1979) Numerical analysis (1 articles)
- 73.90 (1959-1972) Economics, operations research, programming, games
- 73.93 (1959-1972) Systems, control
- 73.94 (1959-1972) Information and communication, circuits, automata
- 73.99 (1959-1972) None of the above, but in this section (3 articles)
74 Mechanics of deformable solids (874 articles)
- 74 Mechanics of deformable solids
- 74-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 74-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 74-02 Research exposition (monographs, survey articles) (1 articles)
- 74-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 74-04 Explicit machine computation and programs (not the theory of computation or programming) (2 articles)
- 74-05 Experimental work
- 74-06 Proceedings, conferences, collections, etc. (3 articles)
- 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids (53 articles)
  - 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids
  - 74A05 Kinematics of deformation (1 articles)
  - 74A10 Stress (1 articles)
  - 74A15 Thermodynamics (11 articles)
  - 74A20 Theory of constitutive functions (5 articles)
  - 74A25 Molecular, statistical, and kinetic theories
  - 74A30 Nonsimple materials
  - 74A35 Polar materials (3 articles)
  - 74A40 Random materials and composite materials (1 articles)
  - 74A45 Theories of fracture and damage (4 articles)
  - 74A50 Structured surfaces and interfaces, coexistent phases (2 articles)
  - 74A55 Theories of friction (tribology) (24 articles)
  - 74A60 Micromechanical theories (1 articles)
  - 74A65 Reactive materials
  - 74A99 None of the above, but in this section
- 74Bxx Elastic materials (82 articles)
  - 74Bxx Elastic materials (2 articles)
  - 74B05 Classical linear elasticity (18 articles)
  - 74B10 Linear elasticity with initial stresses (5 articles)
  - 74B15 Equations linearized about a deformed state (small deformations superposed on large)
  - 74B20 Nonlinear elasticity (23 articles)
  - 74B99 None of the above, but in this section (34 articles)
- 74Cxx Plastic materials, materials of stress-rate and internal-variable type (37 articles)
  - 74Cxx Plastic materials, materials of stress-rate and internal-variable type
  - 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials) (12 articles)
  - 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity) (7 articles)
  - 74C15 Large-strain, rate-independent theories (including nonlinear plasticity) (6 articles)
  - 74C20 Large-strain, rate-dependent theories
  - 74C99 None of the above, but in this section (12 articles)
- 74Dxx Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (32 articles)
  - 74Dxx Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
  - 74D05 Linear constitutive equations (7 articles)
  - 74D10 Nonlinear constitutive equations (14 articles)
  - 74D99 None of the above, but in this section (11 articles)
- 74Exx Material properties given special treatment (25 articles)
  - 74Exx Material properties given special treatment
  - 74E05 Inhomogeneity (5 articles)
  - 74E10 Anisotropy (5 articles)
  - 74E15 Crystalline structure (8 articles)
  - 74E20 Granularity (1 articles)
  - 74E25 Texture
  - 74E30 Composite and mixture properties (6 articles)
  - 74E35 Random structure
  - 74E40 Chemical structure
  - 74E99 None of the above, but in this section
- 74Fxx Coupling of solid mechanics with other effects (31 articles)
  - 74Fxx Coupling of solid mechanics with other effects
  - 74F05 Thermal effects (13 articles)
  - 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (15 articles)
  - 74F15 Electromagnetic effects (2 articles)
  - 74F20 Mixture effects
  - 74F25 Chemical and reactive effects (1 articles)
  - 74F99 None of the above, but in this section
- 74Gxx Equilibrium (steady-state) problems (55 articles)
  - 74Gxx Equilibrium (steady-state) problems
  - 74G05 Explicit solutions
  - 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) (3 articles)
  - 74G15 Numerical approximation of solutions (8 articles)
  - 74G20 Local existence of solutions (near a given solution) (2 articles)
  - 74G25 Global existence of solutions (3 articles)
  - 74G30 Uniqueness of solutions (14 articles)
  - 74G35 Multiplicity of solutions (1 articles)
  - 74G40 Regularity of solutions
  - 74G45 Bounds for solutions
  - 74G50 Saint-Venant's principle (2 articles)
  - 74G55 Qualitative behavior of solutions (1 articles)
  - 74G60 Bifurcation and buckling (13 articles)
  - 74G65 Energy minimization (4 articles)
  - 74G70 Stress concentrations, singularities (1 articles)
  - 74G75 Inverse problems
  - 74G99 None of the above, but in this section (3 articles)
- 74Hxx Dynamical problems (111 articles)
  - 74Hxx Dynamical problems (10 articles)
  - 74H05 Explicit solutions (2 articles)
  - 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) (1 articles)
  - 74H15 Numerical approximation of solutions (10 articles)
  - 74H20 Existence of solutions (8 articles)
  - 74H25 Uniqueness of solutions (17 articles)
  - 74H30 Regularity of solutions (1 articles)
  - 74H35 Singularities, blowup, stress concentrations (2 articles)
  - 74H40 Long-time behavior of solutions (5 articles)
  - 74H45 Vibrations (24 articles)
  - 74H50 Random vibrations
  - 74H55 Stability (2 articles)
  - 74H60 Dynamical bifurcation (1 articles)
  - 74H65 Chaotic behavior (7 articles)
  - 74H99 None of the above, but in this section (21 articles)
- 74Jxx Waves (9 articles)
  - 74Jxx Waves
  - 74J05 Linear waves (1 articles)
  - 74J10 Bulk waves (1 articles)
  - 74J15 Surface waves (3 articles)
  - 74J20 Wave scattering (1 articles)
  - 74J25 Inverse problems
  - 74J30 Nonlinear waves (2 articles)
  - 74J35 Solitary waves
  - 74J40 Shocks and related discontinuities
  - 74J99 None of the above, but in this section (1 articles)
- 74Kxx Thin bodies, structures (119 articles)
  - 74Kxx Thin bodies, structures
  - 74K05 Strings (4 articles)
  - 74K10 Rods (beams, columns, shafts, arches, rings, etc.) (33 articles)
  - 74K15 Membranes (9 articles)
  - 74K20 Plates (62 articles)
  - 74K25 Shells (9 articles)
  - 74K30 Junctions
  - 74K35 Thin films
  - 74K99 None of the above, but in this section (2 articles)
- 74Lxx Special subfields of solid mechanics (8 articles)
  - 74Lxx Special subfields of solid mechanics
  - 74L05 Geophysical solid mechanics (2 articles)
  - 74L10 Soil and rock mechanics (5 articles)
  - 74L15 Biomechanical solid mechanics
  - 74L99 None of the above, but in this section (1 articles)
- 74Mxx Special kinds of problems (83 articles)
  - 74Mxx Special kinds of problems
  - 74M05 Control, switches and devices (``smart materials'') (4 articles)
  - 74M10 Friction (22 articles)
  - 74M15 Contact (53 articles)
  - 74M20 Impact (1 articles)
  - 74M25 Micromechanics (3 articles)
  - 74M99 None of the above, but in this section
- 74Nxx Phase transformations in solids (14 articles)
  - 74Nxx Phase transformations in solids
  - 74N05 Crystals (2 articles)
  - 74N10 Displacive transformations
  - 74N15 Analysis of microstructure (1 articles)
  - 74N20 Dynamics of phase boundaries (1 articles)
  - 74N25 Transformations involving diffusion (2 articles)
  - 74N30 Problems involving hysteresis (6 articles)
  - 74N99 None of the above, but in this section (2 articles)
- 74Pxx Optimization (43 articles)
  - 74Pxx Optimization
  - 74P05 Compliance or weight optimization (2 articles)
  - 74P10 Optimization of other properties (13 articles)
  - 74P15 Topological methods (1 articles)
  - 74P20 Geometrical methods (1 articles)
  - 74P99 None of the above, but in this section (26 articles)
- 74Qxx Homogenization, determination of effective properties (17 articles)
  - 74Qxx Homogenization, determination of effective properties (1 articles)
  - 74Q05 Homogenization in equilibrium problems (4 articles)
  - 74Q10 Homogenization and oscillations in dynamical problems (4 articles)
  - 74Q15 Effective constitutive equations (5 articles)
  - 74Q20 Bounds on effective properties (3 articles)
  - 74Q99 None of the above, but in this section
- 74Rxx Fracture and damage (9 articles)
  - 74Rxx Fracture and damage
  - 74R05 Brittle damage
  - 74R10 Brittle fracture (5 articles)
  - 74R15 High-velocity fracture
  - 74R20 Anelastic fracture and damage
  - 74R99 None of the above, but in this section (4 articles)
- 74Sxx Numerical methods (138 articles)
  - 74Sxx Numerical methods
  - 74S05 Finite element methods (70 articles)
  - 74S10 Finite volume methods (7 articles)
  - 74S15 Boundary element methods (2 articles)
  - 74S20 Finite difference methods (8 articles)
  - 74S25 Spectral and related methods (1 articles)
  - 74S30 Other numerical methods (42 articles)
  - 74S99 None of the above, but in this section (8 articles)
76 Fluid mechanics (626 articles)
- 76 Fluid mechanics
- 76-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (7 articles)
- 76-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 76-02 Research exposition (monographs, survey articles) (2 articles)
- 76-03 Historical (must also be assigned at least one classification number from Section 01)
- 76-04 Explicit machine computation and programs (not the theory of computation or programming)
- 76-05 Experimental work
- 76-06 Proceedings, conferences, collections, etc. (7 articles)
- 76-08 (1980-1990) Computational methods (2 articles)
- 76.0 (1940-1958) Fluid mechanics, acoustics
