La Classification Mathématique par matières 2000
Mathematics subject Classification 2000
Question : CC = T
00-XX General
- 00-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 00-02 Research exposition (monographs, survey articles)
- 00-99 General mathematics (not classified at a more specific level)
- 00Axx General and miscellaneous specific topics
- 00A05 General mathematics
- 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
- 00A08 Recreational mathematics [See also 97A20]
- 00A17 External book reviews
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
00A99
- 00A20 Dictionaries and other general reference works
- 00A30 Philosophy of mathematics [See also 03A05]
- 00A35 Methodology of mathematics, didactics [See also 97Cxx, 97Dxx]
- 00A69 General applied mathematics [For physics, see 00A79 and Sections 70 through 86]
- 00A71 Theory of mathematical modeling
- 00A72 General methods of simulation
- 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
- 00A99 Miscellaneous topics
- 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
- 00B25 Proceedings of conferences of miscellaneous specific interest
- 00B30 Festschriften
- 00B50 Volumes of selected translations
- 00B55 Miscellaneous volumes of translations
- 00B60 Collections of reprinted articles [See also 01A75]
01-XX History and biography
- 01-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 01-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 01-02 Research exposition (monographs, survey articles)
- 01-06 Proceedings, conferences, collections, etc.
- 01-08 Computational methods
- 01-99 History and biography (not classified at a more specific level)
- 01Axx History of mathematics and mathematicians
- 01A05 General histories, source books
- 01A07 Ethnomathematics, general
- 01A10 Paleolithic, Neolithic
- 01A12 Indigenous cultures of the Americas
- 01A13 Other indigenous cultures (non-European)
- 01A15 Indigenous European cultures (pre-Greek, etc.)
- 01A16 Egyptian
- 01A29 Southeast Asia
- 01A40 15th and 16th centuries, Renaissance
- 01A45 17th century
- 01A50 18th century
- 01A55 19th century
- 01A60 20th century
- 01A61 Twenty-first century
[Nouveau code MSC 2000]
- 01A65 Contemporary
- 01A67 Future prospectives
- 01A70 Biographies, obituaries, personalia, bibliographies
- 01A72 Schools of mathematics
- 01A73 Universities
- 01A74 Other institutions and academies
- 01A75 Collected or selected works; reprintings or translations of classics [See also 00B60]
- 01A80 Sociology (and profession) of mathematics
- 01A85 Historiography
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
01A99
- 01A90 Bibliographic studies
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
01A99
- 01A99 Miscellaneous topics
03-XX Mathematical logic and foundations
- 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 03-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 03-02 Research exposition (monographs, survey articles)
- 03-03 Historical (must also be assigned at least one classification number from Section 01)
- 03-04 Explicit machine computation and programs (not the theory of computation or programming)
- 03-06 Proceedings, conferences, collections, etc.
- 03-99 Mathematical logic and foundations (not classified at a more specific level)
- 03A05 Philosophical and critical [For philosophy of mathematics, see also 00A30]
- 03B05 Classical propositional logic
- 03B10 Classical first-order logic
- 03B15 Higher-order logic and type theory
- 03B20 Subsystems of classical logic (including intuitionistic logic)
- 03B22 Abstract deductive systems
- 03B25 Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
- 03B30 Foundations of classical theories (including reverse mathematics) [See also 03F35]
- 03B35 Mechanization of proofs and logical operations [See also 68T15]
- 03B40 Combinatory logic and lambda-calculus [See also 68N18]
- 03B44 Temporal logic
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
03B45
- 03B45 Modal logic [For knowledge and belief see 03B42; for temporal logic see 03B44; for provability logic see also 03F45]
- 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) [For proof-theoretic aspects see 03F52]
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
03B46, 03F50
- 03B48 Probability and inductive logic [See also 60A05]
- 03B52 Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]
- 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
- 03B55 Intermediate logics
- 03B60 Other nonclassical logic
- 03B65 Logic of natural languages [See also 68T50, 91F20]
- 03B70 Logic in computer science [See also 68-XX]
- 03B80 Other applications of logic
- 03B99 None of the above, but in this section
- 03Cxx Model theory
- 03C05 Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]
- 03C07 Basic properties of first-order languages and structures
- 03C10 Quantifier elimination, model completeness and related topics
- 03C13 Finite structures [See also 68Q15, 68Q19]
- 03C15 Denumerable structures
- 03C20 Ultraproducts and related constructions
- 03C25 Model-theoretic forcing
- 03C30 Other model constructions
- 03C35 Categoricity and completeness of theories
- 03C40 Interpolation, preservation, definability
- 03C45 Classification theory, stability and related concepts
- 03C50 Models with special properties (saturated, rigid, etc.)
- 03C52 Properties of classes of models
- 03C55 Set-theoretic model theory
- 03C57 Effective and recursion-theoretic model theory [See also 03D45]
- 03C60 Model-theoretic algebra [See also 08C10, 11U09, 12L12, 13L05, 16B70, 20A15]
- 03C62 Models of arithmetic and set theory [See also 03Hxx]
- 03C64 Model theory of ordered structures; o-minimality
[Nouveau code MSC 2000]
- 03C65 Models of other mathematical theories
- 03C68 Other classical first-order model theory
- 03C70 Logic on admissible sets
- 03C75 Other infinitary logic
- 03C80 Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]
- 03C85 Second- and higher-order model theory
- 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
- 03C95 Abstract model theory
- 03C98 Applications of model theory [See also 03C60]
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- Code MSC1991 affilié :
03C99
- 03C99 None of the above, but in this section
- 03Dxx Computability and recursion theory
- 03D03 Thue and Post systems, etc.
- 03D05 Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]
- 03D10 Turing machines and related notions [See also 68Q05]
- 03D15 Complexity of computation [See also 68Q15, 68Q17]
- 03D20 Recursive functions and relations, subrecursive hierarchies
- 03D25 Recursively (computably) enumerable sets and degrees
- 03D28 Other Turing degree structures
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- Code MSC1991 affilié :
03D30
- 03D30 Other degrees and reducibilities
- 03D35 Undecidability and degrees of sets of sentences
- 03D40 Word problems, etc. [See also 06B25, 08A50, 20F10, 20M05, 68R15]
- 03D45 Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
- 03D50 Recursive equivalence types of sets and structures, isols
- 03D60 Computability and recursion theory on ordinals, admissible sets, etc.
- 03D65 Higher-type and set recursion theory
- 03D70 Inductive definability
- 03D75 Abstract and axiomatic computability and recursion theory
- 03D80 Applications of computability and recursion theory
- 03D99 None of the above, but in this section
- 03Exx Set theory
- 03E02 Partition relations
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
03E05, 03E10, 04A10, 04A20
- 03E04 Ordered sets and their cofinalities; pcf theory
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
03E05, 03E10, 04A10, 04A20
- 03E05 Other combinatorial set theory
- 03E15 Descriptive set theory [See also 26A21, 28A05, 54H05]
- 03E17 Cardinal characteristics of the continuum
[Nouveau code MSC 2000]
- 03E20 Other classical set theory (including functions, relations, and set algebra)
- 03E25 Axiom of choice and related propositions
- 03E30 Axiomatics of classical set theory and its fragments
- 03E35 Consistency and independence results
- 03E40 Other aspects of forcing and Boolean-valued models
- 03E45 Inner models, including constructibility, ordinal definability, and core models
- 03E47 Other notions of set-theoretic definability
- 03E50 Continuum hypothesis and Martin's axiom
- 03E60 Determinacy principles
- 03E65 Other hypotheses and axioms
- 03E70 Nonclassical and second-order set theories
- 03E72 Fuzzy set theory
- 03E75 Applications of set theory
- 03E99 None of the above, but in this section
- 03Fxx Proof theory and constructive mathematics
- 03F03 Proof theory, general
- 03F05 Cut-elimination and normal-form theorems
- 03F07 Structure of proofs
- 03F10 Functionals in proof theory
- 03F15 Recursive ordinals and ordinal notations
- 03F20 Complexity of proofs
- 03F25 Relative consistency and interpretations
- 03F30 First-order arithmetic and fragments
- 03F35 Second- and higher-order arithmetic and fragments [See also 03B30]
- 03F40 Gödel numberings in proof theory
- 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
[Nouveau code MSC 2000]
- 03F50 Metamathematics of constructive systems
- 03F52 Linear logic and other substructural logics [See also 03B47]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
03F50
- 03F55 Intuitionistic mathematics
- 03F60 Constructive and recursive analysis [See also 03B30, 03D45, 26E40, 46S30, 47S30]
- 03F65 Other constructive mathematics [See also 03D45]
- 03F99 None of the above, but in this section
- 03G10 Lattices and related structures [See also 06Bxx]
- 03G12 Quantum logic [See also 06C15, 81P10]
- 03G15 Cylindric and polyadic algebras; relation algebras
- 03G20 Lukasiewicz and Post algebras [See also 06D25, 06D30]
- 03G25 Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
- 03G30 Categorical logic, topoi [See also 18B25, 18C05, 18C10]
- 03G99 None of the above, but in this section
- 03Hxx Nonstandard models [See also 03C62]
- 03H05 Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
- 03H10 Other applications of nonstandard models (economics, physics, etc.)
- 03H15 Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]
- 03H99 None of the above, but in this section
05-XX Combinatorics [For finite fields, see 11Txx]
- 05-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 05-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 05-02 Research exposition (monographs, survey articles)
- 05-03 Historical (must also be assigned at least one classification number from Section 01)
- 05-04 Explicit machine computation and programs (not the theory of computation or programming)
- 05-06 Proceedings, conferences, collections, etc.
- 05-99 Combinatorics (not classified at a more specific level)
- 05Axx Enumerative combinatorics
- 05A05 Combinatorial choice problems (subsets, representatives, permutations)
- 05A10 Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]
- 05A15 Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
- 05A16 Asymptotic enumeration
- 05A17 Partitions of integers [See also 11P81, 11P82, 11P83]
- 05A18 Partitions of sets
- 05A19 Combinatorial identities
- 05A20 Combinatorial inequalities
- 05A30 q-calculus and related topics [See also 33Dxx]
- 05A99 None of the above, but in this section
- 05Bxx Designs and configurations [For applications of design theory, see 94C30]
- 05B07 Triple systems
- 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]
- 05B15 Orthogonal arrays, Latin squares, Room squares
- 05B20 Matrices (incidence, Hadamard, etc.)
- 05B25 Finite geometries [See also 51D20, 51Exx]
- 05B30 Other designs, configurations [See also 51E30]
- 05B35 Matroids, geometric lattices [See also 52B40, 90C27]
- 05B45 Tessellation and tiling problems [See also 52C20, 52C22]
- 05B99 None of the above, but in this section
- 05Cxx Graph theory [For applications of graphs, see 68R10, 90C35, 94C15]
- 05C05 Trees
- 05C10 Topological graph theory, imbedding [See also 57M15, 57M25]
- 05C12 Distance in graphs
- 05C17 Perfect graphs
[Nouveau code MSC 2000]
- 05C20 Directed graphs (digraphs), tournaments
- 05C30 Enumeration of graphs and maps
- 05C35 Extremal problems [See also 90C35]
- 05C38 Paths and cycles [See also 90B10]
- 05C40 Connectivity
- 05C45 Eulerian and Hamiltonian graphs
- 05C50 Graphs and matrices
- 05C55 Generalized Ramsey theory
- 05C60 Isomorphism problems (reconstruction conjecture, etc.)
- 05C62 Graph representations (geometric and intersection representations, etc.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
05C75
- 05C69 Dominating sets, independent sets, cliques
[Nouveau code MSC 2000]
- 05C70 Factorization, matching, covering and packing
- 05C75 Structural characterization of types of graphs
- 05C78 Graph labelling (graceful graphs, bandwidth, etc.)
