La Classification Mathématique par matières 2000
Mathematics subject Classification 2000
Question : CC = Class
00-XX General
- 00-99 General mathematics (not classified at a more specific level)
01-XX History and biography
- 01-99 History and biography (not classified at a more specific level)
- 01A75 Collected or selected works; reprintings or translations of classics [See also 00B60]
03-XX Mathematical logic and foundations
- 03-03 Historical (must also be assigned at least one classification number from Section 01)
- 03-99 Mathematical logic and foundations (not classified at a more specific level)
- 03B05 Classical propositional logic
- 03B10 Classical first-order logic
- 03B20 Subsystems of classical logic (including intuitionistic logic)
- 03B30 Foundations of classical theories (including reverse mathematics) [See also 03F35]
- 03B60 Other nonclassical logic
- 03C05 Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]
- 03C45 Classification theory, stability and related concepts
- 03C52 Properties of classes of models
- 03C68 Other classical first-order model theory
- 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
- 03E20 Other classical set theory (including functions, relations, and set algebra)
- 03E30 Axiomatics of classical set theory and its fragments
- 03E70 Nonclassical and second-order set theories
05-XX Combinatorics [For finite fields, see 11Txx]
- 05-03 Historical (must also be assigned at least one classification number from Section 01)
- 05-99 Combinatorics (not classified at a more specific level)
- 05E15 Combinatorial problems concerning the classical groups [See also 22E45, 33C80]
06-XX Order, lattices, ordered algebraic structures [See also 18B35]
- 06-03 Historical (must also be assigned at least one classification number from Section 01)
- 06-99 Order, lattices, ordered algebraic structures (not classified at a more specific level)
08-XX General algebraic systems
- 08-03 Historical (must also be assigned at least one classification number from Section 01)
- 08-99 General mathematical systems (not classified at a more specific level)
- 08Cxx Other classes of algebras
- 08C10 Axiomatic model classes [See also 03Cxx, in particular 03C60]
11-XX Number theory
- 11-03 Historical (must also be assigned at least one classification number from Section 01)
- 11-99 Number theory (not classified at a more specific level)
- 11E41 Class numbers of quadratic and Hermitian forms
- 11E57 Classical groups [See also 14Lxx, 20Gxx]
- 11G45 Geometric class field theory [See also 11R37, 14C35, 19F05]
- 11N69 Distribution of integers in special residue classes
- 11R29 Class numbers, class groups, discriminants
- 11R37 Class field theory
- 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
- 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
11R58
- 11R65 Class groups and Picard groups of orders
- 11S31 Class field theory; p-adic formal groups [See also 14L05]
- 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
12-XX Field theory and polynomials
- 12-03 Historical (must also be assigned at least one classification number from Section 01)
- 12-99 Algebraic number theory, field theory and polynomials (not classified at a more specific level)
13-XX Commutative rings and algebras
- 13-03 Historical (must also be assigned at least one classification number from Section 01)
- 13-99 Commutative rings and algebras (not classified at a more specific level)
- 13C05 Structure, classification theorems
- 13C20 Class groups [See also 11R29]
14-XX Algebraic geometry
- 14-03 Historical (must also be assigned at least one classification number from Section 01)
- 14-99 Algebraic geometry (not classified at a more specific level)
- 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also 13H15, 55R40, 57R20]
- 14F25 Classical real and complex cohomology
- 14J10 Families, moduli, classification: algebraic theory
- 14J15 Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
- 14K10 Algebraic moduli, classification [See also 11G15, 14D20]
- 14L35 Classical groups (geometric aspects) [See also 20Gxx, 51N30]
- 14N15 Classical problems, Schubert calculus
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14M15
- 14R05 Classification of affine varieties
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
14J99
15-XX Linear and multilinear algebra; matrix theory
- 15-03 Historical (must also be assigned at least one classification number from Section 01)
- 15-99 Linear and multilinear algebra; matrix theory (finite and infinite) (not classified at a more specific level)
- 15A21 Canonical forms, reductions, classification
16-XX Associative rings and algebras [For the commutative case, see 13-XX]
- 16-03 Historical (must also be assigned at least one classification number from Section 01)
- 16-99 Associative rings and algebras (not classified at a more specific level)
- 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
- 16D80 Other classes of modules and ideals [See also 16G50]
- 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
17-XX Nonassociative rings and algebras
- 17-03 Historical (must also be assigned at least one classification number from Section 01)
- 17-99 Nonassociative rings and algebras (not classified at a more specific level)
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]
- 18-03 Historical (must also be assigned at least one classification number from Section 01)
- 18-99 Category theory, homological algebra (not classified at a more specific level)
- 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