- 76.00 (1959-1979) General (2 articles)
- 76.01 (1959-1979) History and biography
- 76.02 (1959-1979) Logic and foundations
- 76.04 (1959-1972) Set theory
- 76.05 (1959-1979) Combinatorics
- 76.06 (1959-1979) Order, lattices, ordered algebraic structures
- 76.08 (1959-1972) General mathematical systems
- 76.1 (1940-1958) Hydrodynamics, aerodynamics, acoustics
- 76.10 (1959-1972) Number theory
- 76.12 (1959-1972) Field theory and polynomials
- 76.13 (1959-1972) Commutative rings and algebras
- 76.14 (1959-1972) Algebraic geometry
- 76.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 76.16 (1959-1972) Associative rings and algebras
- 76.17 (1959-1972) Nonassociative rings and algebras
- 76.18 (1959-1972) Category theory, homological algebra
- 76.20 (1959-1979) Group theory and generalizations
- 76.22 (1959-1979) Topological groups, Lie groups
- 76.26 (1959-1979) Real functions
- 76.28 (1959-1979) Measure and integration
- 76.30 (1959-1979) Functions of a complex variable (1 articles)
- 76.31 (1959-1979) Potential theory
- 76.32 (1959-1972) Several complex variables and analytic spaces
- 76.33 (1959-1979) Special functions
- 76.34 (1959-1979) Ordinary differential equations
- 76.35 (1959-1979) Partial differential equations (1 articles)
- 76.39 (1959-1979) Finite differences and functional equations
- 76.40 (1959-1979) Sequences, series, summability
- 76.41 (1959-1979) Approximations and expansions
- 76.42 (1959-1979) Fourier analysis
- 76.44 (1959-1979) Integral transforms, operational calculus
- 76.45 (1959-1979) Integral equations
- 76.46 (1959-1979) Functional analysis
- 76.47 (1959-1979) Operator theory
- 76.49 (1959-1979) Calculus of variations and optimal control
- 76.50 (1959-1979) Geometry
- 76.52 (1959-1979) Convex sets and geometric inequalities
- 76.53 (1959-1979) Differential geometry
- 76.54 (1959-1979) General topology
- 76.55 (1959-1972) Algebraic topology
- 76.57 (1959-1979) Manifolds and cell complexes
- 76.58 (1973-1979) Global analysis, analysis on manifolds
- 76.60 (1959-1979) Probability theory and stochastic processes
- 76.62 (1959-1979) Statistics
- 76.65 (1959-1979) Numerical analysis (1 articles)
- 76.90 (1959-1972) Economics, operations research, programming, games
- 76.93 (1959-1972) Systems, control
- 76.94 (1959-1972) Information and communication, circuits, automata
- 76.99 (1959-1972) None of the above, but in this section (1 articles)
- 76Axx Foundations, constitutive equations, rheology (50 articles)
  - 76Axx Foundations, constitutive equations, rheology
  - 76A02 Foundations of fluid mechanics (6 articles)
  - 76A05 Non-Newtonian fluids (30 articles)
  - 76A10 Viscoelastic fluids (9 articles)
  - 76A15 Liquid crystals (2 articles)
  - 76A20 Thin fluid films
  - 76A25 Superfluids (classical aspects)
  - 76A99 None of the above, but in this section (3 articles)
- 76Bxx Incompressible inviscid fluids (28 articles)
  - 76Bxx Incompressible inviscid fluids
  - 76B03 Existence, uniqueness, and regularity theory (2 articles)
  - 76B07 Free-surface potential flows (1 articles)
  - 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (5 articles)
  - 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction (10 articles)
  - 76B20 Ship waves
  - 76B25 Solitary waves
  - 76B45 Capillarity (surface tension) (1 articles)
  - 76B47 Vortex flows (3 articles)
  - 76B55 Internal waves
  - 76B60 Atmospheric waves
  - 76B65 Rossby waves
  - 76B70 Stratification effects in inviscid fluids
  - 76B75 Flow control and optimization
  - 76B99 None of the above, but in this section (6 articles)
- 76Dxx Incompressible viscous fluids (199 articles)
  - 76Dxx Incompressible viscous fluids
  - 76D03 Existence, uniqueness, and regularity theory (47 articles)
  - 76D05 Navier-Stokes equations (102 articles)
  - 76D06 Statistical solutions of Navier-Stokes and related equations (4 articles)
  - 76D07 Stokes and related (Oseen, etc.) flows (28 articles)
  - 76D08 Lubrication theory (2 articles)
  - 76D09 Viscous-inviscid interaction
  - 76D10 Boundary-layer theory, separation and reattachment, higher-order effects (4 articles)
  - 76D17 Viscous vortex flows
  - 76D25 Wakes and jets
  - 76D27 Other free-boundary flows; Hele-Shaw flows
  - 76D33 Waves (1 articles)
  - 76D45 Capillarity (surface tension) (1 articles)
  - 76D50 Stratification effects in viscous fluids
  - 76D55 Flow control and optimization (4 articles)
  - 76D99 None of the above, but in this section (6 articles)
- 76Exx Hydrodynamic stability (7 articles)
  - 76Exx Hydrodynamic stability (1 articles)
  - 76E05 Parallel shear flows (1 articles)
  - 76E06 Convection (1 articles)
  - 76E07 Rotation
  - 76E09 Stability and instability of nonparallel flows
  - 76E15 Absolute and convective instability and stability
  - 76E17 Interfacial stability and instability
  - 76E19 Compressibility effects
  - 76E20 Stability and instability of geophysical and astrophysical flows
  - 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
  - 76E30 Nonlinear effects (3 articles)
  - 76E99 None of the above, but in this section (1 articles)
- 76Fxx Turbulence (16 articles)
  - 76Fxx Turbulence
  - 76F02 Fundamentals (1 articles)
  - 76F05 Isotropic turbulence; homogeneous turbulence (3 articles)
  - 76F06 Transition to turbulence
  - 76F10 Shear flows (1 articles)
  - 76F20 Dynamical systems approach to turbulence (1 articles)
  - 76F25 Turbulent transport, mixing (1 articles)
  - 76F30 Renormalization and other field-theoretical methods
  - 76F35 Convective turbulence
  - 76F40 Turbulent boundary layers (1 articles)
  - 76F45 Stratification effects
  - 76F50 Compressibility effects
  - 76F55 Statistical turbulence modeling (1 articles)
  - 76F60 $k$-$varepsilon$ modeling (1 articles)
  - 76F65 Direct numerical and large eddy simulation of turbulence (3 articles)
  - 76F70 Control of turbulent flows
  - 76F99 None of the above, but in this section (3 articles)
- 76G25 General aerodynamics and subsonic flows (9 articles)
- 76H05 Transonic flows (17 articles)
- 76J20 Supersonic flows (1 articles)
- 76K05 Hypersonic flows (1 articles)
- 76L05 Shock waves and blast waves (3 articles)
- 76Mxx Basic methods in fluid mechanics (103 articles)
  - 76Mxx Basic methods in fluid mechanics
  - 76M10 Finite element methods (34 articles)
  - 76M12 Finite volume methods (20 articles)
  - 76M15 Boundary element methods
  - 76M20 Finite difference methods (4 articles)
  - 76M22 Spectral methods (1 articles)
  - 76M23 Vortex methods
  - 76M25 Other numerical methods (18 articles)
  - 76M27 Visualization algorithms
  - 76M28 Particle methods and lattice-gas methods (1 articles)
  - 76M30 Variational methods (4 articles)
  - 76M35 Stochastic analysis (5 articles)
  - 76M40 Complex-variables methods (1 articles)
  - 76M45 Asymptotic methods, singular perturbations (2 articles)
  - 76M50 Homogenization (4 articles)
  - 76M55 Dimensional analysis and similarity
  - 76M60 Symmetry analysis, Lie group and algebra methods (2 articles)
  - 76M99 None of the above, but in this section (7 articles)
- 76Nxx Compressible fluids and gas dynamics, general (77 articles)
  - 76Nxx Compressible fluids and gas dynamics, general (1 articles)
  - 76N10 Existence, uniqueness, and regularity theory (43 articles)
  - 76N15 Gas dynamics, general (25 articles)
  - 76N17 Viscous-inviscid interaction (1 articles)
  - 76N20 Boundary-layer theory (1 articles)
  - 76N25 Flow control and optimization
  - 76N99 None of the above, but in this section (6 articles)
- 76P05 Rarefied gas flows, Boltzmann equation (5 articles)
- 76Q05 Hydro- and aero-acoustics (2 articles)
- 76Rxx Diffusion and convection (11 articles)
  - 76Rxx Diffusion and convection (1 articles)
  - 76R05 Forced convection (1 articles)
  - 76R10 Free convection (2 articles)
  - 76R50 Diffusion (3 articles)
  - 76R99 None of the above, but in this section (4 articles)
- 76S05 Flows in porous media; filtration; seepage (30 articles)
- 76Txx Two-phase and multiphase flows (12 articles)
  - 76Txx Two-phase and multiphase flows (1 articles)
  - 76T10 Liquid-gas two-phase flows, bubbly flows (2 articles)
  - 76T15 Dusty-gas two-phase flows (1 articles)
  - 76T20 Suspensions (1 articles)
  - 76T25 Granular flows
  - 76T30 Three or more component flows
  - 76T99 None of the above, but in this section (7 articles)
- 76U05 Rotating fluids (4 articles)
- 76V05 Reaction effects in flows (4 articles)
- 76W05 Magnetohydrodynamics and electrohydrodynamics (15 articles)
- 76X05 Ionized gas flow in electromagnetic fields; plasmic flow (2 articles)
- 76Y05 Quantum hydrodynamics and relativistic hydrodynamics (3 articles)
- 76Zxx Biological fluid mechanics (3 articles)
  - 76Zxx Biological fluid mechanics
  - 76Z05 Physiological flows (2 articles)
  - 76Z10 Biopropulsion in water and in air (1 articles)
  - 76Z99 None of the above, but in this section
78 Optics, electromagnetic theory (106 articles)
- 78 Optics, electromagnetic theory
- 78-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (2 articles)
- 78-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 78-02 Research exposition (monographs, survey articles)
- 78-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 78-04 Explicit machine computation and programs (not the theory of computation or programming)
- 78-05 Experimental work
- 78-06 Proceedings, conferences, collections, etc.