- 05C85 Graph algorithms [See also 68R10, 68W05]
- 05C90 Applications
- 05C99 None of the above, but in this section
- 05Dxx Extremal combinatorics
- 05D05 Extremal set theory
- 05D10 Ramsey theory
- 05D15 Transversal (matching) theory
- 05D40 Probabilistic methods
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
05A16
- 05D99 None of the above, but in this section
- 05Exx Algebraic combinatorics
- 05E05 Symmetric functions
- 05E10 Tableaux, representations of the symmetric group [See also 20C30]
- 05E15 Combinatorial problems concerning the classical groups [See also 22E45, 33C80]
- 05E20 Group actions on designs, geometries and codes
- 05E25 Group actions on posets and homology groups of posets [See also 06A11]
- 05E30 Association schemes, strongly regular graphs
- 05E35 Orthogonal polynomials [See also 33C45, 33C50, 33D45]
- 05E99 None of the above, but in this section
06-XX Order, lattices, ordered algebraic structures [See also 18B35]
- 06-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 06-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 06-02 Research exposition (monographs, survey articles)
- 06-03 Historical (must also be assigned at least one classification number from Section 01)
- 06-04 Explicit machine computation and programs (not the theory of computation or programming)
- 06-06 Proceedings, conferences, collections, etc.
- 06-99 Order, lattices, ordered algebraic structures (not classified at a more specific level)
- 06Axx Ordered sets
- 06A05 Total order
- 06A06 Partial order, general
- 06A07 Combinatorics of partially ordered sets
- 06A11 Algebraic aspects of posets [See also 05E25, 52B20]
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
06A08, 06A09
- 06A12 Semilattices [See also 20M10; for topological semilattices see 22A26]
- 06A15 Galois correspondences, closure operators
- 06A99 None of the above, but in this section
- 06Bxx Lattices [See also 03G10]
- 06B05 Structure theory
- 06B10 Ideals, congruence relations
- 06B15 Representation theory
- 06B20 Varieties of lattices
- 06B23 Complete lattices, completions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
06A23
- 06B25 Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]
- 06B30 Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]
- 06B35 Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 54F05, 68Q55]
- 06B99 None of the above, but in this section
- 06Cxx Modular lattices, complemented lattices
- 06C05 Modular lattices, Desarguesian lattices
- 06C10 Semimodular lattices, geometric lattices
- 06C15 Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]
- 06C20 Complemented modular lattices, continuous geometries
- 06C99 None of the above, but in this section
- 06Dxx Distributive lattices
- 06D05 Structure and representation theory
- 06D10 Complete distributivity
- 06D15 Pseudocomplemented lattices
- 06D20 Heyting algebras [See also 03G25]
- 06D22 Frames, locales [For topological questions see 54-XX]
[Nouveau code MSC 2000]
- 06D25 Post algebras [See also 03G20]
- 06D50 Lattices and duality
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
06D05
- 06D72 Fuzzy lattices (soft algebras) and related topics
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
06D30
- 06D99 None of the above, but in this section
- 06E05 Structure theory
- 06E10 Chain conditions, complete algebras
- 06E15 Stone space and related constructions
- 06E20 Ring-theoretic properties [See also 16E50, 16G30]
- 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]
- 06E30 Boolean functions [See also 94C10]
- 06E99 None of the above, but in this section
- 06Fxx Ordered structures
- 06F07 Quantales
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
06F05
- 06F10 Noether lattices
- 06F30 Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]
- 06F99 None of the above, but in this section
08-XX General algebraic systems
- 08-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 08-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 08-02 Research exposition (monographs, survey articles)
- 08-03 Historical (must also be assigned at least one classification number from Section 01)
- 08-04 Explicit machine computation and programs (not the theory of computation or programming)
- 08-06 Proceedings, conferences, collections, etc.
- 08-99 General mathematical systems (not classified at a more specific level)
- 08Axx Algebraic structures [See also 03C05]
- 08A02 Relational systems, laws of composition
- 08A05 Structure theory
- 08A30 Subalgebras, congruence relations
- 08A35 Automorphisms, endomorphisms
- 08A40 Operations, polynomials, primal algebras
- 08A45 Equational compactness
- 08A55 Partial algebras
- 08A62 Finitary algebras
- 08A65 Infinitary algebras
- 08A68 Heterogeneous algebras
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
08A55
- 08A70 Applications of universal algebra in computer science
- 08A72 Fuzzy algebraic structures
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
03E72
- 08A99 None of the above, but in this section
- 08Bxx Varieties [See also 03C05]
- 08B05 Equational logic, Mal'tsev conditions
- 08B10 Congruence modularity, congruence distributivity
- 08B15 Lattices of varieties
- 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also 18A30]
- 08B26 Subdirect products and subdirect irreducibility
- 08B30 Injectives, projectives
- 08B99 None of the above, but in this section
- 08Cxx Other classes of algebras
- 08C05 Categories of algebras [See also 18C05]
- 08C10 Axiomatic model classes [See also 03Cxx, in particular 03C60]
- 08C15 Quasivarieties
- 08C99 None of the above, but in this section
11-XX Number theory
- 11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 11-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 11-02 Research exposition (monographs, survey articles)
- 11-03 Historical (must also be assigned at least one classification number from Section 01)
- 11-04 Explicit machine computation and programs (not the theory of computation or programming)
- 11-06 Proceedings, conferences, collections, etc.
- 11-99 Number theory (not classified at a more specific level)
- 11Axx Elementary number theory [For analogues in number fields, see 11R04]
- 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors
- 11A07 Congruences; primitive roots; residue systems
- 11A15 Power residues, reciprocity
- 11A25 Arithmetic functions; related numbers; inversion formulas
- 11A51 Factorization; primality
- 11A55 Continued fractions [For approximation results, see 11J70] [See also 11K50, 30B70, 40A15]
- 11A63 Radix representation; digital problems [For metric results, see 11K16]
- 11A67 Other representations
- 11A99 None of the above, but in this section
- 11Bxx Sequences and sets
- 11B05 Density, gaps, topology
- 11B13 Additive bases [See also 05B10]
- 11B25 Arithmetic progressions [See also 11N13]
- 11B34 Representation functions
- 11B37 Recurrences [For applications to special functions, see 33-XX]
- 11B39 Fibonacci and Lucas numbers and polynomials and generalizations
- 11B57 Farey sequences; the sequences {1k, 2k, .... }
- 11B65 Binomial coefficients; factorials; q-identities [See also 05A10, 05A30]
- 11B73 Bell and Stirling numbers
- 11B75 Other combinatorial number theory
- 11B85 Automata sequences
- 11B99 None of the above, but in this section
- 11Cxx Polynomials and matrices
- 11C20 Matrices, determinants [See also 15A36]
- 11C99 None of the above, but in this section
- 11Dxx Diophantine equations [See also 11Gxx, 14Gxx]
- 11D04 Linear equations
- 11D09 Quadratic and bilinear equations
- 11D25 Cubic and quartic equations
- 11D41 Higher degree equations; Fermat's equation
- 11D45 Counting solutions of Diophantine equations
[Nouveau code MSC 2000]
- 11D57 Multiplicative and norm form equations
- 11D59 Thue-Mahler equations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11D57
- 11D61 Exponential equations
- 11D68 Rational numbers as sums of fractions
- 11D72 Equations in many variables [See also 11P55]
- 11D75 Diophantine inequalities [See also 11J25]
- 11D85 Representation problems [See also 11P55]
- 11D99 None of the above, but in this section
- 11Exx Forms and linear algebraic groups [See also 19Gxx] [For quadratic forms in linear algebra, see 15A63]
- 11E04 Quadratic forms over general fields
- 11E08 Quadratic forms over local rings and fields
- 11E12 Quadratic forms over global rings and fields
- 11E16 General binary quadratic forms
- 11E20 General ternary and quaternary quadratic forms; forms of more than two variables
- 11E25 Sums of squares and representations by other particular quadratic forms
- 11E39 Bilinear and Hermitian forms
- 11E41 Class numbers of quadratic and Hermitian forms
- 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
- 11E70 K-theory of quadratic and Hermitian forms
- 11E76 Forms of degree higher than two
- 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
- 11E88 Quadratic spaces; Clifford algebras [See also 15A63, 15A66]
- 11E95 p-adic theory
- 11E99 None of the above, but in this section
- 11Fxx Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14-XX, 22Exx, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] [For relations with quadratic forms, see 11E45]
- 11F03 Modular and automorphic functions
- 11F06 Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]
- 11F12 Automorphic forms, one variable
- 11F20 Dedekind eta function, Dedekind sums
- 11F22 Relationship to Lie algebras and finite simple groups
- 11F23 Relations with algebraic geometry and topology
[Nouveau code MSC 2000]
- 11F25 Hecke-Petersson operators, differential operators (one variable)
- 11F27 Theta series; Weil representation
- 11F30 Fourier coefficients of automorphic forms
- 11F32 Modular correspondences, etc.
- 11F37 Forms of half-integer weight; nonholomorphic modular forms
- 11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
- 11F46 Siegel modular groups and their modular and automorphic forms
- 11F52 Modular forms associated to Drinfel'd modules
[Nouveau code MSC 2000]
- 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
- 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular symbols
- 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
- 11F85 p-adic theory, local fields [See also 14G20, 22E50]
- 11F99 None of the above, but in this section
- 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14-XX, 14Gxx, 14Kxx]
- 11G05 Elliptic curves over global fields [See also 14H52]
- 11G07 Elliptic curves over local fields [See also 14G20, 14H52]
- 11G09 Drinfeld modules; higher-dimensional motives, etc. [See also 14L05]
- 11G10 Abelian varieties of dimension > 1 [See also 14Kxx]
- 11G15 Complex multiplication and moduli of abelian varieties [See also 14K22]
- 11G16 Elliptic and modular units [See also 11R27]
- 11G18 Arithmetic aspects of modular and Shimura varieties [See also 14G35]
- 11G20 Curves over finite and local fields [See also 14H25]
- 11G25 Varieties over finite and local fields [See also 14G15, 14G20]
- 11G30 Curves of arbitrary genus or genus
 1 over global fields [See also 14H25]
- 11G35 Varieties over global fields [See also 14G25]
- 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
- 11G45 Geometric class field theory [See also 11R37, 14C35, 19F05]
- 11G50 Heights [See also 14G40]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11G35
- 11G55 Polylogarithms and relations with K-theory
[Nouveau code MSC 2000]
- 11G99 None of the above, but in this section
- 11Hxx Geometry of numbers [For applications in coding theory, see 94B75]
- 11H06 Lattices and convex bodies [See also 11P21, 52C05, 52C07]
- 11H31 Lattice packing and covering [See also 05B40, 52C15, 52C17]
- 11H46 Products of linear forms
- 11H55 Quadratic forms (reduction theory, extreme forms, etc.)
