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数学主题分类新变化
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数学主题分类新变化
诸平
之前曾经写过《MSC2010分类号的变化、使用与下载》的博文，是介绍2010年修订的数学主题分类（Mathematics Subject Classification，MSC)即MSC2010的变化。美国《数学评论》（Mathematical Reviews）和德国《数学文摘》（Zentralblatt MATH ）编辑部联合已经对2010版分类标准（MSC2010）进行了修改，现将修改后的MSC2020与MSC2010进行对照，仅供参考。其中MSC2010中有30个一级分类进行了修改，涉及到近160个3级分类。实现MSC2010 TO MSC2020或者MSC2020 TO MSC2010的转化，也可以以下附属的参考表。如果看不清楚，请点击下面链接：https://mathscinet.ams.org/mathscinet/msc/msc2010.html直接下载MSC2020电子版文件 （Entire MSC in PDF）
MSC2010 Classification Codes --> MSC2020 Classification Codes
Update Date: 18 February 2020
MSC2010 | Description | MSC2020 |
General and overarching topics; collections | _ | |||
Dimensional analysis |
History and biography [See also the classification number 鈥�03 in the other sections] | _ | |||
Other indigenous cultures (non-European) |
Mathematical logic and foundations | _ | |||
Higher-order logic and type theory |
Combinatorics {For finite fields, see 11Txx} | _ | |||
Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] |
Order, lattices, ordered algebraic structures [See also 18B35] | _ |
General algebraic systems | _ |
Number theory | _ |
Field theory and polynomials | _ | |||
Computational aspects of field theory and polynomials | ||||
Computational aspects of field theory and polynomials | ||||
None of the above, but in this section |
Commutative rings and algebras | _ |
Algebraic geometry | _ | |||
Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] | ||||
Linear and multilinear algebra; matrix theory | _ |
Associative rings and algebras {For the commutative case, see 13-XX} | _ |
Nonassociative rings and algebras | _ |
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} | _ | |||
Categories of topological spaces and continuous mappings [See also 54-XX] | ||||
Double categories, $2$-categories, bicategories and generalizations | ||||
Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] | ||||
Structured objects in a category (group objects, etc.) | ||||
Operads [See also 55P48] | ||||
Abelian categories, Grothendieck categories | _ | |||
Grothendieck categories | ||||
Derived categories, triangulated categories | ||||
Simplicial sets, simplicial objects (in a category) [See also 55U10] | ||||
Homotopical algebra | ||||
Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22] |
_ |
Group theory and generalizations | _ | |||
Computational methods | ||||
Computational methods |
Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX; for abstract harmonic analysis, see 43-XX} | _ |
Real functions [See also 54C30] | _ |
Measure and integration {For analysis on manifolds, see 58-XX} | _ |
Functions of a complex variable | _ |
Potential theory {For probabilistic potential theory, see 60J45} | _ |
Several complex variables and analytic spaces {For infinite-\newline dimensional holomorphy, see also 46G20, 58B12} | _ | |||
Special domains (Reinhardt, Hartogs, circular, tube) |
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} | _ |
Ordinary differential equations | _ | |||
Numerical approximation of solutions |
Partial differential equations | _ | |||
Initial-boundary value problems for pseudodifferential operators |
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] | _ | |||
Relations between ergodic theory and number theory [See also 11Kxx] | ||||
Multidimensional shifts of finite type | ||||
Symmetries and invariants of dynamical systems | ||||
Hyperbolic systems with singularities (billiards, etc.) | ||||
Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics | ||||
Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps | ||||
General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants | ||||
Symplectic and canonical mappings | ||||
Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems | ||||
Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods | ||||
General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws |
Difference and functional equations | _ |
Sequences, series, summability | _ |
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} | _ |
Harmonic analysis on Euclidean spaces | _ |
Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx} | _ |
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} | _ |
Integral equations | _ |
Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} | _ |
Operator theory | _ |
Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] | _ | |||
Other methods, not based on necessary conditions (penalty function, etc.) |
Geometry {For algebraic geometry, see 14-XX; for differential geometry, see 53-XX} | _ |
Convex and discrete geometry | _ |
Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx} | _ | |||
Differential geometry of submanifolds of M枚bius space | ||||
Geometric evolution equations (mean curvature flow, Ricci flow, etc.) | 53E20 53Exx 53Exx 53E40 53E5053E99 53E30 53E50 53E10 53E1053E99 53E20 53E30 53E40 |
General topology {For the topology of manifolds of all dimensions, see 57Nxx} | _ |
Algebraic topology | _ |
Manifolds and cell complexes {For complex manifolds, see\newline 32Qxx} | _ | |||
Two-dimensional complexes | ||||
Knots and links in $S^3$ {For higher dimensions, see 57Q45} | ||||
Invariants of knots and 3-manifolds | ||||
Dehn's lemma, sphere theorem, loop theorem, asphericity | ||||
Characterizations of $E^3$ and $S^3$ (Poincar茅 conjecture) [See also 57N12] | ||||
Topology of $E^2$, $2$-manifolds | ||||
Topology of general $3$-manifolds [See also 57Mxx] | ||||
Topology of $E^3$ and $S^3$ [See also 57M40] | ||||
Topology of $E^n$, $n$-manifolds ($4 \less n \less \infty$) | ||||
Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} |
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} | _ |
Probability theory and stochastic processes {For additional applications, see 05Cxx, 11Kxx, 34-XX, 35-XX, 62-XX, 90-XX, 76-XX, 81-XX, 82-XX, 91-XX, 92-XX, 93-XX, 94-XX} | _ | |||
Jump processes on discrete state spaces |
Statistics | _ | |||
Data analysis | ||||
Graphical methods |
Numerical analysis | _ | |||
Other computational problems in probability | ||||
Computational problems in statistics | ||||
Other numerical matrix algorithms |
Computer science {For papers containing software, source code, etc. in a specific mathematical area, see the classification number -04 in that area} | _ | |||
Models of computation (Turing machines, etc.) [See also 03D10, 81P68] | ||||
Theorem proving (deduction, resolution, etc.) [See also 03B35] |
Mechanics of particles and systems {For relativistic mechanics, see 83A05, 83C10; for statistical mechanics, see 82-XX} | _ |
Mechanics of deformable solids | _ | |||
Local existence of solutions (near a given solution) | ||||
Existence of solutions of equilibrium problems in solid mechanics | ||||
Other numerical methods applied to problems in solid mechanics |
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} | _ | |||
Atmospheric waves [See also 86A10] | ||||
Other numerical methods applied to problems in fluid mechanics |
Optics, electromagnetic theory {For quantum optics, see 81V80} | _ | |||
Other numerical methods applied to problems in optics and electromagnetic theory |
Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15} | _ | |||
Diffusive and convective heat and mass transfer, heat flow | ||||
Other numerical methods applied to problems in thermodynamics and heat transfer |
Quantum theory | _ | |||
Simulation and numerical modeling |
Statistical mechanics, structure of matter | _ | |||
Computational methods | 82M20 82M60 82M15 82M3682Mxx 82M99 82M12 82M1082M30 82M22 82M37 82M31 |
Relativity and gravitational theory | _ |
Astronomy and astrophysics {For celestial mechanics, see 70F15} | _ |
_ | ||||
Global dynamics, earthquake problems |
Operations research, mathematical programming | _ |
Game theory, economics, finance, and other social and behavioral sciences | _ | |||
Games with infinitely many players | ||||
Asset pricing models | ||||
Risk theory, insurance | ||||
Labor market, contracts |
Biology and other natural sciences | _ |
Systems theory; control {For optimal control, see 49-XX} | _ | |||
Mathematical modeling (models of systems, model-matching, etc.) | ||||
Computational methods | ||||
Other computational methods |
Information and communication theory, circuits | _ | |||
Switching theory, application of Boolean algebra; Boolean functions [See also 06E30] |
Mathematics education | _ | |||
Comprehensive works, reference books | ||||
Recreational mathematics, games [See also 00A08] | ||||
Bibliographies [See also 01-00] | ||||
Theses and postdoctoral theses | ||||
Artificial intelligence |
MSC2010 | Description | MSC2020 |
https://blog.sciencenet.cn/blog-212210-1224739.html
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