- 78-08 (1984-1999) Computational methods (3 articles)
- 78.0 (1940-1958) Optics, electromagnetic theory, circuits
- 78.00 (1959-1979) General (1 articles)
- 78.01 (1959-1979) History and biography
- 78.02 (1959-1972) Logic and foundations
- 78.04 (1959-1972) Set theory
- 78.05 (1959-1979) Combinatorics
- 78.06 (1959-1979) Order lattices, ordered algebraic structures
- 78.08 (1959-1972) General mathematical systems
- 78.10 (1959-1972) Number theory
- 78.12 (1959-1972) Field theory and polynomials
- 78.13 (1959-1972) Commutative rings and algebras
- 78.14 (1959-1972) Algebraic geometry
- 78.15 (1959-1972) Linear and multilinear algebra; matrix theory
- 78.16 (1959-1972) Associative rings and algebras
- 78.17 (1959-1972) Nonassociative rings and algebras
- 78.18 (1959-1972) Category theory, homological algebra
- 78.20 (1959-1972) Group theory and generalizations
- 78.22 (1959-1972) Topological groups, Lie groups
- 78.26 (1959-1972) Real functions
- 78.28 (1959-1972) Measure and integration
- 78.30 (1959-1972) Functions of a complex variable
- 78.31 (1959-1972) Potential theory
- 78.32 (1959-1979) Several complex variables and analytic spaces
- 78.33 (1959-1972) Special functions
- 78.34 (1959-1972) Ordinary differential equations
- 78.35 (1959-721) Partial differential equations
- 78.39 (1959-1972) Finite differences and functional equations
- 78.40 (1959-1972) Sequences, series, summability
- 78.41 (1959-1979) Approximations and expansions
- 78.42 (1959-1979) Fourier analysis
- 78.44 (1959-1979) Integral transforms, operational calculus
- 78.45 (1959-1979) Integral equations
- 78.46 (1959-1979) Functional analysis
- 78.47 (1959-1979) Operator theory
- 78.49 (1959-1979) Calculus of variations and optimal control (1 articles)
- 78.50 (1959-1979) Geometry
- 78.52 (1959-1972) Convex sets and geometric inequalities
- 78.53 (1959-1979) Differential geometry
- 78.54 (1959-1972) General topology (1 articles)
- 78.55 (1959-1979) Algebraic topology
- 78.57 (1959-1972) Manifolds
- 78.58 (1973-1979) Global analysis, analysis on manifolds
- 78.60 (1959-1979) Probability theory and stochastic processes
- 78.62 (1959-1979) Statistics
- 78.65 (1959-1979) Numerical analysis
- 78.90 (1959-1972) Economics, operations research, programming, games
- 78.93 (1959-1972) Systems, control
- 78.94 (1959-1972) Information and communication, circuits, automata
- 78.99 (1959-1972) None of the above, but in this section (1 articles)
- 78Axx General (77 articles)
  - 78Axx General (2 articles)
  - 78A02 Foundations (1 articles)
  - 78A05 Geometric optics (6 articles)
  - 78A10 Physical optics (1 articles)
  - 78A15 Electron optics
  - 78A20 Space charge waves (2 articles)
  - 78A25 Electromagnetic theory, general (19 articles)
  - 78A30 Electro- and magnetostatics (6 articles)
  - 78A35 Motion of charged particles (3 articles)
  - 78A40 Waves and radiation (4 articles)
  - 78A45 Diffraction, scattering (11 articles)
  - 78A46 Inverse scattering problems (3 articles)
  - 78A48 Composite media; random media (2 articles)
  - 78A50 Antennas, wave-guides (3 articles)
  - 78A55 Technical applications (9 articles)
  - 78A60 Lasers, masers, optical bistability, nonlinear optics (1 articles)
  - 78A70 Biological applications
  - 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section) (1 articles)
  - 78A99 Miscellaneous topics (3 articles)
- 78Mxx Basic methods (18 articles)
  - 78Mxx Basic methods
  - 78M05 Method of moments
  - 78M10 Finite element methods (8 articles)
  - 78M15 Boundary element methods (2 articles)
  - 78M20 Finite difference methods (1 articles)
  - 78M25 Other numerical methods (2 articles)
  - 78M30 Variational methods (1 articles)
  - 78M35 Asymptotic analysis
  - 78M40 Homogenization (1 articles)
  - 78M50 Optimization (2 articles)
  - 78M99 None of the above, but in this section (1 articles)
79 (1940-1958) Mathematical physics, physical applications
- 79 (1940-1958) Mathematical physics, physical applications
- 79.0 (1940-1958) Mathematical physics, physical applications
80 Classical thermodynamics, heat transfer (101 articles)
- 80 Classical thermodynamics, heat transfer
- 80-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (3 articles)
- 80-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 80-02 Research exposition (monographs, survey articles) (1 articles)
- 80-03 Historical (must also be assigned at least one classification number from Section 01)
- 80-04 Explicit machine computation and programs (not the theory of computation or programming) (1 articles)
- 80-05 Experimental work
- 80-06 Proceedings, conferences, collections, etc.
- 80-08 (1984-1999) Computational methods
- 80.0 (1940-1958) Classical thermodynamics and heat transfer
- 80.00 (1959-1979) General (1 articles)
- 80.01 (1959-1979) History and biography
- 80.02 (1959-1979) Logic and foundations
- 80.04 (1959-1972) Set theory
- 80.05 (1959-1979) Combinatorics
- 80.06 (1959-1979) Order, lattices, ordered algebraic structures
- 80.08 (1959-1972) General mathematical systems
- 80.1 (1940-1958) Thermodynamics, statistical mechanics
- 80.10 (1959-1972) Number theory
- 80.12 (1959-1972) Field theory and polynomials
- 80.13 (1959-1972) Commutative rings and algebras
- 80.14 (1959-1972) Algebraic geometry
- 80.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 80.16 (1959-1972) Associative rings and algebras
- 80.17 (1959-1972) Nonassociative rings and algebras
- 80.18 (1959-1972) Category theory, homological algebra
- 80.20 (1959-1979) Group theory and generalizations
- 80.22 (1959-1979) Topological groups, Lie groups
- 80.26 (1959-1979) Real functions
- 80.28 (1959-1979) Measure and integration
- 80.30 (1959-1979) Functions of a complex variable
- 80.31 (1959-1979) Potential theory
- 80.32 (1959-1972) Several complex variables and analytic spaces
- 80.33 (1959-1979) Special functions
- 80.34 (1959-1979) Ordinary differential equations
- 80.35 (1959-1979) Partial differential equations (1 articles)
- 80.39 (1959-1972) Finite differences and functional equations
- 80.40 (1959-1972) Sequences, series, summability
- 80.41 (1959-1979) Approximations and expansions
- 80.42 (1959-1979) Fourier analysis
- 80.44 (1959-1979) Integral transforms, operational calculus
- 80.45 (1959-1979) Integral equations
- 80.46 (1959-1979) Functional analysis
- 80.47 (1959-1979) Operator theory
- 80.49 (1959-1979) Calculus of variations and optimal control
- 80.50 (1959-1972) Geometry
- 80.52 (1959-1972) Convex sets and geometric inequalities
- 80.53 (1959-1979) Differential geometry
- 80.54 (1959-1979) General topology
- 80.55 (1959-1979) Algebraic topology
- 80.57 (1959-1972) Manifolds
- 80.58 (1973-1979) Global analysis, analysis on manifolds
- 80.60 (1959-1979) Probability theory and stochastic processes
- 80.62 (1959-1979) Statistics
- 80.65 (1959-1979) Numerical analysis
- 80.90 (1959-1972) Economics, operations research, programming, games
- 80.93 (1959-1972) Systems, control
- 80.94 (1959-1979) Information and communication, circuits, automata
- 80.99 (1959-1972) None of the above, but in this section
- 80Axx Thermodynamics and heat transfer (84 articles)
  - 80Axx Thermodynamics and heat transfer
  - 80A05 Foundations (6 articles)
  - 80A10 Classical thermodynamics, including relativistic (1 articles)
  - 80A17 Thermodynamics of continua (1 articles)
  - 80A20 Heat and mass transfer, heat flow (33 articles)
  - 80A22 Stefan problems, phase changes, etc. (25 articles)
  - 80A23 Inverse problems (2 articles)
  - 80A25 Combustion (4 articles)
  - 80A30 Chemical kinetics (4 articles)
  - 80A32 Chemically reacting flows (4 articles)
  - 80A50 Chemistry (general)
  - 80A99 None of the above, but in this section (4 articles)
- 80Mxx Basic methods (10 articles)
  - 80Mxx Basic methods
  - 80M10 Finite element methods (4 articles)
  - 80M15 Boundary element methods
  - 80M20 Finite difference methods
  - 80M25 Other numerical methods (1 articles)
  - 80M30 Variational methods
  - 80M35 Asymptotic analysis
  - 80M40 Homogenization (1 articles)
  - 80M50 Optimization (4 articles)
  - 80M99 None of the above, but in this section
81 Quantum theory (342 articles)
- 81 Quantum theory
- 81-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 81-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 81-02 Research exposition (monographs, survey articles) (4 articles)
- 81-03 Historical (must also be assigned at least one classification number from Section 01) (4 articles)
- 81-04 Explicit machine computation and programs (not the theory of computation or programming)
- 81-05 Experimental papers
- 81-06 Proceedings, conferences, collections, etc. (1 articles)
- 81-08 Computational methods
- 81.0 (1940-1958) Quantum mechanics
- 81.00 (1959-1979) General (2 articles)
- 81.01 (1959-1979) History and biography
- 81.02 (1959-1979) Logic and foundations (1 articles)
- 81.04 (1959-1979) Set theory
- 81.05 (1959-1979) Combinatorics
- 81.06 (1959-1979) Order, lattices, ordered algebraic structures
- 81.08 (1959-1972) General mathematical systems
- 81.10 (1959-1979) Number theory
- 81.12 (1959-1972) Field theory and polynomials
- 81.13 (1959-1972) Commutative rings and algebras
- 81.14 (1959-1979) Algebraic geometry
- 81.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 81.16 (1959-1979) Associative rings and algebras
- 81.17 (1959-1979) Nonassociative rings and algebras
- 81.18 (1959-1979) Category theory, homological algebra
- 81.20 (1959-1979) Group theory and generalizations
- 81.22 (1959-1979) Topological groups, Lie groups
- 81.26 (1959-1979) Real functions
- 81.28 (1959-1979) Measure and integration
- 81.30 (1959-1979) Functions of a complex variable (2 articles)
- 81.31 (1959-1979) Potential theory
- 81.32 (1959-1979) Several complex variables and analytic spaces
- 81.33 (1959-1979) Special functions
- 81.34 (1959-1979) Ordinary differential equations
- 81.35 (1959-1979) Partial differential equations (2 articles)
- 81.39 (1959-1979) Finite differences and functional equations
- 81.40 (1959-1979) Sequences, series, summability
- 81.41 (1959-1979) Approximations and expansions