- 11H56 Automorphism groups of lattices
- 11H60 Mean value and transfer theorems
- 11H71 Relations with coding theory [See also 94Bxx]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11T71
- 11H99 None of the above, but in this section
- 11Jxx Diophantine approximation, transcendental number theory [See also 11K60]
- 11J04 Homogeneous approximation to one number
- 11J06 Markov and Lagrange spectra and generalizations
- 11J13 Simultaneous homogeneous approximation, linear forms
- 11J17 Approximation by numbers from a fixed field
- 11J25 Diophantine inequalities [See also 11D75]
- 11J54 Small fractional parts of polynomials and generalizations
- 11J61 Approximation in non-Archimedean valuations
- 11J68 Approximation to algebraic numbers
- 11J70 Continued fractions and generalizations [See also 11A55, 11K50]
- 11J71 Distribution modulo one [See also 11K06]
- 11J72 Irrationality; linear independence over a field
- 11J81 Transcendence (general theory)
- 11J82 Measures of irrationality and of transcendence
- 11J83 Metric theory
- 11J85 Algebraic independence; Gelfond's method
- 11J86 Linear forms in logarithms; Baker's method
- 11J89 Transcendence theory of elliptic and abelian functions
- 11J91 Transcendence theory of other special functions
- 11J93 Transcendence theory of Drinfel'd and t-modules
[Nouveau code MSC 2000]
- 11J95 Results involving abelian varieties
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11G10
- 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11J99
- 11J99 None of the above, but in this section
- 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithms
- 11K06 General theory of distribution modulo 1 [See also 11J71]
- 11K16 Normal numbers, radix expansions, etc. [See also 11A63]
- 11K36 Well-distributed sequences and other variations
- 11K38 Irregularities of distribution, discrepancy [See also 11Nxx]
- 11K41 Continuous, p-adic and abstract analogues
- 11K45 Pseudo-random numbers; Monte Carlo methods
- 11K50 Metric theory of continued fractions [See also 11A55, 11J70]
- 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
- 11K60 Diophantine approximation [See also 11Jxx]
- 11K65 Arithmetic functions [See also 11Nxx]
- 11K70 Harmonic analysis and almost periodicity
- 11K99 None of the above, but in this section
- 11Lxx Exponential sums and character sums [For finite fields, see 11Txx]
- 11L03 Trigonometric and exponential sums, general
- 11L05 Gauss and Kloosterman sums; generalizations
- 11L07 Estimates on exponential sums
- 11L10 Jacobsthal and Brewer sums; other complete character sums
- 11L26 Sums over arbitrary intervals
- 11L40 Estimates on character sums
- 11L99 None of the above, but in this section
- 11Mxx Zeta and L-functions: analytic theory
- 11M06
 (s) and L(s, )
- 11M20 Real zeros of L(s,); results on L(1,)
- 11M26 Nonreal zeros of (s) and L(s,); Riemann and other hypotheses
- 11M35 Hurwitz and Lerch zeta functions
- 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
- 11M38 Zeta and L-functions in characteristic p
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11M41
- 11M41 Other Dirichlet series and zeta functions [For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72]
- 11M45 Tauberian theorems [See also 40E05]
- 11M99 None of the above, but in this section
- 11Nxx Multiplicative number theory
- 11N05 Distribution of primes
- 11N25 Distribution of integers with specified multiplicative constraints
- 11N30 Turán theory [See also 30Bxx]
- 11N32 Primes represented by polynomials; other multiplicative structure of polynomial values
- 11N36 Applications of sieve methods
- 11N37 Asymptotic results on arithmetic functions
- 11N45 Asymptotic results on counting functions for algebraic and topological structures
- 11N56 Rate of growth of arithmetic functions
- 11N60 Distribution functions associated with additive and positive multiplicative functions
- 11N64 Other results on the distribution of values or the characterization of arithmetic functions
- 11N69 Distribution of integers in special residue classes
- 11N75 Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]
- 11N80 Generalized primes and integers
- 11N99 None of the above, but in this section
- 11Pxx Additive number theory; partitions
- 11P05 Waring's problem and variants
- 11P21 Lattice points in specified regions
- 11P32 Goldbach-type theorems; other additive questions involving primes
- 11P55 Applications of the Hardy-Littlewood method [See also 11D85]
- 11P70 Inverse problems of additive number theory
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11B75
- 11P81 Elementary theory of partitions [See also 05A17]
- 11P82 Analytic theory of partitions
- 11P83 Partitions; congruences and congruential restrictions
- 11P99 None of the above, but in this section
- 11Rxx Algebraic number theory: global fields [For complex multiplication, see 11G15]
- 11R04 Algebraic numbers; rings of algebraic integers
- 11R06 PV-numbers and generalizations; other special algebraic numbers
- 11R09 Polynomials (irreducibility, etc.)
- 11R11 Quadratic extensions
- 11R16 Cubic and quartic extensions
- 11R18 Cyclotomic extensions
- 11R20 Other abelian and metabelian extensions
- 11R21 Other number fields
- 11R23 Iwasawa theory
- 11R27 Units and factorization
- 11R29 Class numbers, class groups, discriminants
- 11R32 Galois theory
- 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
- 11R37 Class field theory
- 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
- 11R42 Zeta functions and L-functions of number fields [See also 11M41, 19F27]
- 11R44 Distribution of prime ideals [See also 11N05]
- 11R45 Density theorems
- 11R47 Other analytic theory [See also 11Nxx]
- 11R52 Quaternion and other division algebras: arithmetic, zeta functions
- 11R54 Other algebras and orders, and their zeta and L-functions [See also 11S45, 16H05, 16Kxx]
- 11R58 Arithmetic theory of algebraic function fields [See also 14-XX]
- 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11R58
- 11R70 K-theory of global fields [See also 19Fxx]
- 11R80 Totally real and totally positive fields [See also 12J15]
- 11R99 None of the above, but in this section
- 11Sxx Algebraic number theory: local and p-adic fields
- 11S15 Ramification and extension theory
- 11S20 Galois theory
- 11S23 Integral representations
- 11S31 Class field theory; p-adic formal groups [See also 14L05]
- 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
- 11S40 Zeta functions and L-functions [See also 11M41, 19F27]
- 11S45 Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16H05, 16Kxx]
- 11S70 K-theory of local fields [See also 19Fxx]
- 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)
- 11S85 Other nonanalytic theory
- 11S90 Prehomogeneous vector spaces
[Nouveau code MSC 2000]
- 11S99 None of the above, but in this section
- 11Txx Finite fields and commutative rings (number-theoretic aspects) [See also 13Mxx]
- 11T06 Polynomials
- 11T22 Cyclotomy
- 11T23 Exponential sums
- 11T24 Other character sums and Gauss sums
- 11T30 Structure theory
- 11T55 Arithmetic theory of polynomial rings over finite fields
- 11T60 Finite upper half-planes
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11F99
- 11T71 Algebraic coding theory; cryptography
- 11T99 None of the above, but in this section
- 11Uxx Connections with logic
- 11U05 Decidability [See also 03B25]
- 11U07 Ultraproducts [See also 03C20]
- 11U09 Model theory [See also 03Cxx]
- 11U10 Nonstandard arithmetic [See also 03H15]
- 11U99 None of the above, but in this section
- 11Yxx Computational number theory [See also 11-04]
- 11Y05 Factorization
- 11Y11 Primality
- 11Y16 Algorithms; complexity [See also 68Q25]
- 11Y35 Analytic computations
- 11Y40 Algebraic number theory computations
- 11Y50 Computer solution of Diophantine equations
- 11Y55 Calculation of integer sequences
- 11Y60 Evaluation of constants
- 11Y65 Continued fraction calculations
- 11Y70 Values of arithmetic functions; tables
- 11Y99 None of the above, but in this section
- 11Z05 Miscellaneous applications of number theory
12-XX Field theory and polynomials
- 12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 12-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 12-02 Research exposition (monographs, survey articles)
- 12-03 Historical (must also be assigned at least one classification number from Section 01)
- 12-04 Explicit machine computation and programs (not the theory of computation or programming)
- 12-06 Proceedings, conferences, collections, etc.
- 12-99 Algebraic number theory, field theory and polynomials (not classified at a more specific level)
- 12D05 Polynomials: factorization
- 12D10 Polynomials: location of zeros (algebraic theorems) [For the analytic theory, see 26C10, 30C15]
- 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
- 12D99 None of the above, but in this section
- 12Exx General field theory
- 12E05 Polynomials (irreducibility, etc.)
- 12E12 Equations
- 12E20 Finite fields (field-theoretic aspects)
- 12E25 Hilbertian fields; Hilbert's irreducibility theorem
- 12E30 Field arithmetic
[Nouveau code MSC 2000]
- 12E99 None of the above, but in this section
- 12Fxx Field extensions
- 12F05 Algebraic extensions
- 12F10 Separable extensions, Galois theory
- 12F12 Inverse Galois theory
- 12F15 Inseparable extensions
- 12F20 Transcendental extensions
- 12F99 None of the above, but in this section
- 12Gxx Homological methods (field theory)
- 12G99 None of the above, but in this section
- 12Hxx Differential and difference algebra
- 12H05 Differential algebra [See also 13Nxx]
- 12H20 Abstract differential equations [See also 34Mxx]
- 12H25 p-adic differential equations [See also 11S80, 14G20]
- 12H99 None of the above, but in this section
- 12Jxx Topological fields
- 12J17 Topological semifields
- 12J20 General valuation theory [See also 13A18]
- 12J27 Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]
- 12J99 None of the above, but in this section
- 12Kxx Generalizations of fields
- 12K99 None of the above, but in this section
- 12Lxx Connections with logic
- 12L05 Decidability [See also 03B25]
- 12L10 Ultraproducts [See also 03C20]
- 12L12 Model theory [See also 03C60]
- 12L15 Nonstandard arithmetic [See also 03H15]
- 12L99 None of the above, but in this section
- 12Y05 Computational aspects of field theory and polynomials [See also 68W30]
13-XX 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)
- 13-04 Explicit machine computation and programs (not the theory of computation or programming)
- 13-06 Proceedings, conferences, collections, etc.
- 13-99 Commutative rings and algebras (not classified at a more specific level)
- 13Axx General commutative ring theory
- 13A05 Divisibility
- 13A10 Radical theory
- 13A15 Ideals; multiplicative ideal theory
- 13A18 Valuations and their generalizations [See also 12J20, 16W60]
- 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
- 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p ; tight closure [See also 13B22]
- 13A50 Actions of groups on commutative rings; invariant theory [See also 14L24]
- 13A99 None of the above, but in this section
- 13Bxx Ring extensions and related topics
- 13B02 Extension theory
- 13B05 Galois theory
- 13B21 Integral dependence
- 13B22 Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
- 13B24 Going up; going down; going between
- 13B25 Polynomials over commutative rings [See also 11C08, 13F20, 13M10]
- 13B30 Quotients and localization
- 13B35 Completion [See also 13J10]
- 13B40 Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
- 13B99 None of the above, but in this section
- 13Cxx Theory of modules and ideals
- 13C05 Structure, classification theorems
- 13C10 Projective and free modules and ideals [See also 18G05, 19A13]
- 13C11 Injective and flat modules and ideals [See also 18G05]
- 13C12 Torsion modules and ideals
- 13C13 Other special types
- 13C15 Dimension theory, depth, related rings (catenary, etc.)
- 13C40 Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]
- 13C99 None of the above, but in this section
- 13Dxx Homological methods [For noncommutative rings, see 16Exx; for general categories, see 18Gxx]
- 13D02 Syzygies and resolutions
- 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
- 13D07 Homological functors on modules (Tor, Ext, etc.) [See also 18G15]
[Nouveau code MSC 2000]
- 13D10 Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 16S80, 32Gxx]
- 13D15 Grothendieck groups, K-theory [See also 14C35, 18F25, 18F30, 19Axx, 19D50]
- 13D22 Homological conjectures (intersection theorems)
[Nouveau code MSC 2000]
- 13D30 Torsion theory [See also 13C12, 16S90, 18E40]
- 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
- 13D99 None of the above, but in this section
- 13Exx Chain conditions, finiteness conditions
- 13E05 Noetherian rings and modules
- 13E10 Artinian rings and modules, finite-dimensional algebras
- 13E15 Rings and modules of finite generation or presentation; number of generators
- 13E99 None of the above, but in this section
- 13Fxx Arithmetic rings and other special rings
- 13F05 Dedekind, Prüfer and Krull rings and their generalizations
- 13F07 Euclidean rings and generalizations
- 13F15 Factorial rings, unique factorization domains [See also 14M05]
- 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
- 13F30 Valuation rings [See also 13A18]
- 13F40 Excellent rings
- 13F50 Rings with straightening laws, Hodge algebras
- 13F55 Face and Stanley-Reisner rings; simplicial complexes [See also 55U10]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
13F50
- 13F99 None of the above, but in this section
- 13G05 Integral domains
- 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 13C14, 14M05]
- 13H15 Multiplicity theory and related topics [See also 14C17]
- 13H99 None of the above, but in this section
- 13Jxx Topological rings and modules [See also 16W80]
- 13J07 Analytical algebras and rings [See also 32B05]
- 13J10 Complete rings, completion [See also 13B35, 16W60]
- 13J20 Global topological rings
- 13J99 None of the above, but in this section
- 13K05 Witt vectors and related rings
- 13L05 Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
- 13Mxx Finite commutative rings [See also 13A35; for number-theoretic aspects, see 11Txx]
- 13M05 Structure
- 13M99 None of the above, but in this section
- 13Nxx Differential algebra [See also 12H05, 14F10]
- 13N05 Modules of differentials
- 13N10 Rings of differential operators and their modules [See also 16S32, 32C38]
- 13N15 Derivations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
13B10
- 13N99 None of the above, but in this section
- 13Pxx Computational aspects of commutative algebra [See also 68W30]
- 13P05 Polynomials, factorization [See also 12Y05]
- 13P99 None of the above, but in this section
14-XX Algebraic geometry
- 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 14-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 14-02 Research exposition (monographs, survey articles)
- 14-03 Historical (must also be assigned at least one classification number from Section 01)
- 14-04 Explicit machine computation and programs (not the theory of computation or programming)
- 14-06 Proceedings, conferences, collections, etc.