- 18G25 Relative homological algebra, projective classes
19-XX $K$-theory [See also 16E20, 18F25]
- 19-03 Historical (must also be assigned at least one classification number from Section 01)
- 19-99 General (not classified at a more specific level)
- 19F05 Generalized class field theory [See also 11G45]
20-XX Group theory and generalizations
- 20-03 Historical (must also be assigned at least one classification number from Section 01)
- 20-99 Group theory and generalizations (not classified at a more specific level)
- 20D05 Classification of simple and nonsolvable groups
- 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes,
 -length, ranks [See also 20F17]
- 20Exx Structure and classification of infinite or finite groups
- 20E45 Conjugacy classes
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
20E99
- 20F17 Formations of groups, Fitting classes [See also 20D10]
- 20F22 Other classes of groups defined by subgroup chains
- 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]
22-XX Topological groups, Lie groups [For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX]
- 22-03 Historical (must also be assigned at least one classification number from Section 01)
- 22-99 Topological groups, Lie groups (not classified at a more specific level)
26-XX Real functions [See also 54C30]
- 26-03 Historical (must also be assigned at least one classification number from Section 01)
- 26-99 Real functions (not classified at a more specific level)
- 26A16 Lipschitz (Hölder) classes
- 26A21 Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]
28-XX Measure and integration [For analysis on manifolds, see 58-XX]
- 28-03 Historical (must also be assigned at least one classification number from Section 01)
- 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]
30-XX Functions of a complex variable [For analysis on manifolds, see 58-XX]
- 30-03 Historical (must also be assigned at least one classification number from Section 01)
- 30-99 Functions of a complex variable (not classified at a more specific level)
- 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
- 30D15 Special classes of entire functions and growth estimates
- 30D55 Hp-classes
- 30D60 Quasi-analytic and other classes of functions
- 30F20 Classification theory of Riemann surfaces
31-XX Potential theory [For probabilistic potential theory, see 60J45]
- 31-03 Historical (must also be assigned at least one classification number from Section 01)
- 31-99 Potential theory (not classified at a more specific level)
32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]
- 32-03 Historical (must also be assigned at least one classification number from Section 01)
- 32-99 Several complex variables and analytic spaces (not classified at a more specific level)
- 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]
- 32J27 Compact Kähler manifolds: generalizations, classification
- 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)
- 32P05 Non-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
- 32Q57 Classification theorems
[Nouveau code MSC 2000]
- 32S50 Topological aspects: Lefschetz theorems, topological classification, invariants
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]
- 33-03 Historical (must also be assigned at least one classification number from Section 01)
- 33-99 Special functions (not classified at a more specific level)
- 33Bxx Elementary classical functions
- 33C05 Classical hypergeometric functions, 2F1
34-XX Ordinary differential equations
- 34-03 Historical (must also be assigned at least one classification number from Section 01)
- 34-99 Ordinary differential equations (not classified at a more specific level)
- 34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
[Nouveau code MSC 2000]
35-XX Partial differential equations
- 35-03 Historical (must also be assigned at least one classification number from Section 01)
- 35-99 Partial differential equations (not classified at a more specific level)
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
- 37-03 Historical (must also be assigned at least one classification number from Section 01)
[Nouveau code MSC 2000]
- 37-99 Dynamic systems and ergodic theory (not classified at a more specific level)
- 37A35 Entropy and other invariants, isomorphism, classification
[Nouveau code MSC 2000]
- 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
34C99, 58F99
- 37N05 Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
[Nouveau code MSC 2000]
39-XX Difference and functional equations
- 39-03 Historical (must also be assigned at least one classification number from section 01)
- 39-99 Difference and functional equations (not classified at a more specific level)
40-XX Sequences, series, summability
- 40-03 Historical (must also be assigned at least one classification number from Section 01)
- 40-99 Sequences, series, summability (not classified at a more specific level)
- 40B05 Multiple sequences and series (should also be assigned at least one other classification number in this section)
41-XX Approximations and expansions [For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx]
- 41-03 Historical (must also be assigned at least one classification number from Section 01)
- 41-99 Approximations and expansions (not classified at a more specific level)
- 41A30 Approximation by other special function classes
- 41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
42-XX Fourier analysis
- 42-03 Historical (must also be assigned at least one classification number from Section 01)
- 42-99 Fourier analysis (not classified at a more specific level)