- 81.42 (1959-1979) Fourier analysis
- 81.43 (1973-1979) Abstract harmonic analysis
- 81.44 (1959-1979) Integral transforms, operational calculus
- 81.45 (1959-1979) Integral equations
- 81.46 (1959-1979) Functional analysis (2 articles)
- 81.47 (1959-1979) Operator theory
- 81.49 (1959-1979) Calculus of variations and optimal control
- 81.50 (1959-1979) Geometry
- 81.52 (1959-1979) Convex sets and geometric inequalities
- 81.53 (1959-1979) Differential geometry (1 articles)
- 81.54 (1959-1979) General topology
- 81.55 (1959-1979) Algebraic topology
- 81.57 (1959-1979) Manifolds and cell complexes
- 81.58 (1973-1979) Global analysis, analysis on manifolds
- 81.60 (1959-1979) Probability theory and stochastic processes
- 81.62 (1959-1979) Statistics
- 81.65 (1959-1979) Numerical analysis
- 81.90 (1959-1972) Economics, operations research, programming, games
- 81.93 (1959-1972) Systems, control
- 81.94 (1959-1979) Information and communication, circuits, automata
- 81.99 (1959-1972) None of the above, but in this section
- 81Pxx Axiomatics, foundations, philosophy (130 articles)
  - 81Pxx Axiomatics, foundations, philosophy
  - 81P05 General and philosophical (4 articles)
  - 81P10 Logical foundations of quantum mechanics; quantum logic (98 articles)
  - 81P15 Quantum measurement theory (10 articles)
  - 81P20 Stochastic mechanics (including stochastic electrodynamics) (11 articles)
  - 81P68 Quantum computation and quantum cryptography (4 articles)
  - 81P99 None of the above, but in this section (3 articles)
- 81Qxx General mathematical topics and methods in quantum theory (34 articles)
  - 81Qxx General mathematical topics and methods in quantum theory
  - 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations (9 articles)
  - 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis (9 articles)
  - 81Q15 Perturbation theories for operators and differential equations (2 articles)
  - 81Q20 Semiclassical techniques including WKB and Maslov methods
  - 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (4 articles)
  - 81Q40 Bethe-Salpeter and other integral equations
  - 81Q50 Quantum chaos
  - 81Q60 Supersymmetric quantum mechanics (7 articles)
  - 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
  - 81Q99 None of the above, but in this section (3 articles)
- 81Rxx Groups and algebras in quantum theory (47 articles)
  - 81Rxx Groups and algebras in quantum theory
  - 81R05 Finite-dimensional groups and algebras motivated by physics and their representations (10 articles)
  - 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations (6 articles)
  - 81R12 Relations with integrable systems (1 articles)
  - 81R15 Operator algebra methods (1 articles)
  - 81R20 Covariant wave equations (1 articles)
  - 81R25 Spinor and twistor methods (5 articles)
  - 81R30 Coherent states (1 articles)
  - 81R40 Symmetry breaking
  - 81R50 Quantum groups and related algebraic methods (20 articles)
  - 81R60 Noncommutative geometry (1 articles)
  - 81R99 None of the above, but in this section (1 articles)
- 81Sxx General quantum mechanics and problems of quantization (30 articles)
  - 81Sxx General quantum mechanics and problems of quantization
  - 81S05 Commutation relations and statistics (3 articles)
  - 81S10 Geometry and quantization, symplectic methods (13 articles)
  - 81S20 Stochastic quantization (1 articles)
  - 81S25 Quantum stochastic calculus (1 articles)
  - 81S30 Phase space methods including Wigner distributions, etc. (2 articles)
  - 81S40 Path integrals (4 articles)
  - 81S99 None of the above, but in this section (6 articles)
- 81Txx Quantum field theory; related classical field theories (59 articles)
  - 81Txx Quantum field theory; related classical field theories (1 articles)
  - 81T05 Axiomatic quantum field theory; operator algebras (4 articles)
  - 81T08 Constructive quantum field theory (6 articles)
  - 81T10 Model quantum field theories (3 articles)
  - 81T13 Yang-Mills and other gauge theories (12 articles)
  - 81T15 Perturbative methods of renormalization
  - 81T16 Nonperturbative methods of renormalization
  - 81T17 Renormalization group methods
  - 81T18 Feynman diagrams (1 articles)
  - 81T20 Quantum field theory on curved space backgrounds (1 articles)
  - 81T25 Quantum field theory on lattices (2 articles)
  - 81T27 Continuum limits
  - 81T30 String and superstring theories; other extended objects (e.g., branes) (6 articles)
  - 81T40 Two-dimensional field theories, conformal field theories, etc. (6 articles)
  - 81T45 Topological field theories
  - 81T50 Anomalies (1 articles)
  - 81T60 Supersymmetric field theories (10 articles)
  - 81T70 Quantization in field theory; cohomological methods (3 articles)
  - 81T75 Noncommutative geometry methods
  - 81T80 Simulation and numerical modeling (1 articles)
  - 81T99 None of the above, but in this section (2 articles)
- 81Uxx Scattering theory (6 articles)
  - 81Uxx Scattering theory
  - 81U05 $2$-body potential scattering theory
  - 81U10 $n$-body potential scattering theory (1 articles)
  - 81U15 Exactly and quasi-solvable systems (4 articles)
  - 81U20 $S$-matrix theory, etc.
  - 81U30 Dispersion theory, dispersion relations
  - 81U40 Inverse scattering problems (1 articles)
  - 81U99 None of the above, but in this section
- 81Vxx Applications to specific physical systems (14 articles)
  - 81Vxx Applications to specific physical systems
  - 81V05 Strong interaction, including quantum chromodynamics (4 articles)
  - 81V10 Electromagnetic interaction; quantum electrodynamics (1 articles)
  - 81V15 Weak interaction (1 articles)
  - 81V17 Gravitational interaction
  - 81V19 Other fundamental interactions
  - 81V22 Unified theories (1 articles)
  - 81V25 Other elementary particle theory (2 articles)
  - 81V35 Nuclear physics (2 articles)
  - 81V45 Atomic physics
  - 81V55 Molecular physics
  - 81V70 Many-body theory; quantum Hall effect (2 articles)
  - 81V80 Quantum optics
  - 81V99 None of the above, but in this section (1 articles)
82 Statistical mechanics, structure of matter (103 articles)
- 82 Statistical mechanics, structure of matter
- 82-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 82-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 82-02 Research exposition (monographs, survey articles) (3 articles)
- 82-03 Historical (must also be assigned at least one classification number from Section 01)
- 82-04 Explicit machine computation and programs (not the theory of computation or programming)
- 82-05 Experimental papers
- 82-06 Proceedings, conferences, collections, etc.
- 82-08 Computational methods (1 articles)
- 82.0 (1940-1958) Structure of matter
- 82.00 (1959-1979) General
- 82.01 (1959-1979) History and biography
- 82.02 (1959-1979) Logic and foundations
- 82.04 (1959-1972) Set theory
- 82.05 (1959-1979) Combinatorics
- 82.06 (1959-1979) Order, lattices, ordered algebraic structures
- 82.08 (1959-1972) General mathematical systems
- 82.1 (1940-1958) Statistical mechanics
- 82.10 (1959-1979) Number theory
- 82.12 (1959-1972) Field theory and polynomials
- 82.13 (1959-1972) Commutative rings and algebras
- 82.14 (1959-1972) Algebraic geometry
- 82.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 82.16 (1959-1972) Associative rings and algebras
- 82.17 (1959-1979) Nonassociative rings and algebras
- 82.18 (1959-1972) Category theory, homological algebra
- 82.2 (1940-1958) Statistical thermodynamics and mechanics
- 82.20 (1959-1979) Group theory and generalizations
- 82.22 (1959-1979) Topological groups, Lie groups
- 82.26 (1959-1979) Real functions
- 82.28 (1959-1979) Measure and integration
- 82.30 (1959-1979) Functions of a complex variable
- 82.31 (1959-1979) Potential theory
- 82.32 (1959-1979) Several complex variables and analytic spaces
- 82.33 (1959-1979) Special functions
- 82.34 (1959-1979) Ordinary differential equations
- 82.35 (1959-1979) Partial differential equations (2 articles)
- 82.39 (1959-1979) Finite differences and functional equations
- 82.40 (1959-1979) Sequences, series, summability
- 82.41 (1959-1979) Approximations and expansions (1 articles)
- 82.42 (1959-1979) Fourier analysis
- 82.44 (1959-1979) Integral transforms, operational calculus
- 82.45 (1959-1979) Integral equations (1 articles)
- 82.46 (1959-1979) Functional analysis
- 82.47 (1959-1979) Operator theory
- 82.49 (1959-1979) Calculus of variations and optimal control
- 82.50 (1959-1979) Geometry
- 82.52 (1959-1972) Convex sets and geometric inequalities
- 82.53 (1959-1979) Differential geometry
- 82.54 (1959-1979) General topology
- 82.55 (1959-1979) Algebraic topology
- 82.57 (1959-1979) Manifolds
- 82.58 (1973-1979) Global analysis, analysis on manifolds
- 82.60 (1959-1979) Probability theory and stochastic processes
- 82.62 (1959-1979) Statistics
- 82.65 (1959-1979) Numerical analysis (1 articles)
- 82.90 (1959-1972) Economics, operations research, programming, games
- 82.93 (1959-1972) Systems, control
- 82.94 (1959-1972) Information and communication, circuits, automata
- 82.99 (1959-1972) None of the above, but in this section
- 82Bxx Equilibrium statistical mechanics (26 articles)
  - 82Bxx Equilibrium statistical mechanics
  - 82B03 Foundations (1 articles)
  - 82B05 Classical equilibrium statistical mechanics (general) (3 articles)
  - 82B10 Quantum equilibrium statistical mechanics (general) (2 articles)
  - 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs (1 articles)
  - 82B21 Continuum models (systems of particles, etc.) (1 articles)
  - 82B23 Exactly solvable models; Bethe ansatz (3 articles)
  - 82B24 Interface problems; diffusion-limited aggregation (1 articles)
  - 82B26 Phase transitions (general) (4 articles)
  - 82B27 Critical phenomena
  - 82B28 Renormalization group methods
  - 82B30 Statistical thermodynamics (1 articles)
  - 82B31 Stochastic methods (3 articles)
  - 82B35 Irreversible thermodynamics, including Onsager-Machlup theory (2 articles)
  - 82B40 Kinetic theory of gases (2 articles)
  - 82B41 Random walks, random surfaces, lattice animals, etc.