- 14-99 Algebraic geometry (not classified at a more specific level)
- 14Axx Foundations
- 14A05 Relevant commutative algebra [See also 13-XX]
- 14A10 Varieties and morphisms
- 14A20 Generalizations (algebraic spaces, stacks)
- 14A22 Noncommutative algebraic geometry [See also 16S38]
- 14A25 Elementary questions
- 14A99 None of the above, but in this section
- 14Bxx Local theory
- 14B05 Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
- 14B07 Deformations of singularities [See also 14D10, 14D15, 32S30]
- 14B10 Infinitesimal methods [See also 13D10]
- 14B12 Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
- 14B25 Local structure of morphisms: étale, flat, etc. [See also 13B40]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14E40
- 14B99 None of the above, but in this section
- 14C05 Parametrization (Chow and Hilbert schemes)
- 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also 13H15, 55R40, 57R20]
- 14C20 Divisors, linear systems, invertible sheaves
- 14C21 Pencils, nets, webs [See also 53A60]
- 14C30 Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
- 14C34 Torelli problem
- 14C35 Applications of methods of algebraic K-theory [See also 19Exx]
- 14C40 Riemann-Roch theorems [See also 19E20, 19L10]
- 14C99 None of the above, but in this section
- 14Dxx Families, fibrations
- 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
- 14D06 Fibrations, degenerations
[Nouveau code MSC 2000]
- 14D07 Variation of Hodge structures [See also 14C30, 32G20]
- 14D10 Arithmetic ground fields (finite, local, global)
- 14D15 Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
- 14D20 Algebraic moduli problems, moduli of vector bundles [For analytic moduli problems, see 32G13]
- 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14D20
- 14D99 None of the above, but in this section
- 14Exx Birational geometry
- 14E05 Rational and birational maps
- 14E07 Birational automorphisms, Cremona group and generalizations
- 14E08 Rationality questions [See also 14G05, 14M20]
[Nouveau code MSC 2000]
- 14E15 Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
- 14E22 Ramification problems [See also 11S15]
- 14E30 Minimal model program (Mori theory, extremal rays)
- 14E99 None of the above, but in this section
- 14Fxx (Co)homology theory [See also 13Dxx]
- 14F05 Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
- 14F10 Differentials and other special sheaves [See also 13Nxx, 32C38]
- 14F17 Vanishing theorems [See also 32L20]
- 14F20 Étale and other Grothendieck topologies and (co)homologies
- 14F30 p-adic cohomology, crystalline cohomology
- 14F35 Homotopy theory; fundamental groups [See also 14H30]
- 14F42 Motivic cohomology [See also 19E15]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14F99
- 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
14F32, 14F99
- 14F45 Topological properties
- 14F99 None of the above, but in this section
- 14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
- 14G05 Rational points
- 14G10 Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)
- 14G15 Finite ground fields
- 14G22 Rigid analytic geometry
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14G20
- 14G27 Other nonalgebraically closed ground fields
- 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
[Nouveau code MSC 2000]
- 14G35 Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
- 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50]
- 14G50 Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
94B27
- 14G99 None of the above, but in this section
- 14H05 Algebraic functions; function fields [See also 11R58]
- 14H15 Families, moduli (analytic) [See also 30F10, 32G15]
- 14H20 Singularities, local rings [See also 13Hxx, 14B05]
- 14H25 Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
- 14H30 Coverings, fundamental group [See also 14E20, 14F35]
- 14H37 Automorphisms of curves [See also 14E07]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14E09
- 14H40 Jacobians, Prym varieties
- 14H42 Theta functions; Schottky problem [See also 14K25]
- 14H51 Special divisors (gonality, Brill-Noether theory)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14C20
- 14H52 Elliptic curves [See also 11G05, 11G07, 14Kxx]
- 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
- 14H60 Vector bundles on curves and their moduli [See also 14D20, 14F05]
- 14H70 Relationships with integrable systems
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14H99
- 14H81 Relationships with physics
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14H99
- 14H99 None of the above, but in this section
- 14Jxx Surfaces and higher-dimensional varieties [For analytic theory, see 32Jxx]
- 14J10 Families, moduli, classification: algebraic theory
- 14J15 Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
- 14J17 Singularities [See also 14B05, 14E15]
- 14J20 Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
- 14J25 Special surfaces [For Hilbert modular surfaces, see 14G35]
- 14J26 Rational and ruled surfaces
- 14J27 Elliptic surfaces
- 14J29 Surfaces of general type
- 14J32 Calabi-Yau manifolds, mirror symmetry [See also 32Q25]
- 14J45 Fano varieties
- 14J50 Automorphisms of surfaces and higher-dimensional varieties [See also 14E07]
- 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
- 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14J99
- 14J81 Relationships with physics
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14J99
- 14J99 None of the above, but in this section
- 14Kxx Abelian varieties and schemes
- 14K05 Algebraic theory
- 14K10 Algebraic moduli, classification [See also 11G15, 14D20]
- 14K12 Subvarieties
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14K05
- 14K15 Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
- 14K20 Analytic theory; abelian integrals and differentials
- 14K22 Complex multiplication [See also 11G15]
- 14K25 Theta functions [See also 14H42]
- 14K99 None of the above, but in this section
- 14L10 Group varieties
- 14L17 Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
- 14L24 Geometric invariant theory [See also 13A50]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14D25
- 14L30 Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17, 14R20, 57S25]
- 14L35 Classical groups (geometric aspects) [See also 20Gxx, 51N30]
- 14L40 Other algebraic groups (geometric aspects)
- 14L99 None of the above, but in this section
- 14Mxx Special varieties
- 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]
- 14M10 Complete intersections [See also 13C40]
- 14M12 Determinantal varieties [See also 13C40]
- 14M15 Grassmannians, Schubert varieties, flag manifolds [See also 51M35]
- 14M17 Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
- 14M20 Rational and unirational varieties [See also 05A15]
- 14M25 Toric varieties, Newton polyhedra [See also 52B20]
- 14M30 Supervarieties [See also 32C11, 58A50]
- 14M99 None of the above, but in this section
- 14Nxx Projective and enumerative geometry [See also 51-XX]
- 14N05 Projective techniques [See also 51N35]
- 14N10 Enumerative problems (combinatorial problems)
- 14N15 Classical problems, Schubert calculus
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14M15
- 14N20 Configurations of linear subspaces
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14N05
- 14N25 Varieties of low degree
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14N05
- 14N30 Adjunction problems
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14C20
- 14N35 Gromov-Witten invariants, quantum cohomology [See also 53D45]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14N10
- 14N99 None of the above, but in this section
- 14Pxx Real algebraic and real analytic geometry
- 14P05 Real algebraic sets [See also 12D15, 13J30]
- 14P10 Semialgebraic sets and related spaces
- 14P15 Real analytic and semianalytic sets [See also 32B20, 32C05]
- 14P20 Nash functions and manifolds [See also 32C07, 58A07]
- 14P25 Topology of real algebraic varieties
- 14P99 None of the above, but in this section
- 14Qxx Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]
- 14Q15 Higher-dimensional varieties
- 14Q20 Effectivity
- 14Q99 None of the above, but in this section
- 14Rxx Affine geometry
- 14R05 Classification of affine varieties
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14J99
- 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
14E09, 14E25
- 14R20 Group actions on affine varieties [See also 13A50, 14L30]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14L30
- 14R25 Affine fibrations [See also 14D06]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14D99
- 14R99 None of the above, but in this section
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14J99
15-XX Linear and multilinear algebra; matrix theory
- 15-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 15-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 15-02 Research exposition (monographs, survey articles)
- 15-03 Historical (must also be assigned at least one classification number from Section 01)
- 15-04 Explicit machine computation and programs (not the theory of computation or programming)
- 15-06 Proceedings, conferences, collections, etc.
- 15-99 Linear and multilinear algebra; matrix theory (finite and infinite) (not classified at a more specific level)
- 15A03 Vector spaces, linear dependence, rank
- 15A04 Linear transformations, semilinear transformations
- 15A06 Linear equations
- 15A09 Matrix inversion, generalized inverses
- 15A12 Conditioning of matrices [See also 65F35]
- 15A15 Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
- 15A18 Eigenvalues, singular values, and eigenvectors
- 15A21 Canonical forms, reductions, classification
- 15A22 Matrix pencils [See also 47A56]
- 15A23 Factorization of matrices
- 15A24 Matrix equations and identities
- 15A27 Commutativity
- 15A30 Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]
- 15A33 Matrices over special rings (quaternions, finite fields, etc.)
- 15A36 Matrices of integers [See also 11C20]
- 15A39 Linear inequalities
- 15A42 Inequalities involving eigenvalues and eigenvectors
- 15A45 Miscellaneous inequalities involving matrices
- 15A48 Positive matrices and their generalizations; cones of matrices
- 15A51 Stochastic matrices
- 15A52 Random matrices
- 15A54 Matrices over function rings in one or more variables
- 15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
- 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
- 15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx]
- 15A69 Multilinear algebra, tensor products
- 15A72 Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]
- 15A75 Exterior algebra, Grassmann algebras
- 15A78 Other algebras built from modules
- 15A90 Applications of matrix theory to physics
- 15A99 Miscellaneous topics
16-XX Associative rings and algebras [For the commutative case, see 13-XX]
- 16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 16-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 16-02 Research exposition (monographs, survey articles)
- 16-03 Historical (must also be assigned at least one classification number from Section 01)
- 16-04 Explicit machine computation and programs (not the theory of computation or programming)
- 16-06 Proceedings, conferences, collections, etc.
- 16-99 Associative rings and algebras (not classified at a more specific level)
- 16B50 Category-theoretic methods and results (except as in 16D90) [See also 18-XX]
- 16B70 Applications of logic [See also 03Cxx]
- 16B99 None of the above, but in this section
- 16D10 General module theory
- 16D30 Infinite-dimensional simple rings (except as in 16Kxx)
- 16D40 Free, projective, and flat modules and ideals [See also 18G05, 19A13]
- 16D50 Injective modules, self-injective rings [See also 16L60]
- 16D60 Simple and semisimple modules, primitive rings and ideals
- 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
- 16D80 Other classes of modules and ideals [See also 16G50]
- 16D90 Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality
- 16D99 None of the above, but in this section
- 16Exx Homological methods [For commutative rings, see 13Dxx; for general categories, see 18Gxx]
- 16E05 Syzygies, resolutions, complexes
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16E10
- 16E20 Grothendieck groups, K-theory, etc. [See also 18F30, 19Axx, 19D50]
- 16E30 Homological functors on modules (Tor, Ext, etc.)
- 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
- 16E45 Differential graded algebras and applications
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16E99
- 16E50 von Neumann regular rings and generalizations
- 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
- 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16E99
- 16E99 None of the above, but in this section
- 16Gxx Representation theory of rings and algebras
- 16G10 Representations of Artinian rings
- 16G20 Representations of quivers and partially ordered sets
- 16G30 Representations of orders, lattices, algebras over commutative rings [See also 16H05]
- 16G60 Representation type (finite, tame, wild, etc.)
