MSC2020 Classification Codes --> MSC2010 Classification CodesUpdate Date: 18 February 2020
MSC2020DescriptionMSC2010
00-XX General and overarching topics; collections _
00A08 Recreational mathematics 97A20
00A79 Physics [Use more specific entries from Sections 70-XX through 86-XX when possible] 00A73
01-XX History and biography [See also the classification number –03 in the other sections] _
01A11 History of mathematics of the indigenous cultures of Africa, Asia, and Oceania 01A13
03-XX Mathematical logic and foundations _
03B16 Higher-order logic 03B15
03B38 Type theory 03B15
03C66 Continuous model theory, model theory of metric structures 03B15
05-XX Combinatorics {For finite fields, see 11Txx} _
05E14 Combinatorial aspects of algebraic geometry [See also 14Nxx] 05E15
05E16 Combinatorial aspects of groups and algebras [See also 22E45, 33C80] 05E15
06-XX Order, lattices, ordered algebraic structures [See also 18B35] _
08-XX General algebraic systems _
11-XX Number theory _
12-XX Field theory and polynomials _
12-08 Computational methods for problems pertaining to field theory [See also 68W30] 12Y99 12Y05 12Yxx
13-XX Commutative rings and algebras _
14-XX Algebraic geometry _
14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx} 14F05
14F06 Sheaves in algebraic geometry [See also 14F08, 14H60, 14J60, 18F20, 32L10, 46M20] 14F05
14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx] 14F05
14T10 Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80} 14T05
14T15 Combinatorial aspects of tropical varieties 14T05
14T20 Geometric aspects of tropical varieties 14T05
14T25 Arithmetic aspects of tropical varieties 14T05
14T90 Applications of tropical geometry 14T05
15-XX Linear and multilinear algebra; matrix theory _
16-XX Associative rings and algebras {For the commutative case, see 13-XX} _
17-XX Nonassociative rings and algebras _
18-XX Category theory; homological algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} _
18C40 Structured objects in a category (group objects, etc.) 18D35
18E10 Abelian categories, Grothendieck categories _
18F60 Categories of topological spaces and continuous mappings [See also 54-XX] 18B30
18G80 Derived categories, triangulated categories 18E30
18G90 Other (co)homology theories (category-theoretic aspects) [See also 19D55, 46L80, 58J20, 58J22] 18G60
18M05 Monoidal categories, symmetric monoidal categories [See also 19D23] 18D10
18M15 Braided monoidal categories and ribbon categories {For applications to knot theory, see also 57Kxx; for applications to quantum groups, see also 16T20, 17B37, 81R50} 18D10
18M60 Operads (general) 18D50
18N10 2-categories, bicategories, double categories 18D05
18N40 Homotopical algebra, Quillen model categories, derivators [See also 55U35] 18G55
18N50 Simplicial sets, simplicial objects [See also 55U10] 18G30
19-XX $K$-theory [See also 16E20, 18F25] _
20-XX Group theory and generalizations _
20-08 Computational methods for problems pertaining to group theory 20C40 20B40
22-XX Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX; for abstract harmonic analysis, see 43-XX} _
26-XX Real functions [See also 54C30] _
28-XX Measure and integration {For analysis on manifolds, see 58-XX} _
30-XX Functions of a complex variable _
31-XX Potential theory {For probabilistic potential theory, see 60J45} _
32-XX Several complex variables and analytic spaces {For infinite-\newline dimensional holomorphy, see also 46G20, 58B12} _
32Q02 Special domains (Reinhardt, Hartogs, circular, tube, etc.) in $\mathbb{C}^n$ and complex manifolds 32A07
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} _
34-XX Ordinary differential equations _
35-XX Partial differential equations _
35S16 Initial-boundary value problems for PDEs with pseudodifferential operators 35S11
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] _
37A44 Relations between ergodic theory and number theory [See also 11Kxx] 37A45
37A46 Relations between ergodic theory and harmonic analysis 37A45
37B51 Multidimensional shifts of finite type 37B50
37B52 Tiling dynamics 37B50
37C79 Symmetries and invariants of dynamical systems [See also 34C14, 34K04] 37C80
37C81 Equivariant dynamical systems 37C80