  - 82B43 Percolation
  - 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) (2 articles)
  - 82B80 Numerical methods (Monte Carlo, series resummation, etc.)
  - 82B99 None of the above, but in this section
- 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) (27 articles)
  - 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)
  - 82C03 Foundations
  - 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
  - 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general) (1 articles)
  - 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
  - 82C21 Dynamic continuum models (systems of particles, etc.)
  - 82C22 Interacting particle systems (1 articles)
  - 82C23 Exactly solvable dynamic models
  - 82C24 Interface problems; diffusion-limited aggregation (2 articles)
  - 82C26 Dynamic and nonequilibrium phase transitions (general) (5 articles)
  - 82C27 Dynamic critical phenomena
  - 82C28 Dynamic renormalization group methods
  - 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.)
  - 82C32 Neural nets (2 articles)
  - 82C35 Irreversible thermodynamics, including Onsager-Machlup theory
  - 82C40 Kinetic theory of gases (2 articles)
  - 82C41 Dynamics of random walks, random surfaces, lattice animals, etc.
  - 82C43 Time-dependent percolation
  - 82C44 Dynamics of disordered systems (random Ising systems, etc.)
  - 82C70 Transport processes (13 articles)
  - 82C80 Numerical methods (Monte Carlo, series resummation, etc.) (1 articles)
  - 82C99 None of the above, but in this section
- 82Dxx Applications to specific types of physical systems (40 articles)
  - 82Dxx Applications to specific types of physical systems (1 articles)
  - 82D05 Gases
  - 82D10 Plasmas (2 articles)
  - 82D15 Liquids (1 articles)
  - 82D20 Solids (1 articles)
  - 82D25 Crystals (6 articles)
  - 82D30 Random media, disordered materials (including liquid crystals and spin glasses) (2 articles)
  - 82D35 Metals
  - 82D37 Semiconductors (8 articles)
  - 82D40 Magnetic materials (4 articles)
  - 82D45 Ferroelectrics (3 articles)
  - 82D50 Superfluids (1 articles)
  - 82D55 Superconductors (3 articles)
  - 82D60 Polymers (2 articles)
  - 82D75 Nuclear reactor theory; neutron transport (6 articles)
  - 82D99 None of the above, but in this section
83 Relativity and gravitational theory (48 articles)
- 83 Relativity and gravitational theory
- 83-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 83-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 83-02 Research exposition (monographs, survey articles) (2 articles)
- 83-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 83-04 Explicit machine computation and programs (not the theory of computation or programming)
- 83-05 Experimental work
- 83-06 Proceedings, conferences, collections, etc.
- 83-08 Computational methods
- 83.0 (1940-1958) Relativity
- 83.00 (1959-1979) General
- 83.01 (1959-1979) History and biography
- 83.02 (1959-1979) Logic and foundations
- 83.04 (1959-1972) Set theory
- 83.05 (1959-1979) Combinatorics
- 83.06 (1959-1979) Order, lattices, ordered algebraic structures
- 83.08 (1959-1972) General mathematical systems
- 83.10 (1959-1979) Number theory
- 83.12 (1959-1972) Field theory and polynomials
- 83.13 (1959-1972) Commutative rings and algebras
- 83.14 (1959-1972) Algebraic geometry
- 83.15 (1959-1979) Linear and multilinear algebra; matrix theory
- 83.16 (1959-1972) Associative rings and algebras
- 83.17 (1959-1979) Nonassociative rings and algebras (1 articles)
- 83.18 (1959-1972) Category theory, homological algebra
- 83.20 (1959-1979) Group theory and generalizations
- 83.22 (1959-1979) Topological groups, Lie groups (1 articles)
- 83.26 (1959-1979) Real functions
- 83.28 (1959-1979) Measure and integration
- 83.30 (1959-1979) Functions of a complex variable
- 83.31 (1959-1979) Potential theory
- 83.32 (1959-1979) Several complex variables and analytic spaces
- 83.33 (1959-1979) Special functions
- 83.34 (1959-1979) Ordinary differential equations
- 83.35 (1959-1979) Partial differential equations
- 83.39 (1959-1979) Finite differences and functional equations
- 83.40 (1959-1972) Sequences, series, summability
- 83.41 (1959-1979) Approximations and expansions
- 83.42 (1959-1972) Fourier analysis
- 83.44 (1959-1972) Integral transforms, operational calculus
- 83.45 (1959-1979) Integral equations
- 83.46 (1959-1979) Functional analysis
- 83.47 (1959-1979) Operator theory
- 83.49 (1959-1979) Calculus of variations and optimal control
- 83.50 (1959-1979) Geometry
- 83.52 (1959-1979) Convex sets and geometric inequalities
- 83.53 (1959-1979) Differential geometry (1 articles)
- 83.54 (1959-1979) General topology
- 83.55 (1959-1979) Algebraic topology
- 83.57 (1959-1979) Manifolds and cell complexes
- 83.58 (1973-1979) Global analysis, analysis on manifolds
- 83.60 (1959-1979) Probability theory and stochastic processes
- 83.62 (1959-1979) Statistics
- 83.65 (1959-1979) Numerical analysis
- 83.90 (1959-1972) Economics, operations research, programming, games
- 83.93 (1959-1972) Systems, control
- 83.94 (1959-1972) Information and communication, circuits, automata
- 83.99 (1959-1972) None of the above, but in this section
- 83A05 Special relativity (4 articles)
- 83B05 Observational and experimental questions
- 83Cxx General relativity (25 articles)
  - 83Cxx General relativity
  - 83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems) (4 articles)
  - 83C10 Equations of motion
  - 83C15 Exact solutions (3 articles)
  - 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries (2 articles)
  - 83C22 Einstein-Maxwell equations
  - 83C25 Approximation procedures, weak fields
  - 83C27 Lattice gravity, Regge calculus and other discrete methods (1 articles)
  - 83C30 Asymptotic procedures (radiation, news functions,
  - 83C35 Gravitational waves
  - 83C40 Gravitational energy and conservation laws; groups of motions
  - 83C45 Quantization of the gravitational field (1 articles)
  - 83C47 Methods of quantum field theory (1 articles)
  - 83C50 Electromagnetic fields
  - 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) (1 articles)
  - 83C57 Black holes (1 articles)
  - 83C60 Spinor and twistor methods; Newman-Penrose formalism (2 articles)
  - 83C65 Methods of noncommutative geometry (1 articles)
  - 83C75 Space-time singularities, cosmic censorship, etc.
  - 83C80 Analogues in lower dimensions (2 articles)
  - 83C99 None of the above, but in this section (6 articles)
- 83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories (1 articles)
- 83Exx Unified, higher-dimensional and super field theories (7 articles)
  - 83Exx Unified, higher-dimensional and super field theories
  - 83E05 Geometrodynamics (1 articles)
  - 83E15 Kaluza-Klein and other higher-dimensional theories (2 articles)
  - 83E30 String and superstring theories
  - 83E50 Supergravity (3 articles)
  - 83E99 None of the above, but in this section (1 articles)
- 83F05 Cosmology (2 articles)
84 (1940-1958) Relativity, astronomy
- 84 (1940-1958) Relativity, astronomy
- 84.0 (1940-1958) Relativity, astronomy
85 Astronomy and astrophysics (13 articles)
- 85 Astronomy and astrophysics
- 85-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 85-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 85-02 Research exposition (monographs, survey articles)
- 85-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 85-04 Explicit machine computation and programs (not the theory of computation or programming)
- 85-05 Experimental work (2 articles)
- 85-06 Proceedings, conferences, collections, etc.
- 85-08 Computational methods (1 articles)
- 85.0 (1940-1958) Astronomy
- 85.00 (1959-1979) General
- 85.01 (1959-1979) History and biography
- 85.02 (1959-1972) Logic and foundations
- 85.04 (1959-1972) Set theory
- 85.05 (1959-1972) Combinatorics
- 85.06 (1959-1972) Order, lattices, ordered algebraic structures
- 85.08 (1959-1972) General mathematical systems
- 85.10 (1959-1972) Number theory
- 85.12 (1959-1972) Field theory and polynomials
- 85.13 (1959-1972) Commutative rings and algebras
- 85.14 (1959-1972) Algebraic geometry
- 85.15 (1959-1972) Linear and multilinear algebra; matrix theory
- 85.16 (1959-1972) Associative rings and algebras
- 85.17 (1959-1972) Nonassociative rings and algebras
- 85.18 (1959-1972) Category theory, homological algebra
- 85.20 (1959-1972) Group theory and generalizations
- 85.22 (1959-1972) Topological groups, Lie groups
- 85.26 (1959-1979) Real functions
- 85.28 (1959-1972) Measure and integration
- 85.30 (1959-1979) Functions of a complex variable
- 85.31 (1959-1979) Potential theory
- 85.32 (1959-1972) Several complex variables and analytic spaces
- 85.33 (1959-1979) Special functions
- 85.34 (1959-1979) Ordinary differential equations
- 85.35 (1959-1979) Partial differential equations
- 85.39 (1959-1972) Finite differences and functional equations
- 85.40 (1959-1972) Sequences, series, summability
- 85.41 (1959-1979) Approximations and expansions
- 85.42 (1959-1979) Fourier analysis
- 85.44 (1959-1979) Integral transforms, operational calculus
- 85.45 (1959-1979) Integral equations
- 85.46 (1959-1979) Functional analysis
- 85.47 (1959-1979) Operator theory
- 85.49 (1959-1979) Calculus of variations and optimal control
- 85.50 (1959-1979) Geometry
- 85.52 (1959-1972) Convex sets and geometric inequalities
- 85.53 (1959-1979) Differential geometry
- 85.54 (1959-1979) General topology
- 85.55 (1959-1979) Algebraic topology
- 85.57 (1959-1979) Manifolds and cell complexes
- 85.58 (1973-1979) Global analysis, analysis on manifolds
- 85.60 (1959-1979) Probability theory and stochastic processes
- 85.62 (1959-1979) Statistics
- 85.65 (1959-1979) Numerical analysis
- 85.90 (1959-1972) Economics, operations research, programming, games
- 85.93 (1959-1972) Systems, control
- 85.94 (1959-1972) Information and communication, circuits, automata
- 85.99 (1959-1972) None of the above, but in this section
- 85A04 General (1 articles)
- 85A05 Galactic and stellar dynamics (1 articles)
- 85A15 Galactic and stellar structure (1 articles)
- 85A20 Planetary atmospheres (1 articles)
- 85A25 Radiative transfer (2 articles)
- 85A30 Hydrodynamic and hydromagnetic problems
- 85A35 Statistical astronomy
- 85A40 Cosmology (1 articles)
- 85A99 Miscellaneous topics (1 articles)
86 Geophysics (42 articles)
- 86 Geophysics
- 86-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 86-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 86-02 Research exposition (monographs, survey articles)
- 86-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 86-04 Explicit machine computation and programs (not the theory of computation or programming)
- 86-05 Experimental work
- 86-06 Proceedings, conferences, collections, etc.