- 42A75 Classical almost periodic functions, mean periodic functions [See also 43A60]
43-XX Abstract harmonic analysis [For other analysis on topological and Lie groups, see 22Exx]
- 43-03 Historical (must also be assigned at least one classification number from Section 01)
- 43-99 Abstract harmonic analysis (not classified at a more specific level)
44-XX Integral transforms, operational calculus [For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10]
- 44-03 Historical (must also be assigned at least one classification number from Section 01)
- 44-99 Integral transforms (not classified at a more specific level)
- 44A45 Classical operational calculus
45-XX Integral equations
- 45-03 Historical (must also be assigned at least one classification number from section 01)
- 45-99 Integral equations (not classified at a more specific level)
46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
- 46-03 Historical (must also be assigned at least one classification number from Section 01)
- 46-99 Functional analysis (not classified at a more specific level)
- 46B25 Classical Banach spaces in the general theory
- 46H20 Structure, classification of topological algebras
- 46J40 Structure, classification of commutative topological algebras
- 46L35 Classifications of C*-algebras, factors
- 46L37 Subfactors and their classification
- 46Sxx Other (nonclassical) types of functional analysis [See also 47Sxx]
47-XX Operator theory
- 47-03 Historical (must also be assigned at least one classification number from Section 01)
- 47-99 Operator theory (not classified at a more specific level)
- 47Bxx Special classes of linear operators
- 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
- 47Sxx Other (nonclassical) types of operator theory [See also 46Sxx]
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
- 49-03 Historical (must also be assigned at least one classification number from Section 01)
- 49-99 Calculus of variations and optimal control; optimization (not classified at a more specific level)
- 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
- 49K30 Optimal solutions belonging to restricted classes
51-XX Geometry [For algebraic geometry, see 14-XX]
- 51-03 Historical (must also be assigned at least one classification number from Section 01)
- 51-99 Geometry (not classified at a more specific level)
- 51N30 Geometry of classical groups [See also 20Gxx, 14L35]
- 51N35 Questions of classical algebraic geometry [See also 14Nxx]
- 51P05 Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)
52-XX Convex and discrete geometry
- 52-03 Historical (must also be assigned at least one classification number from Section 01)
- 52-99 Convex sets and related geometric topics (not classified at a more specific level)
53-XX Differential geometry [For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx]
- 53-03 Historical (must also be assigned at least one classification number from Section 01)
- 53-99 Differential geometry (not classified at a more specific level)
- 53Axx Classical differential geometry
54-XX General topology [For the topology of manifolds of all dimensions, see 57Nxx]
- 54-03 Historical (must also be assigned at least one classification number from Section 01)
- 54-99 General topology (not classified at a more specific level)
55-XX Algebraic topology
- 55-03 Historical (must also be assigned at least one classification number from Section 01)
- 55-99 Algebraic topology (not classified at a more specific level)
- 55Mxx Classical topics [For the topology of Euclidean spaces and manifolds, see 57Nxx]
- 55P15 Classification of homotopy type
- 55Q05 Homotopy groups, general; sets of homotopy classes
- 55R15 Classification
- 55R35 Classifying spaces of groups and H-spaces
- 55R37 Maps between classifying spaces
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
55R35
- 55R40 Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
- 55R50 Stable classes of vector space bundles, K-theory [See also 19Lxx] [For algebraic K-theory, see 18F25, 19-XX]
- 55S37 Classification of mappings
57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]
- 57-03 Historical (must also be assigned at least one classification number from Section 01)
- 57-99 Manifolds and cell complexes (not classified at a more specific level)
- 57Q25 Comparison of PL-structures: classification, Hauptvermutung
- 57R20 Characteristic classes and numbers
- 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]
- 58-03 Historical (must also be assigned at least one classification number from Section 01)
- 58-99 Global analysis, analysis on manifolds (not classified at a more specific level)
- 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
- 58K40 Classification; finite determinacy of map germs
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
58C27
60-XX Probability theory and stochastic processes [For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX]
- 60-03 Historical (must also be assigned at least one classification number from Section 01)
- 60-08 Computational methods (not classified at a more specific level) [See also 65C50]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
60-04
- 60-99 Probability theory and stochastic processes (not classified at a more specific level)
- 60G46 Martingales and classical analysis
62-XX Statistics
- 62-03 Historical (must also be assigned at least one classification number from Section 01)
- 62-99 Statistics (not classified at a more specific level)
- 62C07 Complete class results
- 62H30 Classification and discrimination; cluster analysis [See also 91C20]