37C83 Dynamical systems with singularities (billiards, etc.) 37D50
37F31 Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics 37F30
37F32 Fuchsian and Kleinian groups as dynamical systems 37F30
37F34 Teichmüller theory; moduli spaces of holomorphic dynamical systems 37F30
37F44 Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps 37F45
37F46 Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets 37F45
37J06 General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants 37J05
37J11 Symplectic and canonical mappings 37J10
37J12 Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems 37J10
37J39 Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) [See also 53D20] 37J05
37J46 Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems 37J45 37J50
37J51 Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods 37J50 37J45
37K06 General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws 37K05
39-XX Difference and functional equations _
40-XX Sequences, series, summability _
41-XX Approximations and expansions {For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx} _
42-XX Harmonic analysis on Euclidean spaces _
43-XX Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx} _
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} _
45-XX Integral equations _
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} _
47-XX Operator theory _
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] _
49M99 None of the above, but in this section 49M30
51-XX Geometry {For algebraic geometry, see 14-XX; for differential geometry, see 53-XX} _
52-XX Convex and discrete geometry _
53-XX Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx} _
53A31 Differential geometry of submanifolds of Möbius space 53A30
53C18 Conformal structures on manifolds 53A30
53Exx Geometric evolution equations 53C44
53E10 Flows related to mean curvature 53C44
53E20 Ricci flows 53C44
53E30 Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) 53C44
53E40 Higher-order geometric flows 53C44
53E50 Flows related to symplectic and contact structures 53C44
53E99 None of the above, but in this section 53C44
54-XX General topology {For the topology of manifolds of all dimensions, see 57Nxx} _
55-XX Algebraic topology _
57-XX Manifolds and cell complexes {For complex manifolds, see\newline 32Qxx} _
57K10 Knot theory 57M25
57K14 Knot polynomials 57M27
57K16 Finite-type and quantum invariants, topological quantum field theories (TQFT) 57M27
57K18 Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) 57M27
57K20 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) 57N05 57M20
57K30 General topology of 3-manifolds 57M35 57N12 57N10 57M40
57K31 Invariants of 3-manifolds (including skein modules, character varieties) 57M27 57N10
57K32 Hyperbolic 3-manifolds 57N10
57K33 Contact structures in 3 dimensions [See also 57R17] 57N10
57K35 Other geometric structures on 3-manifolds 57N10
57K40 General topology of 4-manifolds 57N13
57K45 Higher-dimensional knots and links 57Q45
57K50 Low-dimensional manifolds of specific dimension 5 or higher 57N15
57Nxx Topological manifolds 57N15
58-XX Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 53Cxx] {For nonlinear operators, see 47Hxx; for geometric integration theory, see 49Q15} _
60-XX Probability theory and stochastic processes {For additional applications, see 05Cxx, 11Kxx, 34-XX, 35-XX, 62-XX, 76-XX, 81-XX, 82-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} _
60-08 Computational methods for problems pertaining to probability theory 65C50
60J74 Jump processes on discrete state spaces 60J75
60J76 Jump processes on general state spaces 60J75
62-XX Statistics _
62-08 Computational methods for problems pertaining to statistics 65C60
62A09 Graphical methods in statistics 62-09
62D10 Missing data 62-07
62D20 Causal inference from observational studies 62-07
62R07 Statistical aspects of big data and data science {For computer science aspects, see 68T09; for information-theoretic aspects, see 94A16} 62-07
65-XX Numerical analysis _
65F99 None of the above, but in this section 65F30
65L03 Numerical methods for functional-differential equations 34K28