- 86-08 Computational methods (3 articles)
- 86.0 (1940-1958) Geophysics
- 86.00 (1959-1979) General
- 86.01 (1959-1979) History and biography
- 86.02 (1959-1972) Logic and foundations
- 86.04 (1959-1972) Set theory
- 86.05 (1959-1979) Combinatorics
- 86.06 (1959-1972) Order, lattices, ordered algebraic structures
- 86.08 (1959-1972) General mathematical systems
- 86.10 (1959-1972) Number theory
- 86.12 (1959-1972) Field theory and polynomials
- 86.13 (1959-1972) Commutative rings and algebras
- 86.14 (1959-1972) Algebraic geometry
- 86.15 (1959-1972) Linear and multilinear algebra; matrix theory
- 86.16 (1959-1972) Associative rings and algebras
- 86.17 (1959-1972) Nonassociative rings and algebras
- 86.18 (1959-1972) Category theory, homological algebra
- 86.20 (1959-1972) Group theory and generalizations
- 86.22 (1959-1979) Topological groups, Lie groups
- 86.26 (1959-1972) Real functions
- 86.28 (1959-1972) Measure and integration
- 86.30 (1959-1979) Functions of a complex variable
- 86.31 (1959-1979) Potential theory
- 86.32 (1959-1972) Several complex variables and analytic spaces
- 86.33 (1959-1979) Special functions
- 86.34 (1959-1979) Ordinary differential equations
- 86.35 (1959-1979) Partial differential equations (1 articles)
- 86.39 (1959-1972) Finite difference and functional equations
- 86.40 (1959-1979) Sequences, series, summability
- 86.41 (1959-1979) Approximations and expansions
- 86.42 (1959-1972) Fourier analysis
- 86.44 (1959-1979) Integral transforms, operational calculus
- 86.45 (1959-1979) Integral equations
- 86.46 (1959-1972) Functional analysis
- 86.47 (1959-1979) Operator theory
- 86.49 (1959-1979) Calculus of variations and optimal control
- 86.50 (1959-1979) Geometry
- 86.52 (1959-1979) Convex sets and geometric inequalities
- 86.53 (1959-1979) Differential geometry
- 86.54 (1959-1972) General topology
- 86.55 (1959-1972) Algebraic topology
- 86.57 (1959-1972) Manifolds
- 86.60 (1959-1979) Probability theory and stochastic processes
- 86.62 (1959-1979) Statistics
- 86.65 (1959-1979) Numerical analysis
- 86.90 (1959-1972) Economics, operations research, programming, games
- 86.93 (1959-1972) Systems, control
- 86.94 (1959-1972) Information and communication, circuits, automata
- 86.99 (1959-1972) None of the above, but in this section
- 86A04 General
- 86A05 Hydrology, hydrography, oceanography (6 articles)
- 86A10 Meteorology and atmospheric physics (10 articles)
- 86A15 Seismology
- 86A17 Global dynamics, earthquake problems
- 86A20 Potentials, prospecting
- 86A22 Inverse problems
- 86A25 Geo-electricity and geomagnetism (2 articles)
- 86A30 Geodesy, mapping problems (10 articles)
- 86A32 Geostatistics (4 articles)
- 86A40 Glaciology (1 articles)
- 86A60 Geological problems (3 articles)
- 86A99 Miscellaneous topics (1 articles)
90 Operations research, mathematical programming (998 articles)
- 90 Operations research, mathematical programming
- 90-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (4 articles)
- 90-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 90-02 Research exposition (monographs, survey articles) (6 articles)
- 90-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 90-04 Explicit machine computation and programs (not the theory of computation or programming)
- 90-06 Proceedings, conferences, collections, etc. (1 articles)
- 90-08 Computational methods (4 articles)
- 90.0 (1940-1958) Economics, management science, games, programming, resource allocation
- 90.00 (1959-1972) General (1 articles)
- 90.10 (1959-1972) Economics (2 articles)
- 90.30 (1959-1972) Operations research (2 articles)
- 90.40 (1959-1972) Multi-stage decision processes, dynamic programming (general) (3 articles)
- 90.50 (1959-1972) Linear programming (2 articles)
- 90.56 (1959-1972) Integer programming
- 90.57 (1959-1972) Stochastic programming (1 articles)
- 90.58 (1959-1972) Nonlinear programming, general
- 90.59 (1959-1972) Quadratic programming (1 articles)
- 90.60 (1959-1972) Convex programming
- 90.70 (1959-1972) Game theory (2 articles)
- 90.72 (1959-1972) Stochastic games
- 90.75 (1959-1972) Differential and continuous games
- 90.99 (1959-1972) None of the above, but in this section
- 90Bxx Operations research and management science (163 articles)
  - 90Bxx Operations research and management science (2 articles)
  - 90B05 Inventory, storage, reservoirs (11 articles)
  - 90B06 Transportation, logistics (9 articles)
  - 90B10 Network models, deterministic (15 articles)
  - 90B15 Network models, stochastic (5 articles)
  - 90B18 Communication networks (7 articles)
  - 90B20 Traffic problems (7 articles)
  - 90B22 Queues and service (19 articles)
  - 90B25 Reliability, availability, maintenance, inspection (17 articles)
  - 90B30 Production models (11 articles)
  - 90B35 Scheduling theory, deterministic (19 articles)
  - 90B36 Scheduling theory, stochastic
  - 90B40 Search theory (5 articles)
  - 90B50 Management decision making, including multiple objectives (19 articles)
  - 90B60 Marketing, advertising (1 articles)
  - 90B70 Theory of organizations, manpower planning
  - 90B80 Discrete location and assignment (6 articles)
  - 90B85 Continuous location (1 articles)
  - 90B90 Case-oriented studies (2 articles)
  - 90B99 None of the above, but in this section (7 articles)
- 90Cxx Mathematical programming (803 articles)
  - 90Cxx Mathematical programming (2 articles)
  - 90C05 Linear programming (56 articles)
  - 90C06 Large-scale problems (11 articles)
  - 90C08 Special problems of linear programming (transportation, multi-index, etc.) (9 articles)
  - 90C09 Boolean programming (3 articles)
  - 90C10 Integer programming (14 articles)
  - 90C11 Mixed integer programming (4 articles)
  - 90C15 Stochastic programming (56 articles)
  - 90C20 Quadratic programming (29 articles)
  - 90C22 Semidefinite programming (5 articles)
  - 90C25 Convex programming (59 articles)
  - 90C26 Nonconvex programming (26 articles)
  - 90C27 Combinatorial optimization (17 articles)
  - 90C29 Multi-objective and goal programming (27 articles)
  - 90C30 Nonlinear programming (116 articles)
  - 90C31 Sensitivity, stability, parametric optimization (51 articles)
  - 90C32 Fractional programming (8 articles)
  - 90C33 Complementarity problems (34 articles)
  - 90C34 Semi-infinite programming (2 articles)
  - 90C35 Programming involving graphs or networks (15 articles)
  - 90C39 Dynamic programming (20 articles)
  - 90C40 Markov and semi-Markov decision processes (58 articles)
  - 90C46 Optimality conditions, duality (18 articles)
  - 90C47 Minimax problems (19 articles)
  - 90C48 Programming in abstract spaces (25 articles)
  - 90C49 Extreme-point and pivoting methods
  - 90C51 Interior-point methods (17 articles)
  - 90C52 Methods of reduced gradient type (6 articles)
  - 90C53 Methods of quasi-Newton type (7 articles)
  - 90C55 Methods of successive quadratic programming type (7 articles)
  - 90C56 Derivative-free methods (2 articles)
  - 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut (2 articles)
  - 90C59 Approximation methods and heuristics (13 articles)
  - 90C60 Abstract computational complexity for mathematical programming problems (1 articles)
  - 90C70 Fuzzy programming (18 articles)
  - 90C90 Applications of mathematical programming (39 articles)
  - 90C99 None of the above, but in this section (7 articles)
91 Game theory, economics, social and behavioral sciences (465 articles)
- 91 Game theory, economics, social and behavioral sciences
- 91-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 91-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 91-02 Research exposition (monographs, survey articles) (1 articles)
- 91-03 Historical (must also be assigned at least one classification number from section 01)
- 91-04 Explicit machine computation and programs (not the theory of computation or programming)
- 91-06 Proceedings, conferences, collections, etc.