- 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
- 16G99 None of the above, but in this section
- 16H05 Orders and arithmetic, separable algebras, Azumaya algebras [See also 11R52, 11R54, 11S45]
- 16Kxx Division rings and semisimple Artin rings [See also 12E15, 15A30]
- 16K20 Finite-dimensional [For crossed products, see 16S35]
- 16K40 Infinite-dimensional and general
- 16K99 None of the above, but in this section
- 16Lxx Local rings and generalizations
- 16L30 Noncommutative local and semilocal rings, perfect rings
- 16L99 None of the above, but in this section
- 16Nxx Radicals and radical properties of rings
- 16N20 Jacobson radical, quasimultiplication
- 16N40 Nil and nilpotent radicals, sets, ideals, rings
- 16N80 General radicals and rings [For radicals in module categories, see 16S90]
- 16N99 None of the above, but in this section
- 16Pxx Chain conditions, growth conditions, and other forms of finiteness
- 16P10 Finite rings and finite-dimensional algebras [For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx]
- 16P20 Artinian rings and modules
- 16P40 Noetherian rings and modules
- 16P50 Localization and Noetherian rings [See also 16U20]
- 16P60 Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension
- 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
- 16P90 Growth rate, Gelfand-Kirillov dimension
- 16P99 None of the above, but in this section
- 16Rxx Rings with polynomial identity
- 16R10 T-ideals, identities, varieties of rings and algebras
- 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
- 16R30 Trace rings and invariant theory
- 16R40 Identities other than those of matrices over commutative rings
- 16R50 Other kinds of identities (generalized polynomial, rational, involution)
- 16R99 None of the above, but in this section
- 16Sxx Rings and algebras arising under various constructions
- 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
- 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
- 16S20 Centralizing and normalizing extensions
- 16S32 Rings of differential operators [See also 13N10, 32C38]
- 16S34 Group rings [See also 20C05, 20C07], Laurent polynomial rings
- 16S35 Twisted and skew group rings, crossed products
- 16S37 Quadratic and Koszul algebras
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16S99
- 16S38 Rings arising from non-commutative algebraic geometry
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16S99
- 16S40 Smash products of general Hopf actions [See also 16W30]
- 16S50 Endomorphism rings; matrix rings [See also 15-XX]
- 16S60 Rings of functions, subdirect products, sheaves of rings
- 16S70 Extensions of rings by ideals
- 16S80 Deformations of rings [See also 13D10, 14D15]
- 16S90 Maximal ring of quotients, torsion theories, radicals on module categories [See also 13D30, 18E40] [For radicals of rings, see 16Nxx]
- 16S99 None of the above, but in this section
- 16Uxx Conditions on elements
- 16U10 Integral domains
- 16U20 Ore rings, multiplicative sets, Ore localization
- 16U30 Divisibility, noncommutative UFDs
- 16U60 Units, groups of units
- 16U70 Center, normalizer (invariant elements)
- 16U80 Generalizations of commutativity
- 16U99 None of the above, but in this section
- 16Wxx Rings and algebras with additional structure
- 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
- 16W20 Automorphisms and endomorphisms
- 16W22 Actions of groups and semigroups; invariant theory
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16W20
- 16W25 Derivations, actions of Lie algebras
- 16W30 Coalgebras, bialgebras, Hopf algebras [See also 16S40, 57T05]; rings, modules, etc. on which these act
- 16W35 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16W30
- 16W55 ``Super'' (or ``skew'') structure [See also 17A70, 17Bxx, 17C70] [For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66]
- 16W60 Valuations, completions, formal power series and related constructions [See also 13A18, 13F25, 13J10]
- 16W70 Filtered rings; filtrational and graded techniques
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16W60
- 16W80 Topological and ordered rings and modules [See also 06F25, 13Jxx]
- 16W99 None of the above, but in this section
- 16Yxx Generalizations [For nonassociative rings, see 17-XX]
- 16Y99 None of the above, but in this section
- 16Z05 Computational aspects of associative rings [See also 68W30]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
16-04
17-XX 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)
- 17-04 Explicit machine computation and programs (not the theory of computation or programming)
- 17-06 Proceedings, conferences, collections, etc.
- 17-08 Computational methods
- 17-99 Nonassociative rings and algebras (not classified at a more specific level)
- 17Axx General nonassociative rings
- 17A01 General theory
- 17A05 Power-associative rings
- 17A15 Noncommutative Jordan algebras
- 17A30 Algebras satisfying other identities
- 17A36 Automorphisms, derivations, other operators
- 17A40 Ternary compositions
- 17A42 Other n-ary compositions (n >= 3)
- 17A45 Quadratic algebras (but not quadratic Jordan algebras)
- 17A60 Structure theory
- 17A65 Radical theory
- 17A75 Composition algebras
- 17A99 None of the above, but in this section
- 17B01 Identities, free Lie (super)algebras
- 17B05 Structure theory
- 17B10 Representations, algebraic theory (weights)
- 17B15 Representations, analytic theory
- 17B20 Simple, semisimple, reductive (super)algebras (roots)
- 17B25 Exceptional (super)algebras
- 17B30 Solvable, nilpotent (super)algebras
- 17B37 Quantum groups (quantized enveloping algebras) and related deformations [See also 16W35, 20G42, 81R50, 82B23]
- 17B40 Automorphisms, derivations, other operators
- 17B55 Homological methods in Lie (super)algebras
- 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]
- 17B65 Infinite-dimensional Lie (super)algebras [See also 22E65]
- 17B66 Lie algebras of vector fields and related (super) algebras
- 17B67 Kac-Moody algebras (structure and representation theory)
- 17B68 Virasoro and related algebras
- 17B69 Vertex operators; vertex operator algebras and related structures
- 17B80 Applications to integrable systems
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
17B99
- 17B81 Applications to physics
- 17B99 None of the above, but in this section
- 17Cxx Jordan algebras (algebras, triples and pairs)
- 17C05 Identities and free Jordan structures
- 17C10 Structure theory
- 17C27 Idempotents, Peirce decompositions
- 17C30 Associated groups, automorphisms
- 17C36 Associated manifolds
- 17C37 Associated geometries
- 17C40 Exceptional Jordan structures
- 17C50 Jordan structures associated with other structures [See also 16W10]
- 17C55 Finite-dimensional structures
- 17C65 Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]
- 17C70 Super structures
- 17C90 Applications to physics
- 17C99 None of the above, but in this section
- 17Dxx Other nonassociative rings and algebras
- 17D05 Alternative rings
- 17D10 Malcev (Maltsev) rings and algebras
- 17D15 Right alternative rings
- 17D20 (
 ,  )-rings, including (1,-1)-rings
- 17D92 Genetic algebras
- 17D99 None of the above, but in this section
18-XX Category theory; homological algebra [For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology]
- 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 18-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 18-02 Research exposition (monographs, survey 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.
- 18-99 Category theory, homological algebra (not classified at a more specific level)
- 18Axx General theory of categories and functors
- 18A05 Definitions, generalizations
- 18A10 Graphs, diagram schemes, precategories [See especially 20L05]
- 18A15 Foundations, relations to logic and deductive systems [See also 03-XX]
- 18A22 Special properties of functors (faithful, full, etc.)
- 18A23 Natural morphisms, dinatural morphisms
- 18A25 Functor categories, comma categories
- 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
- 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgams
- 18A35 Categories admitting limits (complete categories), functors preserving limits, completions
- 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
- 18A99 None of the above, but in this section
- 18Bxx Special categories
- 18B05 Category of sets, characterizations [See also 03-XX]
- 18B10 Category of relations, additive relations
- 18B15 Embedding theorems, universal categories [See also 18E20]
- 18B20 Categories of machines, automata, operative categories [See also 03D05, 68Qxx]
- 18B25 Topoi [See also 03G30]
- 18B30 Categories of topological spaces and continuous mappings [See also 54-XX]
- 18B35 Preorders, orders and lattices (viewed as categories) [See also 06-XX]
- 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
- 18B99 None of the above, but in this section
- 18Cxx Categories and theories
- 18C05 Equational categories [See also 03C05, 08C05]
- 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]
- 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]
- 18C20 Algebras and Kleisli categories associated with monads
- 18C30 Sketches and generalizations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
18C10
- 18C35 Accessible and locally presentable categories
[Nouveau code MSC 2000]
- 18C50 Categorical semantics of formal languages [See also 68Q55, 68Q65]
[Nouveau code MSC 2000]
- 18C99 None of the above, but in this section
- 18Dxx Categories with structure
- 18D05 Double categories, 2-categories, bicategories and generalizations
- 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
- 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
- 18D20 Enriched categories (over closed or monoidal categories)
- 18D25 Strong functors, strong adjunctions
- 18D30 Fibered categories
- 18D35 Structured objects in a category (group objects, etc.)
- 18D99 None of the above, but in this section
- 18Exx Abelian categories
- 18E05 Preadditive, additive categories
- 18E10 Exact categories, abelian categories
- 18E15 Grothendieck categories
- 18E20 Embedding theorems [See also 18B15]
- 18E25 Derived functors and satellites
- 18E30 Derived categories, triangulated categories
- 18E35 Localization of categories
- 18E40 Torsion theories, radicals [See also 13D30, 16S90]
- 18E99 None of the above, but in this section
- 18Fxx Categories and geometry
- 18F05 Local categories and functors
- 18F10 Grothendieck topologies [See also 14F20]
- 18F15 Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]
- 18F25 Algebraic K-theory and L-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
- 18F30 Grothendieck groups [See also 13D15, 16E20, 19Axx]
- 18F99 None of the above, but in this section
- 18Gxx Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]
- 18G05 Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]
- 18G10 Resolutions; derived functors [See also 13D02, 16E05, 18E25]
- 18G15 Ext and Tor, generalizations, Künneth formula [See also 13D07, 55U25]
- 18G25 Relative homological algebra, projective classes
- 18G30 Simplicial sets, simplicial objects (in a category) [See also 55U10]
- 18G40 Spectral sequences, hypercohomology [See also 55Txx]
- 18G55 Homotopical algebra
- 18G60 Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]
- 18G99 None of the above, but in this section
19-XX $K$-theory [See also 16E20, 18F25]
- 19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 19-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 19-02 Research exposition (monographs, survey 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.