68-XX Computer science {For papers containing software, source code, etc. in a specific mathematical area, see the classification number –04 in that area} _
68Q04 Classical models of computation (Turing machines, etc.) [See also 03D10] 68Q05
68Q06 Networks and circuits as models of computation; circuit complexity [See also 94C11] 68Q05
68Q07 Biologically inspired models of computation (DNA computing, membrane computing, etc.) 68Q05
68Q09 Other nonclassical models of computation {For quantum computing, see mainly 68Q12, 81P68} 68Q05
68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.) [See also 03B35] 68T15
70-XX Mechanics of particles and systems {For relativistic mechanics, see 83A05, 83C10; for statistical mechanics, see 82-XX} _
74-XX Mechanics of deformable solids _
74G22 Existence of solutions of equilibrium problems in solid mechanics 74G20 74G25
74S99 None of the above, but in this section 74S30
76-XX Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} _
76M99 None of the above, but in this section 76M25
76U65 Rossby waves [See also 86A05, 86A10] 76B65
78-XX Optics, electromagnetic theory {For quantum optics, see 81V80} _
78M99 None of the above, but in this section 78M25
80-XX Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15} _
80A19 Diffusive and convective heat and mass transfer, heat flow 80A20
80A21 Radiative heat transfer 80A20
80M99 None of the above, but in this section 80M25
81-XX Quantum theory _
81-10 Mathematical modeling or simulation for problems pertaining to quantum theory 81T80
82-XX Statistical mechanics, structure of matter _
82Mxx Basic methods in statistical mechanics [See also 65-XX] 82-08
82M10 Finite element, Galerkin and related methods applied to problems in statistical mechanics 82-08
82M12 Finite volume methods applied to problems in statistical mechanics 82-08
82M15 Boundary element methods applied to problems in statistical mechanics 82-08
82M20 Finite difference methods applied to problems in statistical mechanics 82-08
82M22 Spectral, collocation and related (meshless) methods applied to problems in statistical mechanics 82-08
82M30 Variational methods applied to problems in statistical mechanics 82-08
82M31 Monte Carlo methods applied to problems in statistical mechanics [See also 65C05] 82-08
82M36 Computational density functional analysis in statistical mechanics 82-08
82M37 Computational molecular dynamics in statistical mechanics 82-08
82M60 Stochastic analysis in statistical mechanics [See also 65C35] 82-08
82M99 None of the above, but in this section 82-08
83-XX Relativity and gravitational theory _
85-XX Astronomy and astrophysics {For celestial mechanics, see 70F15} _
86-XX Geophysics [See also 76U05, 76V05] _
86A10 Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76Uxx] 76B60
86A15 Seismology (including tsunami modeling), earthquakes 86A17
90-XX Operations research, mathematical programming _
91-XX Game theory, economics, finance, and other social and behavioral sciences _
91A07 Games with infinitely many players 91A13
91B05 Risk models (general) {For actuarial and financial risk, see 91Gxx} 91B30
91B39 Labor markets 91B40
91B41 Contract theory (moral hazard, adverse selection) 91B40
91G05 Actuarial mathematics 91B30
91G30 Interest rates, asset pricing, etc. (stochastic models) 91B25
92-XX Biology and other natural sciences _
93-XX Systems theory; control {For optimal control, see 49-XX} _
93-08 Computational methods for problems pertaining to systems and control theory 93E25 93B40
93-10 Mathematical modeling or simulation for problems pertaining to systems and control theory 93A30
94-XX Information and communication theory, circuits _
94C11 Switching theory, applications of Boolean algebras to circuits and networks 94C10
94D10 Boolean functions [See also 06E30] {For connections with circuits and networks, see 94C11} 94C10
97-XX Mathematics education _
97-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematics education 97A10 97A50
97-02 Research exposition (monographs, survey articles) pertaining to mathematics education 97A70
97P30 Systems, databases (educational aspects) 97R50
MSC2020DescriptionMSC2010
 
 
© Copyright 2024, American Mathematical Society
Privacy Statement
American Mathematical Society