MSC2010 Classification Codes --> MSC2020 Classification CodesUpdate Date: 18 February 2020
MSC2010DescriptionMSC2020
00-XX General and overarching topics; collections _
00A73 Dimensional analysis 00A79
01-XX History and biography [See also the classification number –03 in the other sections] _
01A13 Other indigenous cultures (non-European) 01A11
03-XX Mathematical logic and foundations _
03B15 Higher-order logic and type theory 03B38 03C66 03B16
05-XX Combinatorics {For finite fields, see 11Txx} _
05E15 Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 05E16 05E14 05E16 05E14
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 _
12Yxx Computational aspects of field theory and polynomials 12-08
12Y05 Computational aspects of field theory and polynomials 12-08
12Y99 None of the above, but in this section 12-08
13-XX Commutative rings and algebras _
14-XX Algebraic geometry _
14F05 Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14F06 14F08 14A30 14F06 14A30 14F08
14T05 Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 14T10 14T25 14T20 14T15 14T90
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} _
18B30 Categories of topological spaces and continuous mappings [See also 54-XX] 18F60
18D05 Double categories, $2$-categories, bicategories and generalizations 18N10
18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 18M05 18M15
18D35 Structured objects in a category (group objects, etc.) 18C40
18D50 Operads [See also 55P48] 18M60
18E10 Abelian categories, Grothendieck categories _
18E15 Grothendieck categories 18E10
18E30 Derived categories, triangulated categories 18G80
18G30 Simplicial sets, simplicial objects (in a category) [See also 55U10] 18N50
18G55 Homotopical algebra 18N40
18G60 Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22] 18G90
19-XX $K$-theory [See also 16E20, 18F25] _
20-XX Group theory and generalizations _
20B40 Computational methods 20-08
20C40 Computational methods 20-08
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} _
32A07 Special domains (Reinhardt, Hartogs, circular, tube) 32Q02
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 _
34K28 Numerical approximation of solutions 65L03
35-XX Partial differential equations _
35S11 Initial-boundary value problems for pseudodifferential operators 35S16
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] _
37A45 Relations between ergodic theory and number theory [See also 11Kxx] 37A46 37A44
37B50 Multidimensional shifts of finite type 37B51 37B52
37C80 Symmetries and invariants of dynamical systems 37C79 37C81
37D50 Hyperbolic systems with singularities (billiards, etc.) 37C83
37F30 Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics 37F34 37F31 37F32
37F45 Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps 37F46 37F44
37J05 General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants 37J06 37J39
37J10 Symplectic and canonical mappings 37J11 37J12
37J45 Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems 37J46 37J51
37J50 Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods 37J51 37J46
37K05 General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws 37K06
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] _
49M30 Other methods, not based on necessary conditions (penalty function, etc.) 49M99 49M99
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} _
53A30 Differential geometry of submanifolds of Möbius space 53C18 53A31
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 53E20 53Exx 53Exx 53E40 53E50 53E99 53E30 53E50 53E10 53E10 53E99 53E20 53E30 53E40
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} _
57M20 Two-dimensional complexes 57K20
57M25 Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57K10
57M27 Invariants of knots and 3-manifolds 57K31 57K16 57K18 57K14
57M35 Dehn's lemma, sphere theorem, loop theorem, asphericity 57K30
57M40 Characterizations of $E^3$ and $S^3$ (Poincaré conjecture) [See also 57N12] 57K30
57N05 Topology of $E^2$, $2$-manifolds 57K20
57N10 Topology of general $3$-manifolds [See also 57Mxx] 57K35 57K33 57K30 57K31 57K32
57N12 Topology of $E^3$ and $S^3$ [See also 57M40] 57K30
57N13 Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx] 57K40
57N15 Topology of $E^n$, $n$-manifolds ($4 \less n \less \infty$) 57Nxx 57K50 57Nxx 57K50
57Q45 Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} 57K45
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} _
60J75 Jump processes on discrete state spaces 60J74 60J76
62-XX Statistics _
62-07 Data analysis 62R07 62T09 62D20 62D10
62-09 Graphical methods 62A09
65-XX Numerical analysis _
65C50 Other computational problems in probability 60-08
65C60 Computational problems in statistics 62-08
65F30 Other numerical matrix algorithms 65F99
68-XX Computer science {For papers containing software, source code, etc. in a specific mathematical area, see the classification number –04 in that area} _
68Q05 Models of computation (Turing machines, etc.) [See also 03D10, 81P68] 68Q06 68Q04 68Q04 68Q07 68Q06 68Q09 68Q09 68Q07
68T15 Theorem proving (deduction, resolution, etc.) [See also 03B35] 68V15
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 _
74G20 Local existence of solutions (near a given solution) 74G22
74G25 Existence of solutions of equilibrium problems in solid mechanics 74G22
74S30 Other numerical methods applied to problems in solid mechanics 74S99
76-XX Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} _
76B60 Atmospheric waves [See also 86A10] 86A10
76B65 Rossby waves [See also 86A05, 86A10] 76U65
76M25 Other numerical methods applied to problems in fluid mechanics 76M99
78-XX Optics, electromagnetic theory {For quantum optics, see 81V80} _
78M25 Other numerical methods applied to problems in optics and electromagnetic theory 78M99
80-XX Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15} _
80A20 Diffusive and convective heat and mass transfer, heat flow 80A21 80A19
80M25 Other numerical methods applied to problems in thermodynamics and heat transfer 80M99
81-XX Quantum theory _
81T80 Simulation and numerical modeling 81-10
82-XX Statistical mechanics, structure of matter _
82-08 Computational methods 82M20 82M60 82M15 82M36 82Mxx 82M99 82M12 82M10 82M30 82M22 82M37 82M31
83-XX Relativity and gravitational theory _
85-XX Astronomy and astrophysics {For celestial mechanics, see 70F15} _
86-XX Geophysics [See also 76U05, 76V05] _
86A17 Global dynamics, earthquake problems 86A15
90-XX Operations research, mathematical programming _
91-XX Game theory, economics, finance, and other social and behavioral sciences _
91A13 Games with infinitely many players 91A07
91B25 Asset pricing models 91G30
91B30 Risk theory, insurance 91G05 91B05
91B40 Labor market, contracts 91B41 91B39
92-XX Biology and other natural sciences _
93-XX Systems theory; control {For optimal control, see 49-XX} _
93A30 Mathematical modeling (models of systems, model-matching, etc.) 93-10
93B40 Computational methods 93-08
93E25 Other computational methods 93-08
94-XX Information and communication theory, circuits _
94C10 Switching theory, application of Boolean algebra; Boolean functions [See also 06E30] 94D10 94C11
97-XX Mathematics education _
97A10 Comprehensive works, reference books 97-00
97A20 Recreational mathematics, games [See also 00A08] 00A08 00A08
97A50 Bibliographies [See also 01-00] 97-00
97A70 Theses and postdoctoral theses 97-02
97R40 Artificial intelligence 97P80
MSC2010DescriptionMSC2020
 
 
American Mathematical Society