65-XX Numerical analysis
- 65-03 Historical (must also be assigned at least one classification number from Section 01)
- 65-99 Numerical analysis (not classified at a more specific level)
- 65Y10 Algorithms for specific classes of architectures
68-XX Computer science [For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area]
- 68-03 Historical (must also be assigned at least one classification number from Section 01)
- 68-99 Computer science (not classified at a more specific level)
- 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]
70-XX Mechanics of particles and systems [For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX]
- 70-03 Historical (must also be assigned at least one classification number from Section 01)
- 70-99 Mechanics of particles and systems (not classified at a more specific level)
- 70Sxx Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]
74-XX Mechanics of deformable solids
- 74-03 Historical (must also be assigned at least one classification number from section 01)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
73-03
- 74-99 Mechanics of deformable solids (not classified at a more specific level)
- 74B05 Classical linear elasticity
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
73C02
76-XX Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX]
- 76-03 Historical (must also be assigned at least one classification number from Section 01)
- 76-99 Fluid mechanics (not classified at a more specific level)
- 76A25 Superfluids (classical aspects)
[Nouveau code MSC 2000]
78-XX Optics, electromagnetic theory [For quantum optics, see 81V80]
- 78-03 Historical (must also be assigned at least one classification number from Section 01)
- 78-99 Optics, electromagnetic theory (not classified at a more specific level)
- 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)
80-XX Classical thermodynamics, heat transfer [For thermodynamics of solids, see 74A15]
- 80-03 Historical (must also be assigned at least one classification number from Section 01)
- 80-99 Classical thermodynamics, heat transfer (not classified at a more specific level)
- 80A10 Classical thermodynamics, including relativistic
81-XX Quantum theory
- 81-03 Historical (must also be assigned at least one classification number from Section 01)
- 81-99 Quantum mechanics (not classified at a more specific level)
- 81Q20 Semiclassical techniques including WKB and Maslov methods
- 81Txx Quantum field theory; related classical field theories [See also 70Sxx]
82-XX Statistical mechanics, structure of matter
- 82-03 Historical (must also be assigned at least one classification number from Section 01)
- 82-99 Statistical physics, structure of matter (not classified at a more specific level)
- 82B05 Classical equilibrium statistical mechanics (general)
- 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
83-XX Relativity and gravitational theory
- 83-03 Historical (must also be assigned at least one classification number from Section 01)
- 83-99 Relativity (not classified at a more specific level)
- 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
85-XX Astronomy and astrophysics [For celestial mechanics, see 70F15]
- 85-03 Historical (must also be assigned at least one classification number from Section 01)
- 85-99 Astronomy and astrophysics (not classified at a more specific level)
86-XX Geophysics [See also 76U05, 76V05]
- 86-03 Historical (must also be assigned at least one classification number from Section 01)
- 86-99 Geophysics (not classified at a more specific level)
90-XX Operations research, mathematical programming
- 90-03 Historical (must also be assigned at least one classification number from Section 01)
- 90-99 Operations research, programming (not classified at a more specific level)
91-XX Game theory, economics, social and behavioral sciences
- 91-03 Historical (must also be assigned at least one classification number from section 01)
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
90-03
- 91-99 Game theory, economics, social and behavioral sciences (not classified at a more specific level)
92-XX Biology and other natural sciences
- 92-03 Historical (must also be assigned at least one classification number from Section 01)
- 92-99 Biology and other natural sciences (not classified at a more specific level)
- 92E20 Classical flows, reactions, etc. [See also 80A30, 80A32]
93-XX Systems theory; control [For optimal control, see 49-XX]
- 93-03 Historical (must also be assigned at least one classification number from Section 01)
- 93-99 Systems theory; control (not classified at a more specific level)
- 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)
94-XX Information and communication, circuits
- 94-03 Historical (must also be assigned at least one classification number from Section 01)
- 94-99 Information and communication, circuits (not classified at a more specific level)
97-XX Mathematics education
- 97-03 Historical (must also be assigned at least one classification number from Section 01)
- 97-99 Mathematics education (not classified at a more specific level)
- 97D40 Teaching methods and classroom techniques. Lesson preparation. Educational principles [For research aspects see 97Cxx]
- 97U20 Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom
- 97U60 Manipulative materials and their use in the classroom [For research aspects see 97C80]
- 97U70 Technological tools (computers, calculators, software, etc.) and their use in the classroom
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