- 19-99 General (not classified at a more specific level)
- 19Axx Grothendieck groups and K0 [See also 13D15, 18F30]
- 19A13 Stability for projective modules [See also 13C10]
- 19A15 Efficient generation
- 19A22 Frobenius induction, Burnside and representation rings
- 19A49 K0 of other rings
- 19A99 None of the above, but in this section
- 19Bxx Whitehead groups and K1
- 19B10 Stable range conditions
- 19B14 Stability for linear groups
- 19B99 None of the above, but in this section
- 19Cxx Steinberg groups and K2
- 19C09 Central extensions and Schur multipliers
- 19C20 Symbols, presentations and stability of K2
- 19C30 K2 and the Brauer group
- 19C99 None of the above, but in this section
- 19Dxx Higher algebraic K-theory
- 19D06 Q- and plus-constructions
- 19D10 Algebraic K-theory of spaces
- 19D23 Symmetric monoidal categories [See also 18D10]
- 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 [See also 13D15, 16E20]
- 19D55 K-theory and homology; cyclic homology and cohomology [See also 18G60]
- 19D99 None of the above, but in this section
- 19Exx K-theory in geometry
- 19E08 K-theory of schemes [See also 14C35]
- 19E15 Algebraic cycles and motivic cohomology [See also 14C25, 14F42]
- 19E20 Relations with cohomology theories [See also 14Fxx]
- 19E99 None of the above, but in this section
- 19Fxx K-theory in number theory [See also 11R70, 11S70]
- 19F05 Generalized class field theory [See also 11G45]
- 19F15 Symbols and arithmetic [See also 11R37]
- 19F27 Étale cohomology, higher regulators, zeta and L-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]
- 19F99 None of the above, but in this section
- 19Gxx K-theory of forms [See also 11Exx]
- 19G05 Stability for quadratic modules
- 19G12 Witt groups of rings [See also 11E81]
- 19G24 L-theory of group rings [See also 11E81]
- 19G38 Hermitian K-theory, relations with K-theory of rings
- 19G99 None of the above, but in this section
- 19Jxx Obstructions from topology
- 19J05 Finiteness and other obstructions in K0
- 19J10 Whitehead (and related) torsion
- 19J25 Surgery obstructions [See also 57R67]
- 19J35 Obstructions to group actions
- 19J99 None of the above, but in this section
- 19Kxx K-theory and operator algebras [See mainly 46L80, and also 46M20]
- 19K14 K0 as an ordered group, traces
- 19K33 EXT and K-homology [See also 55N22]
- 19K35 Kasparov theory (KK-theory) [See also 58J22]
- 19K56 Index theory [See also 58J20, 58J22]
- 19K99 None of the above, but in this section
- 19Lxx Topological K-theory [See also 55N15, 55R50, 55S25]
- 19L10 Riemann-Roch theorems, Chern characters
- 19L20 J-homomorphism, Adams operations [See also 55Q50]
- 19L41 Connective K-theory, cobordism [See also 55N22]
- 19L47 Equivariant K-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
- 19L64 Computations, geometric applications
- 19L99 None of the above, but in this section
- 19M05 Miscellaneous applications of K-theory
20-XX Group theory and generalizations
- 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 20-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 20-02 Research exposition (monographs, survey articles)
- 20-03 Historical (must also be assigned at least one classification number from Section 01)
- 20-04 Explicit machine computation and programs (not the theory of computation or programming)
- 20-06 Proceedings, conferences, collections, etc.
- 20-99 Group theory and generalizations (not classified at a more specific level)
- 20Axx Foundations
- 20A05 Axiomatics and elementary properties
- 20A10 Metamathematical considerations [For word problems, see 20F10]
- 20A15 Applications of logic to group theory
- 20A99 None of the above, but in this section
- 20Bxx Permutation groups
- 20B05 General theory for finite groups
- 20B07 General theory for infinite groups
- 20B10 Characterization theorems
- 20B15 Primitive groups
- 20B20 Multiply transitive finite groups
- 20B22 Multiply transitive infinite groups
- 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]
- 20B27 Infinite automorphism groups [See also 12F10]
- 20B30 Symmetric groups
- 20B35 Subgroups of symmetric groups
- 20B40 Computational methods
- 20B99 None of the above, but in this section
- 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
- 20C05 Group rings of finite groups and their modules [See also 16S34]
- 20C07 Group rings of infinite groups and their modules [See also 16S34]
- 20C08 Hecke algebras and their representations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
20C99
- 20C10 Integral representations of finite groups
- 20C11 p-adic representations of finite groups
- 20C12 Integral representations of infinite groups
- 20C15 Ordinary representations and characters
- 20C20 Modular representations and characters
- 20C25 Projective representations and multipliers
- 20C30 Representations of finite symmetric groups
- 20C32 Representations of infinite symmetric groups
- 20C33 Representations of finite groups of Lie type
- 20C34 Representations of sporadic groups
- 20C35 Applications of group representations to physics
- 20C40 Computational methods
- 20C99 None of the above, but in this section
- 20Dxx Abstract finite groups
- 20D05 Classification of simple and nonsolvable groups
- 20D06 Simple groups: alternating groups and groups of Lie type [See also 20Gxx]
- 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes,
 -length, ranks [See also 20F17]
- 20D15 Nilpotent groups, p-groups
- 20D20 Sylow subgroups, Sylow properties, -groups, -structure
- 20D25 Special subgroups (Frattini, Fitting, etc.)
- 20D30 Series and lattices of subgroups
- 20D40 Products of subgroups
- 20D45 Automorphisms
- 20D60 Arithmetic and combinatorial problems
- 20D99 None of the above, but in this section
- 20Exx Structure and classification of infinite or finite groups
- 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
- 20E07 Subgroup theorems; subgroup growth
- 20E08 Groups acting on trees [See also 20F65]
- 20E10 Quasivarieties and varieties of groups
- 20E15 Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
- 20E18 Limits, profinite groups
- 20E22 Extensions, wreath products, and other compositions [See also 20J05]
- 20E25 Local properties
- 20E26 Residual properties and generalizations
- 20E34 General structure theorems
- 20E36 General theorems concerning automorphisms of groups
- 20E42 Groups with a BN-pair; buildings [See also 51E24]
- 20E99 None of the above, but in this section
- 20Fxx Special aspects of infinite or finite groups
- 20F05 Generators, relations, and presentations
- 20F06 Cancellation theory; application of van Kampen diagrams [See also 57M05]
- 20F10 Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]
- 20F12 Commutator calculus
- 20F14 Derived series, central series, and generalizations
- 20F17 Formations of groups, Fitting classes [See also 20D10]
- 20F18 Nilpotent groups [See also 20D15]
- 20F19 Generalizations of solvable and nilpotent groups
- 20F22 Other classes of groups defined by subgroup chains
- 20F24 FC-groups and their generalizations
- 20F28 Automorphism groups of groups [See also 20E36]
- 20F29 Representations of groups as automorphism groups of algebraic systems
- 20F34 Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
- 20F36 Braid groups; Artin groups
- 20F38 Other groups related to topology or analysis
- 20F40 Associated Lie structures
- 20F45 Engel conditions
- 20F50 Periodic groups; locally finite groups
- 20F55 Reflection groups, Coxeter groups [See also 22E40, 51F15]
- 20F65 Geometric group theory [See also 05C25, 20E08, 57Mxx]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
20F32
- 20F67 Hyperbolic groups, nonpositively curved groups
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
20F32
- 20F69 Asymptotic properties of groups
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
20F32
- 20F99 None of the above, but in this section
- 20Gxx Linear algebraic groups (classical groups) [For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55]
- 20G05 Representation theory
- 20G10 Cohomology theory
- 20G15 Linear algebraic groups over arbitrary fields
- 20G20 Linear algebraic groups over the reals, the complexes, the quaternions
- 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
- 20G42 Quantum groups (quantized function algebras) and their representations [See also 16W35, 17B37, 81R50]
[Nouveau code MSC 2000]
- 20G45 Applications to physics
- 20G99 None of the above, but in this section
- 20Hxx Other groups of matrices [See also 15A30]
- 20H10 Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
- 20H15 Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]
- 20H20 Other matrix groups over fields
- 20H25 Other matrix groups over rings
- 20H30 Other matrix groups over finite fields
- 20H99 None of the above, but in this section
- 20Jxx Connections with homological algebra and category theory
- 20J05 Homological methods in group theory
- 20J15 Category of groups
- 20J99 None of the above, but in this section
- 20K01 Finite abelian groups
- 20K10 Torsion groups, primary groups and generalized primary groups
- 20K15 Torsion-free groups, finite rank
- 20K20 Torsion-free groups, infinite rank
- 20K25 Direct sums, direct products, etc.
- 20K30 Automorphisms, homomorphisms, endomorphisms, etc.
- 20K35 Extensions
- 20K40 Homological and categorical methods
- 20K45 Topological methods [See also 22A05, 22B05]
- 20K99 None of the above, but in this section
- 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) [For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05]
- 20M05 Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]
- 20M07 Varieties of semigroups
- 20M10 General structure theory
- 20M11 Radical theory
- 20M12 Ideal theory
- 20M14 Commutative semigroups
- 20M19 Orthodox semigroups
- 20M20 Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]
- 20M25 Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
- 20M30 Representation of semigroups; actions of semigroups on sets
- 20M35 Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]
- 20M50 Connections of semigroups with homological algebra and category theory
- 20M99 None of the above, but in this section
- 20Nxx Other generalizations of groups
- 20N02 Sets with a single binary operation (groupoids)
- 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
- 20N15 n-ary systems (n >= 3)
- 20N99 None of the above, but in this section
- 20P05 Probabilistic methods in group theory [See also 60Bxx]
22-XX Topological groups, Lie groups [For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX]
- 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 22-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 22-02 Research exposition (monographs, survey articles)
- 22-03 Historical (must also be assigned at least one classification number from Section 01)
- 22-04 Explicit machine computation and programs (not the theory of computation or programming)
- 22-06 Proceedings, conferences, collections, etc.
- 22-99 Topological groups, Lie groups (not classified at a more specific level)
- 22Axx Topological and differentiable algebraic systems [For topological rings and fields, see 12Jxx, 13Jxx, 16W80]
- 22A05 Structure of general topological groups
- 22A10 Analysis on general topological groups
- 22A15 Structure of topological semigroups
- 22A20 Analysis on topological semigroups
- 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]
- 22A25 Representations of general topological groups and semigroups
- 22A26 Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]
- 22A30 Other topological algebraic systems and their representations
- 22A99 None of the above, but in this section
- 22Bxx Locally compact abelian groups (LCA groups)
- 22B05 General properties and structure of LCA groups
- 22B10 Structure of group algebras of LCA groups
- 22B99 None of the above, but in this section
- 22C05 Compact groups
- 22Dxx Locally compact groups and their algebras
- 22D05 General properties and structure of locally compact groups
- 22D10 Unitary representations of locally compact groups
- 22D12 Other representations of locally compact groups
- 22D15 Group algebras of locally compact groups
- 22D20 Representations of group algebras
- 22D25 C*-algebras and W*-algebras in relation to group representations [See also 46Lxx]
- 22D30 Induced representations
- 22D35 Duality theorems
- 22D40 Ergodic theory on groups [See also 28Dxx]
- 22D45 Automorphism groups of locally compact groups
- 22D99 None of the above, but in this section
- 22Exx Lie groups [For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90]
- 22E10 General properties and structure of complex Lie groups [See also 32M05]
- 22E15 General properties and structure of real Lie groups
- 22E20 General properties and structure of other Lie groups
- 22E25 Nilpotent and solvable Lie groups
- 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
- 22E40 Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
- 22E41 Continuous cohomology [See also 57R32, 57Txx, 58H10]
- 22E43 Structure and representation of the Lorentz group
- 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods [For the purely algebraic theory, see 20G05]
- 22E46 Semisimple Lie groups and their representations
- 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
- 22E50 Representations of Lie and linear algebraic groups over local fields [See also 20G05]
- 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings [See also 20G05]
- 22E60 Lie algebras of Lie groups [For the algebraic theory of Lie algebras, see 17Bxx]
- 22E65 Infinite-dimensional Lie groups and their Lie algebras [See also 17B65, 58B25, 58H05]
- 22E67 Loop groups and related constructions, group-theoretic treatment [See also 58D05]
- 22E70 Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]
- 22E99 None of the above, but in this section
- 22Fxx Noncompact transformation groups
- 22F05 General theory of group and pseudogroup actions [For topological properties of spaces with an action, see 57S20]
[Nouveau code MSC 2000]
- 22F10 Measurable group actions [See also 22D40, 28Dxx, 37Axx]
[Nouveau code MSC 2000]
- 22F30 Homogeneous spaces [For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups see especially 22E40]
[Nouveau code MSC 2000]
- 22F50 Groups as automorphisms of other structures
[Nouveau code MSC 2000]
26-XX Real functions [See also 54C30]
- 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 26-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 26-02 Research exposition (monographs, survey articles)
- 26-03 Historical (must also be assigned at least one classification number from Section 01)
- 26-04 Explicit machine computation and programs (not the theory of computation or programming)
- 26-06 Proceedings, conferences, collections, etc.
