MSC2010 | Description | MSC2020 |
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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 |
MSC2010 | Description | MSC2020 |
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