- 91-08 Computational methods (1 articles)
- 91Axx Game theory (165 articles)
  - 91Axx Game theory
  - 91A05 2-person games (17 articles)
  - 91A06 $n$-person games, $n>2$ (4 articles)
  - 91A10 Noncooperative games (21 articles)
  - 91A12 Cooperative games (37 articles)
  - 91A13 Games with infinitely many players (1 articles)
  - 91A15 Stochastic games (10 articles)
  - 91A18 Games in extensive form (1 articles)
  - 91A20 Multistage and repeated games (5 articles)
  - 91A22 Evolutionary games (1 articles)
  - 91A23 Differential games (11 articles)
  - 91A24 Positional games (pursuit and evasion, etc.) (1 articles)
  - 91A25 Dynamic games (2 articles)
  - 91A26 Rationality, learning
  - 91A28 Signaling, communication
  - 91A30 Utility theory for games
  - 91A35 Decision theory for games (4 articles)
  - 91A40 Game-theoretic models (9 articles)
  - 91A43 Games involving graphs (2 articles)
  - 91A44 Games involving topology or set theory (6 articles)
  - 91A46 Combinatorial games (2 articles)
  - 91A50 Discrete-time games (4 articles)
  - 91A55 Games of timing
  - 91A60 Probabilistic games; gambling (3 articles)
  - 91A65 Hierarchical games (3 articles)
  - 91A70 Spaces of games
  - 91A80 Applications of game theory (8 articles)
  - 91A90 Experimental studies
  - 91A99 None of the above, but in this section (13 articles)
- 91Bxx Mathematical economics (220 articles)
  - 91Bxx Mathematical economics (2 articles)
  - 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in general) (40 articles)
  - 91B06 Decision theory (18 articles)
  - 91B08 Individual preferences (12 articles)
  - 91B10 Group preferences (3 articles)
  - 91B12 Voting theory (2 articles)
  - 91B14 Social choice (2 articles)
  - 91B16 Utility theory (9 articles)
  - 91B18 Public goods
  - 91B24 Price theory and market structure (7 articles)
  - 91B26 Market models (auctions, bargaining, bidding, selling, etc.) (3 articles)
  - 91B28 Finance, portfolios, investment (26 articles)
  - 91B30 Risk theory, insurance (28 articles)
  - 91B32 Resource and cost allocation (1 articles)
  - 91B38 Production theory, theory of the firm (3 articles)
  - 91B40 Labor market, contracts (2 articles)
  - 91B42 Consumer behavior, demand theory (1 articles)
  - 91B44 Informational economics
  - 91B50 Equilibrium: general theory (14 articles)
  - 91B52 Special types of equilibria (1 articles)
  - 91B54 Special types of economies
  - 91B60 General economic models, trade models (3 articles)
  - 91B62 Dynamic economic models, growth models (8 articles)
  - 91B64 Macro-economic models (monetary models, models of taxation) (2 articles)
  - 91B66 Multisectoral models
  - 91B68 Matching models (1 articles)
  - 91B70 Stochastic models (4 articles)
  - 91B72 Spatial models
  - 91B74 Models of real-world systems (2 articles)
  - 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
  - 91B82 Statistical methods; economic indices and measures (6 articles)
  - 91B84 Economic time series analysis (10 articles)
  - 91B99 None of the above, but in this section (10 articles)
- 91Cxx Social and behavioral sciences: general topics (5 articles)
  - 91Cxx Social and behavioral sciences: general topics
  - 91C05 Measurement theory (1 articles)
  - 91C15 One- and multidimensional scaling
  - 91C20 Clustering (2 articles)
  - 91C99 None of the above, but in this section (2 articles)
- 91Dxx Mathematical sociology (including anthropology) (21 articles)
  - 91Dxx Mathematical sociology (including anthropology)
  - 91D10 Models of societies, social and urban evolution (1 articles)
  - 91D20 Mathematical geography and demography (13 articles)
  - 91D25 Spatial models
  - 91D30 Social networks (3 articles)
  - 91D35 Manpower systems
  - 91D99 None of the above, but in this section (4 articles)
- 91Exx Mathematical psychology (14 articles)
  - 91Exx Mathematical psychology
  - 91E10 Cognitive psychology (2 articles)
  - 91E30 Psychophysics and psychophysiology; perception (2 articles)
  - 91E40 Memory and learning (2 articles)
  - 91E45 Measurement and performance
  - 91E99 None of the above, but in this section (8 articles)
- 91Fxx Other social and behavioral sciences (mathematical treatment) (35 articles)
  - 91Fxx Other social and behavioral sciences (mathematical treatment) (1 articles)
  - 91F10 History, political science (1 articles)
  - 91F20 Linguistics (31 articles)
  - 91F99 None of the above, but in this section (2 articles)
92 Biology and other natural sciences (220 articles)
- 92 Biology and other natural sciences
- 92-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 92-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 92-02 Research exposition (monographs, survey articles) (1 articles)
- 92-03 Historical (must also be assigned at least one classification number from Section 01) (2 articles)
- 92-04 Explicit machine computation and programs (not the theory of computation or programming) (3 articles)
- 92-06 Proceedings, conferences, collections, etc.
- 92-08 Computational methods (2 articles)
- 92.0 (1940-1958) Biology and sociology
- 92.00 (1959-1972) General (1 articles)
- 92.10 (1959-1972) Biology (1 articles)
- 92.20 (1959-1972) Genetics
- 92.30 (1959-1972) Population dynamics, epidemiology
- 92.40 (1959-1972) Sociology
- 92.50 (1959-1972) Psychology
- 92.99 (1959-1972) None of the above, but in this section
- 92Bxx Mathematical biology in general (33 articles)
  - 92Bxx Mathematical biology in general
  - 92B05 General biology and biomathematics (14 articles)
  - 92B10 Taxonomy, statistics
  - 92B15 General biostatistics
  - 92B20 Neural networks, artificial life and related topics (17 articles)
  - 92B99 None of the above, but in this section (2 articles)
- 92Cxx Physiological, cellular and medical topics (84 articles)
  - 92Cxx Physiological, cellular and medical topics (3 articles)
  - 92C05 Biophysics (1 articles)
  - 92C10 Biomechanics
  - 92C15 Developmental biology, pattern formation (4 articles)
  - 92C17 Cell movement (chemotaxis, etc.) (14 articles)
  - 92C20 Neural biology (13 articles)
  - 92C30 Physiology (general) (3 articles)
  - 92C35 Physiological flow
  - 92C37 Cell biology (4 articles)
  - 92C40 Biochemistry, molecular biology (5 articles)
  - 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (8 articles)
  - 92C50 Medical applications (general) (17 articles)
  - 92C55 Biomedical imaging and signal processing (11 articles)
  - 92C60 Medical epidemiology (1 articles)
  - 92C80 Plant biology
  - 92C99 None of the above, but in this section
- 92Dxx Genetics and population dynamics (80 articles)
  - 92Dxx Genetics and population dynamics
  - 92D10 Genetics (4 articles)
  - 92D15 Problems related to evolution (2 articles)
  - 92D20 Protein sequences, DNA sequences (3 articles)
  - 92D25 Population dynamics (general) (49 articles)
  - 92D30 Epidemiology (12 articles)
  - 92D40 Ecology (8 articles)
  - 92D50 Animal behavior (2 articles)
  - 92D99 None of the above, but in this section
- 92Exx Chemistry (7 articles)
  - 92Exx Chemistry (1 articles)
  - 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (2 articles)
  - 92E20 Classical flows, reactions, etc. (4 articles)
  - 92E99 None of the above, but in this section
- 92F05 Other natural sciences (2 articles)
93 Systems theory; control (2733 articles)
- 93 Systems theory; control
- 93-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (3 articles)
- 93-01 Instructional exposition (textbooks, tutorial papers, etc.) (2 articles)
- 93-02 Research exposition (monographs, survey articles) (8 articles)
- 93-03 Historical (must also be assigned at least one classification number from Section 01) (3 articles)
- 93-04 Explicit machine computation and programs (not the theory of computation or programming) (2 articles)
- 93-06 Proceedings, conferences, collections, etc. (10 articles)
- 93.0 (1940-1958) Control systems
- 93.00 (1959-1972) General (5 articles)
- 93.10 (1959-1972) Systems, general (7 articles)
- 93.20 (1959-1972) Stability, qualitative behavior (5 articles)
- 93.40 (1959-1972) Optimal control (3 articles)
- 93.60 (1959-1972) Stochastic control (3 articles)
- 93.70 (1959-1972) Adaptive control
- 93.99 (1959-1972) None of the above, but in this section
- 93Axx General (167 articles)
  - 93Axx General (1 articles)
  - 93A05 Axiomatic system theory (7 articles)
  - 93A10 General systems (24 articles)
  - 93A13 Hierarchical systems (7 articles)
  - 93A14 Decentralized systems (44 articles)
  - 93A15 Large scale systems (35 articles)
  - 93A30 Mathematical modeling (models of systems, model-matching, etc.) (37 articles)
  - 93A99 None of the above, but in this section (12 articles)
- 93Bxx Controllability, observability, and system structure (775 articles)
  - 93Bxx Controllability, observability, and system structure (4 articles)
  - 93B03 Attainable sets (23 articles)
  - 93B05 Controllability (74 articles)
  - 93B07 Observability (40 articles)
  - 93B10 Canonical structure (24 articles)
  - 93B11 System structure simplification (18 articles)
  - 93B12 Variable structure systems (14 articles)
  - 93B15 Realizations from input-output data (28 articles)
  - 93B17 Transformations (22 articles)
  - 93B18 Linearizations (8 articles)
  - 93B20 Minimal systems representations (10 articles)
  - 93B25 Algebraic methods (76 articles)
  - 93B27 Geometric methods (including algebro-geometric) (38 articles)
  - 93B28 Operator-theoretic methods (6 articles)
  - 93B29 Differential-geometric methods (4 articles)
  - 93B30 System identification (36 articles)
  - 93B35 Sensitivity (robustness) (25 articles)
  - 93B36 $ (24 articles)
  - 93B40 Computational methods (62 articles)
  - 93B50 Synthesis problems (45 articles)
  - 93B51 Design techniques (robust design, computer-aided design, etc.) (52 articles)
  - 93B52 Feedback control (78 articles)
  - 93B55 Pole and zero placement problems (40 articles)
  - 93B60 Eigenvalue problems (15 articles)
  - 93B99 None of the above, but in this section (9 articles)
- 93Cxx Control systems, guided systems (1041 articles)
  - 93Cxx Control systems, guided systems (12 articles)
  - 93C05 Linear systems (206 articles)
  - 93C10 Nonlinear systems (159 articles)