- 26-99 Real functions (not classified at a more specific level)
- 26Axx Functions of one variable
- 26A03 Foundations: limits and generalizations, elementary topology of the line
- 26A09 Elementary functions
- 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]
- 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) [For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27]
- 26A16 Lipschitz (Hölder) classes
- 26A18 Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]
- 26A21 Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]
- 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
- 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
- 26A30 Singular functions, Cantor functions, functions with other special properties
- 26A33 Fractional derivatives and integrals
- 26A36 Antidifferentiation
- 26A39 Denjoy and Perron integrals, other special integrals
- 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]
- 26A45 Functions of bounded variation, generalizations
- 26A46 Absolutely continuous functions
- 26A48 Monotonic functions, generalizations
- 26A51 Convexity, generalizations
- 26A99 None of the above, but in this section
- 26Bxx Functions of several variables
- 26B05 Continuity and differentiation questions
- 26B10 Implicit function theorems, Jacobians, transformations with several variables
- 26B12 Calculus of vector functions
- 26B15 Integration: length, area, volume [See also 28A75, 51M25]
- 26B20 Integral formulas (Stokes, Gauss, Green, etc.)
- 26B25 Convexity, generalizations
- 26B30 Absolutely continuous functions, functions of bounded variation
- 26B35 Special properties of functions of several variables, Hölder conditions, etc.
- 26B40 Representation and superposition of functions
- 26B99 None of the above, but in this section
- 26Cxx Polynomials, rational functions
- 26C05 Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]
- 26C10 Polynomials: location of zeros [See also 12D10, 30C15, 65H05]
- 26C15 Rational functions [See also 14Pxx]
- 26C99 None of the above, but in this section
- 26Dxx Inequalities [For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15]
- 26D05 Inequalities for trigonometric functions and polynomials
- 26D07 Inequalities involving other types of functions
- 26D10 Inequalities involving derivatives and differential and integral operators
- 26D15 Inequalities for sums, series and integrals
- 26D20 Other analytical inequalities
- 26D99 None of the above, but in this section
- 26Exx Miscellaneous topics [See also 58Cxx]
- 26E05 Real-analytic functions [See also 32B05, 32C05]
- 26E10 C
 -functions, quasi-analytic functions [See also 58C25]
- 26E15 Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]
- 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]
- 26E25 Set-valued functions [See also 28B20, 49J53, 54C60] [For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx]
- 26E35 Nonstandard analysis [See also 03H05, 28E05, 54J05]
- 26E40 Constructive real analysis [See also 03F60]
- 26E99 None of the above, but in this section
28-XX Measure and integration [For analysis on manifolds, see 58-XX]
- 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 28-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 28-02 Research exposition (monographs, survey articles)
- 28-03 Historical (must also be assigned at least one classification number from Section 01)
- 28-04 Explicit machine computation and programs (not the theory of computation or programming)
- 28-06 Proceedings, conferences, collections, etc.
- 28-99 Measure and integration (not classified at a more specific level)
- 28Axx Classical measure theory
- 28A05 Classes of sets (Borel fields,
 -rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
- 28A10 Real- or complex-valued set functions
- 28A12 Contents, measures, outer measures, capacities
- 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24]
- 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
- 28A25 Integration with respect to measures and other set functions
- 28A35 Measures and integrals in product spaces
- 28A50 Integration and disintegration of measures
- 28A51 Lifting theory [See also 46G15]
- 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
- 28A80 Fractals [See also 37Fxx]
- 28A99 None of the above, but in this section
- 28Bxx Set functions, measures and integrals with values in abstract spaces
- 28B05 Vector-valued set functions, measures and integrals [See also 46G10]
- 28B10 Group- or semigroup-valued set functions, measures and integrals
- 28B15 Set functions, measures and integrals with values in ordered spaces
- 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 49J53, 54C60, 54C65]
- 28B99 None of the above, but in this section
- 28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]
- 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
- 28C10 Set functions and measures on topological groups, Haar measures, invariant measures [See also 22Axx, 43A05]
- 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
- 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
- 28C99 None of the above, but in this section
- 28Dxx Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]
- 28D05 Measure-preserving transformations
- 28D10 One-parameter continuous families of measure-preserving transformations
- 28D15 General groups of measure-preserving transformations
- 28D20 Entropy and other invariants
- 28D99 None of the above, but in this section
- 28Exx Miscellaneous topics in measure theory
- 28E05 Nonstandard measure theory [See also 03H05, 26E35]
- 28E10 Fuzzy measure theory [See also 03E72, 26E50, 94D05]
- 28E15 Other connections with logic and set theory
- 28E99 None of the above, but in this section
30-XX Functions of a complex variable [For analysis on manifolds, see 58-XX]
- 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 30-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 30-02 Research exposition (monographs, survey articles)
- 30-03 Historical (must also be assigned at least one classification number from Section 01)
- 30-04 Explicit machine computation and programs (not the theory of computation or programming)
- 30-06 Proceedings, conferences, collections, etc.
- 30-99 Functions of a complex variable (not classified at a more specific level)
- 30Axx General properties
- 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
- 30A10 Inequalities in the complex domain
- 30A99 None of the above, but in this section
- 30B40 Analytic continuation
- 30B50 Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]
- 30B60 Completeness problems, closure of a system of functions
- 30B70 Continued fractions [See also 11A55, 40A15]
- 30B99 None of the above, but in this section
- 30Cxx Geometric function theory
- 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) [For algebraic theory, see 12D10; for real methods, see 26C10]
- 30C25 Covering theorems in conformal mapping theory
- 30C30 Numerical methods in conformal mapping theory [See also 65E05]
- 30C35 General theory of conformal mappings
- 30C40 Kernel functions and applications
- 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
- 30C50 Coefficient problems for univalent and multivalent functions
- 30C55 General theory of univalent and multivalent functions
- 30C62 Quasiconformal mappings in the plane
- 30C65 Quasiconformal mappings in Rn, other generalizations
- 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
- 30C75 Extremal problems for conformal and quasiconformal mappings, other methods
- 30C80 Maximum principle; Schwarz' lemma, Lindelöf principle, analogues and generalizations; subordination
- 30C85 Capacity and harmonic measure in the complex plane [See also 31A15]
- 30C99 None of the above, but in this section
- 30Dxx Entire and meromorphic functions, and related topics
- 30D05 Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
- 30D10 Representations of entire functions by series and integrals
- 30D15 Special classes of entire functions and growth estimates
- 30D20 Entire functions, general theory
- 30D30 Meromorphic functions, general theory
- 30D35 Distribution of values, Nevanlinna theory
- 30D40 Cluster sets, prime ends, boundary behavior
- 30D45 Bloch functions, normal functions, normal families
- 30D50 Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
- 30D60 Quasi-analytic and other classes of functions
- 30D99 None of the above, but in this section
- 30Exx Miscellaneous topics of analysis in the complex domain
- 30E05 Moment problems, interpolation problems
- 30E10 Approximation in the complex domain
- 30E15 Asymptotic representations in the complex domain
- 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]
- 30E99 None of the above, but in this section
- 30F10 Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
- 30F15 Harmonic functions on Riemann surfaces
- 30F20 Classification theory of Riemann surfaces
- 30F25 Ideal boundary theory
- 30F30 Differentials on Riemann surfaces
- 30F35 Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
- 30F45 Conformal metrics (hyperbolic, Poincaré, distance functions)
- 30F60 Teichmüller theory [See also 32G15]
- 30F99 None of the above, but in this section
- 30Gxx Generalized function theory
- 30G06 Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]
- 30G12 Finely holomorphic functions and topological function theory
- 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)
- 30G25 Discrete analytic functions
- 30G30 Other generalizations of analytic functions (including abstract-valued functions)
- 30G35 Functions of hypercomplex variables and generalized variables
- 30G99 None of the above, but in this section
- 30H05 Spaces and algebras of analytic functions [See also 32A38, 46Exx, 46J15]
31-XX Potential theory [For probabilistic potential theory, see 60J45]
- 31-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 31-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 31-02 Research exposition (monographs, survey articles)
- 31-03 Historical (must also be assigned at least one classification number from Section 01)
- 31-04 Explicit machine computation and programs (not the theory of computation or programming)
- 31-06 Proceedings, conferences, collections, etc.
- 31-99 Potential theory (not classified at a more specific level)
- 31Axx Two-dimensional theory
- 31A05 Harmonic, subharmonic, superharmonic functions
- 31A10 Integral representations, integral operators, integral equations methods
- 31A15 Potentials and capacity, harmonic measure, extremal length [See also 30C85]
- 31A20 Boundary behavior (theorems of Fatou type, etc.)
- 31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation
- 31A35 Connections with differential equations
- 31A99 None of the above, but in this section
- 31Bxx Higher-dimensional theory
- 31B05 Harmonic, subharmonic, superharmonic functions
- 31B10 Integral representations, integral operators, integral equations methods
- 31B15 Potentials and capacities, extremal length
- 31B30 Biharmonic and polyharmonic equations and functions
- 31B35 Connections with differential equations
- 31B99 None of the above, but in this section
- 31Cxx Other generalizations
- 31C05 Harmonic, subharmonic, superharmonic functions
- 31C10 Pluriharmonic and plurisubharmonic functions [See also 32U05]
- 31C12 Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]
- 31C15 Potentials and capacities
- 31C20 Discrete potential theory and numerical methods
- 31C25 Dirichlet spaces
- 31C35 Martin boundary theory [See also 60J50]
- 31C40 Fine potential theory
- 31C45 Other generalizations (nonlinear potential theory, etc.)
- 31C99 None of the above, but in this section
- 31D05 Axiomatic potential theory
32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]
- 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 32-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 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.
- 32-99 Several complex variables and analytic spaces (not classified at a more specific level)
- 32Axx Holomorphic functions of several complex variables
- 32A05 Power series, series of functions
- 32A07 Special domains (Reinhardt, Hartogs, circular, tube)
- 32A10 Holomorphic functions
- 32A12 Multifunctions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A99
- 32A15 Entire functions
- 32A17 Special families of functions
- 32A18 Bloch functions, normal functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A37
- 32A19 Normal families of functions, mappings
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A17
- 32A20 Meromorphic functions
- 32A22 Nevanlinna theory (local); growth estimates; other inequalities [For geometric theory, see 32H25, 32H30]
- 32A25 Integral representations; canonical kernels (Szegö, Bergman, etc.)