  - 93C15 Systems governed by ordinary differential equations (92 articles)
  - 93C20 Systems governed by partial differential equations (36 articles)
  - 93C23 Systems governed by functional-differential equations (37 articles)
  - 93C25 Systems in abstract spaces (15 articles)
  - 93C30 Systems governed by functional relations other than differential equations (29 articles)
  - 93C35 Multivariable systems (71 articles)
  - 93C40 Adaptive control (44 articles)
  - 93C41 Problems with incomplete information (13 articles)
  - 93C42 Fuzzy control (15 articles)
  - 93C55 Discrete-time systems (113 articles)
  - 93C57 Sampled-data systems (29 articles)
  - 93C62 Digital systems (5 articles)
  - 93C65 Discrete event systems (23 articles)
  - 93C70 Time-scale analysis and singular perturbations (5 articles)
  - 93C73 Perturbations (17 articles)
  - 93C80 Frequency-response methods (12 articles)
  - 93C83 Control problems involving computers (process control, etc.) (7 articles)
  - 93C85 Automated systems (robots, etc.) (20 articles)
  - 93C95 Applications (37 articles)
  - 93C99 None of the above, but in this section (44 articles)
- 93Dxx Stability (352 articles)
  - 93Dxx Stability (11 articles)
  - 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) (61 articles)
  - 93D09 Robust stability (42 articles)
  - 93D10 Popov-type stability of feedback systems (9 articles)
  - 93D15 Stabilization of systems by feedback (127 articles)
  - 93D20 Asymptotic stability (35 articles)
  - 93D21 Adaptive or robust stabilization (33 articles)
  - 93D25 Input-output approaches (9 articles)
  - 93D30 Scalar and vector Lyapunov functions (6 articles)
  - 93D99 None of the above, but in this section (19 articles)
- 93Exx Stochastic systems and control (347 articles)
  - 93Exx Stochastic systems and control (2 articles)
  - 93E03 Stochastic systems, general (21 articles)
  - 93E10 Estimation and detection (64 articles)
  - 93E11 Filtering (40 articles)
  - 93E12 System identification (77 articles)
  - 93E14 Data smoothing (6 articles)
  - 93E15 Stochastic stability (21 articles)
  - 93E20 Optimal stochastic control (80 articles)
  - 93E24 Least squares and related methods (9 articles)
  - 93E25 Other computational methods (17 articles)
  - 93E35 Stochastic learning and adaptive control (5 articles)
  - 93E99 None of the above, but in this section (5 articles)
94 Information and communication, circuits (544 articles)
- 94 Information and communication, circuits
- 94-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (7 articles)
- 94-01 Instructional exposition (textbooks, tutorial papers, etc.) (1 articles)
- 94-02 Research exposition (monographs, survey articles) (2 articles)
- 94-03 Historical (must also be assigned at least one classification number from Section 01) (1 articles)
- 94-04 Explicit machine computation and programs (not the theory of computation or programming)
- 94-06 Proceedings, conferences, collections, etc. (1 articles)
- 94.0 (1940-1958) Information and communication theory
- 94.00 (1959-1972) General (6 articles)
- 94.10 (1959-1972) Communication theory (9 articles)
- 94.15 (1959-1972) Coding theory
- 94.20 (1959-1972) Information theory (8 articles)
- 94.30 (1959-1972) Circuits, networks; applications of graph theory, Boolean algebra (5 articles)
- 94.35 (1959-1972) Artificial intelligence, pattern recognition, learning processes
- 94.40 (1959-1972) Automata, general (10 articles)
- 94.45 (1959-1972) Probabilistic automata (1 articles)
- 94.50 (1959-1972) Linguistics, formal languages (20 articles)
- 94.99 (1959-1972) None of the above, but in this section
- 94Axx Communication, information (356 articles)
  - 94Axx Communication, information
  - 94A05 Communication theory (27 articles)
  - 94A08 Image processing (compression, reconstruction, etc.) (11 articles)
  - 94A11 Application of orthogonal functions in communication (3 articles)
  - 94A12 Signal theory (characterization, reconstruction, etc.) (25 articles)
  - 94A13 Detection theory (5 articles)
  - 94A14 Modulation and demodulation (3 articles)
  - 94A15 Information theory, general (70 articles)
  - 94A17 Measures of information, entropy (106 articles)
  - 94A20 Sampling theory (13 articles)
  - 94A24 Coding theorems (Shannon theory) (17 articles)
  - 94A29 Source coding (17 articles)
  - 94A34 Rate-distortion theory (5 articles)
  - 94A40 Channel models (22 articles)
  - 94A45 Prefix, length-variable, comma-free codes
  - 94A50 Theory of questionnaires (3 articles)
  - 94A55 Shift register sequences and sequences over finite alphabets (1 articles)
  - 94A60 Cryptography (19 articles)
  - 94A62 Authentication and secret sharing (3 articles)
  - 94A99 None of the above, but in this section (6 articles)
- 94Bxx Theory of error-correcting codes and error-detecting codes (32 articles)
  - 94Bxx Theory of error-correcting codes and error-detecting codes
  - 94B05 Linear codes, general (6 articles)
  - 94B10 Convolutional codes (1 articles)
  - 94B12 Combined modulation schemes (including trellis codes)
  - 94B15 Cyclic codes
  - 94B20 Burst-correcting codes (1 articles)
  - 94B25 Combinatorial codes (3 articles)
  - 94B27 Geometric methods (including applications of algebraic geometry)
  - 94B30 Majority codes (1 articles)
  - 94B35 Decoding (1 articles)
  - 94B40 Arithmetic codes
  - 94B50 Synchronization error-correcting codes
  - 94B60 Other types of codes (5 articles)
  - 94B65 Bounds on codes (2 articles)
  - 94B70 Error probability (2 articles)
  - 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
  - 94B99 None of the above, but in this section (10 articles)
- 94Cxx Circuits, networks (54 articles)
  - 94Cxx Circuits, networks (2 articles)
  - 94C05 Analytic circuit theory (8 articles)
  - 94C10 Switching theory, application of Boolean algebra; Boolean functions (20 articles)
  - 94C12 Fault detection; testing (2 articles)
  - 94C15 Applications of graph theory (12 articles)
  - 94C30 Applications of design theory (3 articles)
  - 94C99 None of the above, but in this section (7 articles)
- 94D05 Fuzzy sets and logic (in connection with questions of Section 94) (31 articles)
97 Mathematics education (834 articles)
- 97 Mathematics education
- 97-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1 articles)
- 97-01 Instructional exposition (textbooks, tutorial papers, etc.) (3 articles)
- 97-02 Research exposition (monographs, survey articles)
- 97-03 Historical (must also be assigned at least one classification number from Section 01) (20 articles)
- 97-04 Explicit machine computation and programs (not the theory of computation or programming)
- 97-06 Proceedings, conferences, collections, etc. (3 articles)
- 97Axx General (8 articles)
  - 97Axx General (2 articles)
  - 97A20 Recreational mathematics (5 articles)
  - 97A40 Sociological issues (1 articles)
  - 97A80 Standards
  - 97A90 Fiction and games
- 97Bxx Educational policy and educational systems (65 articles)
  - 97Bxx Educational policy and educational systems (2 articles)
  - 97B10 Educational research and planning (2 articles)
  - 97B20 General education (29 articles)
  - 97B30 Vocational education (1 articles)
  - 97B40 Higher education (8 articles)
  - 97B50 Teacher education (6 articles)
  - 97B60 Out-of-school education. Adult and further education (1 articles)
  - 97B70 Syllabuses. Curriculum guides, official documents (1 articles)
  - 97B99 None of the above, but in this section (15 articles)
- 97Cxx Psychology of and research in mathematics education (42 articles)
  - 97Cxx Psychology of and research in mathematics education (3 articles)
  - 97C20 Affective aspects (motivation, anxiety, persistence, etc.)
  - 97C30 Student learning and thinking (misconceptions, cognitive development, problem solving, etc.) (17 articles)
  - 97C40 Assessment (large scale assessment, validity, reliability, etc.)
  - 97C50 Theoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.)
  - 97C60 Sociological aspects of learning (culture, group interactions, equity issues, etc.)
  - 97C70 Teachers, and research on teacher education (teacher development, etc.) (7 articles)
  - 97C80 Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.)
  - 97C90 Teaching and curriculum (innovations, teaching practices, studies of curriculum materials, effective teaching, etc. )
  - 97C99 None of the above, but in this section (15 articles)
- 97Dxx Education and instruction in mathematics (116 articles)
  - 97Dxx Education and instruction in mathematics (12 articles)
  - 97D10 Comparative studies on mathematics education (2 articles)
  - 97D20 Philosophical and theoretical contributions to mathematical education (3 articles)
  - 97D30 Goals of mathematics teaching. Curriculum development (1 articles)
  - 97D40 Teaching methods and classroom techniques. Lesson preparation. Educational principles (34 articles)
  - 97D50 Teaching problem solving and heuristic strategies (5 articles)
  - 97D60 Achievement control and rating (17 articles)
  - 97D70 Diagnosis, analysis and remediation of learning difficulties and student errors (3 articles)
  - 97D80 Teaching units, draft lessons and master lessons (1 articles)
  - 97D99 None of the above, but in this section (38 articles)
- 97Uxx Educational material and media. Educational technology (576 articles)
  - 97Uxx Educational material and media. Educational technology (5 articles)
  - 97U20 Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom (14 articles)
  - 97U30 Teacher manuals and planning aids (1 articles)
  - 97U40 Problem books; student competitions, examination questions (469 articles)
  - 97U50 Computer assisted instruction and programmed instruction (34 articles)
  - 97U60 Manipulative materials and their use in the classroom (31 articles)
  - 97U70 Technological tools (computers, calculators, software, etc.) and their use in the classroom (16 articles)
  - 97U80 Audiovisual media and their use in instruction
  - 97U99 None of the above, but in this section (6 articles)
99 (1940-1958) Miscellaneous
- 99 (1940-1958) Miscellaneous
- 99.0 (1940-1958) Miscellaneous

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