- 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A25
- 32A27 Local theory of residues [See also 32C30]
- 32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) [For functions of several hypercomplex variables, see 30G35]
- 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA) [See also 46Exx]
- 32A38 Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32E25
- 32A40 Boundary behavior of holomorphic functions
- 32A45 Hyperfunctions [See also 46F15]
- 32A55 Singular integrals
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A99
- 32A60 Zero sets of holomorphic functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A10
- 32A65 Banach algebra techniques [See mainly 46Jxx]
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
32E25, 32E99
- 32A70 Functional analysis techniques [See mainly 46Exx]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A99
- 32A99 None of the above, but in this section
- 32Bxx Local analytic geometry [See also 13-XX and 14-XX]
- 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 [See also 14P15]
- 32B25 Triangulation and related questions
- 32B99 None of the above, but in this section
- 32Cxx Analytic spaces
- 32C05 Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]
- 32C07 Real-analytic sets, complex Nash functions [See also 14P15, 14P20]
- 32C09 Embedding of real analytic manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F25
- 32C11 Complex supergeometry [See also 14A22, 14M30, 58A50]
- 32C18 Topology of analytic spaces
- 32C20 Normal analytic spaces
- 32C22 Embedding of analytic spaces
[Nouveau code MSC 2000]
- 32C25 Analytic subsets and submanifolds
- 32C30 Integration on analytic sets and spaces, currents [For local theory, see 32A25 or 32A27]
- 32C35 Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]
- 32C36 Local cohomology of analytic spaces
- 32C37 Duality theorems
- 32C38 Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15]
- 32C55 The Levi problem in complex spaces; generalizations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32E99
- 32C81 Applications to physics
- 32C99 None of the above, but in this section
- 32Dxx Analytic continuation
- 32D15 Continuation of analytic objects
- 32D20 Removable singularities
- 32D99 None of the above, but in this section
- 32Exx Holomorphic convexity
- 32E05 Holomorphically convex complex spaces, reduction theory
- 32E10 Stein spaces, Stein manifolds
- 32E20 Polynomial convexity
- 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation
- 32E35 Global boundary behavior of holomorphic functions
- 32E40 The Levi problem
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32E99
- 32E99 None of the above, but in this section
- 32Fxx Geometric convexity
- 32F10 q-convexity, q-concavity
- 32F17 Other notions of convexity
[Nouveau code MSC 2000]
- 32F18 Finite-type conditions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F99
- 32F27 Topological consequences of geometric convexity
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F99
- 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)
[Nouveau code MSC 2000]
- 32F45 Invariant metrics and pseudodistances
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32H15
- 32F99 None of the above, but in this section
- 32Gxx Deformations of analytic structures
- 32G05 Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
- 32G07 Deformations of special (e.g. CR) structures
- 32G08 Deformations of fiber bundles
- 32G10 Deformations of submanifolds and subspaces
- 32G13 Analytic moduli problems [For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10] [See also 14H15, 14J15]
- 32G15 Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
- 32G20 Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07]
- 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation) [See also 34Mxx]
- 32G81 Applications to physics
- 32G99 None of the above, but in this section
- 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions
- 32H25 Picard-type theorems and generalizations [For function-theoretic properties, see 32A22]
- 32H30 Value distribution theory in higher dimensions [For function-theoretic properties, see 32A22]
- 32H35 Proper mappings, finiteness theorems
- 32H40 Boundary regularity of mappings
- 32H50 Iteration problems
- 32H99 None of the above, but in this section
- 32Jxx Compact analytic spaces [For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx]
- 32J05 Compactification of analytic spaces
- 32J10 Algebraic dependence theorems
- 32J15 Compact surfaces
- 32J17 Compact 3-folds
- 32J18 Compact n-folds
- 32J25 Transcendental methods of algebraic geometry [See also 14C30]
- 32J27 Compact Kähler manifolds: generalizations, classification
- 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)
- 32K05 Banach analytic spaces [See also 58Bxx]
- 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]
- 32K99 None of the above, but in this section
- 32L05 Holomorphic bundles and generalizations
- 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
- 32L15 Bundle convexity [See also 32F10]
- 32L20 Vanishing theorems
- 32L25 Twistor theory, double fibrations [See also 53C28]
- 32L81 Applications to physics
- 32L99 None of the above, but in this section
- 32Mxx Complex spaces with a group of automorphisms
- 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
- 32M10 Homogeneous complex manifolds [See also 14M17, 57T15]
- 32M12 Almost homogeneous manifolds and spaces [See also 14M17]
- 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
- 32M17 Automorphism groups of Cn and affine manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32M05
- 32M25 Complex vector fields
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32S65
- 32M99 None of the above, but in this section
- 32Nxx Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]
- 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)
- 32Q05 Negative curvature manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C10
- 32Q10 Positive curvature manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C10
- 32Q20 Kähler-Einstein manifolds [See also 53Cxx]
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
53C25, 32L07
- 32Q25 Calabi-Yau theory [See also 14J32]
[Nouveau code MSC 2000]
- 32Q28 Stein manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32E10
- 32Q30 Uniformization
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C10
- 32Q40 Embedding theorems
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C10
- 32Q55 Topological aspects of complex manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C10
- 32Q57 Classification theorems
[Nouveau code MSC 2000]
- 32Q60 Almost complex manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
53C15
- 32Q99 None of the above, but in this section
[ section nouvelle ]
- 32Sxx Singularities [See also 58Kxx]
- 32S05 Local singularities [See also 14J17]
- 32S10 Invariants of analytic local rings
- 32S15 Equisingularity (topological and analytic) [See also 14E15]
- 32S20 Global theory of singularities; cohomological properties [See also 14E15]
- 32S22 Relations with arrangements of hyperplanes [See also 52C30]
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
52B30, 32S20
- 32S25 Surface and hypersurface singularities [See also 14J17]
- 32S30 Deformations of singularities; vanishing cycles [See also 14B07]
- 32S35 Mixed Hodge theory of singular varieties [See also 14C30, 14D07]
- 32S40 Monodromy; relations with differential equations and D-modules
- 32S45 Modifications; resolution of singularities [See also 14E15]
- 32S50 Topological aspects: Lefschetz theorems, topological classification, invariants
- 32S55 Milnor fibration; relations with knot theory [See also 57M25, 57Q45]
- 32S60 Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]
- 32S65 Singularities of holomorphic vector fields and foliations
- 32S70 Other operations on singularities
- 32S99 None of the above, but in this section
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32S70
- 32Txx Pseudoconvex domains
- 32T05 Domains of holomorphy
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32D05
- 32T15 Strongly pseudoconvex domains
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F15
- 32T20 Worm domains
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F15
- 32T25 Finite type domains
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F15
- 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F15
- 32T35 Exhaustion functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F15
- 32T40 Peak functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32E25
- 32T99 None of the above, but in this section
[ section nouvelle ]
- 32Uxx Pluripotential theory
- 32U05 Plurisubharmonic functions and generalizations [See also 31C10]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F05
- 32U10 Plurisubharmonic exhaustion functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F05
- 32U15 General pluripotential theory
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F05
- 32U20 Capacity theory and generalizations
[Nouveau code MSC 2000]
- 32U30 Removable sets
[Nouveau code MSC 2000]
- 32U35 Pluricomplex Green functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32F05
- 32U40 Currents
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C30
- 32U99 None of the above, but in this section
[ section nouvelle ]
- 32V05 CR structures, CR operators, and generalizations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C16
- 32V10 CR functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C16
- 32V25 Extension of functions and other analytic objects from CR manifolds
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
32C16, 32D15
- 32V35 Finite type conditions on CR manifolds
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32C16
- 32V99 None of the above, but in this section
[ section nouvelle ]
- 32Wxx Differential operators in several variables
- 32W05
 and -Neumann operators
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
32F20, 35N15
- 32W10 b and b-Neumann operators
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
32F20, 35N15
- 32W20 Complex Monge-Ampère operators
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
32F07, 35J99
- 32W25 Pseudodifferential operators in several complex variables
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
35S05
- 32W30 Heat kernels in several complex variables
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
58G11, 35K99
- 32W50 Other partial differential equations of complex analysis
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
35A20
- 32W99 None of the above, but in this section
[ section nouvelle ]
33-XX Special functions (33-XX deals with the properties of functions as functions) [For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx]
- 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 33-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 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)
- 33-06 Proceedings, conferences, collections, etc.
- 33-99 Special functions (not classified at a more specific level)
- 33Bxx Elementary classical functions
- 33B10 Exponential and trigonometric functions
- 33B15 Gamma, beta and polygamma functions
- 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
- 33B30 Higher logarithm functions
[Nouveau code MSC 2000]
- 33B99 None of the above, but in this section
- 33Cxx Hypergeometric functions
- 33C05 Classical hypergeometric functions, 2F1
- 33C10 Bessel and Airy functions, cylinder functions, 0F1
- 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
- 33C20 Generalized hypergeometric series, pFq
- 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See 42C05 for general orthogonal polynomials and functions]
- 33C47 Other special orthogonal polynomials and functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33C45
- 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
- 33C52 Orthogonal polynomials and functions associated with root systems
[Nouveau code MSC 2000]
- 33C60 Hypergeometric integrals and functions defined by them (E, G and H functions)
- 33C65 Appell, Horn and Lauricella functions
- 33C67 Hypergeometric functions associated with root systems
[Nouveau code MSC 2000]
- 33C70 Other hypergeometric functions and integrals in several variables
- 33C75 Elliptic integrals as hypergeometric functions
- 33C80 Connections with groups and algebras, and related topics
- 33C90 Applications
- 33C99 None of the above, but in this section
- 33Dxx Basic hypergeometric functions
- 33D05 q-gamma functions, q-beta functions and integrals
- 33D15 Basic hypergeometric functions in one variable, r
 s
- 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
- 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33D45
- 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33D80
- 33D60 Basic hypergeometric integrals and functions defined by them
- 33D65 Bibasic functions and multiple bases
- 33D67 Basic hypergeometric functions associated with root systems
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33D80
- 33D70 Other basic hypergeometric functions and integrals in several variables
- 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics
- 33D90 Applications
- 33D99 None of the above, but in this section
- 33Exx Other special functions
- 33E05 Elliptic functions and integrals
- 33E10 Lamé, Mathieu, and spheroidal wave functions
- 33E12 Mittag-Leffler functions and generalizations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33E15
- 33E15 Other wave functions
- 33E17 Painlevé-type functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33E30
- 33E20 Other functions defined by series and integrals
- 33E30 Other functions coming from differential, difference and integral equations
- 33E50 Special functions in characteristic p (gamma functions, etc.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33E99
- 33E99 None of the above, but in this section
- 33Fxx Computational aspects
- 33F05 Numerical approximation [See also 65D20]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33-04
- 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]
[Nouveau code MSC 2000]
- 33F99 None of the above, but in this section
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
33-04
34-XX Ordinary differential equations
- 34-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 34-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 34-02 Research exposition (monographs, survey articles)
- 34-03 Historical (must also be assigned at least one classification number from Section 01)
- 34-04 Explicit machine computation and programs (not the theory of computation or programming)
- 34-06 Proceedings, conferences, collections, etc.
- 34-99 Ordinary differential equations (not classified at a more specific level)
- 34Axx General theory
- 34A05 Explicit solutions and reductions
- 34A09 Implicit equations, differential-algebraic equations [See also 65L80]
- 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
- 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]
- 34A26 Geometric methods in differential equations
- 34A30 Linear equations and systems, general
- 34A34 Nonlinear equations and systems, general
- 34A35 Differential equations of infinite order
- 34A36 Discontinuous equations
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
34A99
- 34A37 Differential equations with impulses
- 34A40 Differential inequalities [See also 26D20]
- 34A45 Theoretical approximation of solutions [For numerical analysis, see 65Lxx]
- 34A60 Differential inclusions [See also 49J24, 49K24]
- 34A99 None of the above, but in this section
- 34Bxx Boundary value problems [For ordinary differential operators, see 34Lxx]
- 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameter
[Nouveau code MSC 2000]
- 34B08 Multi-parameter boundary value problems
[Nouveau code MSC 2000]
- 34B09 Boundary value problems with an indefinite weight
[Nouveau code MSC 2000]
- 34B10 Multipoint boundary value problems
- 34B18 Positive solutions of nonlinear boundary value problems
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
34B15
- 34B20 Weyl theory and its generalizations
- 34B24 Sturm-Liouville theory [See also 34Lxx]
- 34B27 Green functions
- 34B30 Special equations (Mathieu, Hill, Bessel, etc.)
- 34B37 Boundary value problems with impulses
[Nouveau code MSC 2000]
- 34B40 Boundary value problems on infinite intervals
[Nouveau code MSC 2000]
- 34B45 Boundary value problems on graphs and networks
[Nouveau code MSC 2000]
- 34B60 Applications
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
34B99
- 34B99 None of the above, but in this section
- 34Cxx Qualitative theory [See also 37-XX]
- 34C05 Location of integral curves, singular points, limit cycles
- 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
34C05, 58F21
- 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
[Nouveau code MSC 2000]
- 34C10 Oscillation theory, zeros, disconjugacy and comparison theory
- 34C11 Growth, boundedness, comparison of solutions
- 34C12 Monotone systems
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
34C35, 34C99
- 34C14 Symmetries, invariants
[Nouveau code MSC 2000]
- 34C15 Nonlinear oscillations, coupled oscillators
- 34C20 Transformation and reduction of equations and systems, normal forms
- 34C23 Bifurcation [See mainly 37Gxx]
- 34C25 Periodic solutions
- 34C26 Relaxation oscillations
[Nouveau code MSC 2000]
- 34C27 Almost periodic solutions
- 34C28 Complex behavior, chaotic systems [See mainly 37Dxx]
- 34C29 Averaging method
- 34C30 Manifolds of solutions
- 34C37 Homoclinic and heteroclinic solutions
- 34C40 Equations and systems on manifolds
- 34C41 Equivalence, asymp
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