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再议MSC2010分类号的变化、使用与下载
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再议MSC2010分类号的变化、使用与下载
诸平
2010年7月6日，本人曾经写过“MSC2010分类号的变化、使用与下载”的博文，5年过去了，还是有新人不知道或者不习惯使用其对于数学或者应用数学论文（特别是被国际著名数据库收录的论文）进行分类，这种情况反映出我们的本科生教育、研究生教育中对于文献检索技巧培养，不能不说存在着严重缺陷。一个数学或者与数学相关专业的大学生及其以上学历的受教育者，如果你对于数学界的世界著名数据库——美国《数学评论》（Mathematical Reviews）和德国《数学文摘》（Zentralblatt MATH ）以及其使用的数学主题分类不了解，本身就是一种悲哀！文献检索是人终身学习研究必备的一种技能，本科生应该掌握，研究生更应该熟练应用。由于受博文字数所限，今天对于5年前的博文——“MSC2010分类号的变化、使用与下载”进行补充。
MSC2010是2010年修订的数学主题分类（Mathematics Subject Classification，MSC)，美国《数学评论》（Mathematical Reviews，MR）和德国《数学文摘》（Zentralblatt MATH ）编辑部已经决定从2010年6月开始使用新修订的2010版分类标准，详细情况请看下面的通告，也可以从以下网址直接下载MSC2010的pdf文档（正文114页）。笔者曾经得到MR当时执行总编辑的同意，将MSC2000翻译成中文，有MSC2000中译本的朋友们，可以通过美国数学会网站（http://www.ams.org/mathscinet/msc/msc2010.html），实现MSC2000 TO MSC2010或者MSC2010 TO MSC2000的转化，也可以直接下载MSC2010英文版(Download MSC2010).以下附属的参考表2是MSC2010分类号与MSC2000分类号的转化。本人2012年4月以来的数论文献最新题录（MR2015年10月份数论最新文献题录252条（见附件）），每月一次的统计结果就是利用11-Number Theory,通过MR数据库网络版MathSciNet检索所得。
注意下面的代码都有相关链接，点击可以细读相关内容。
Table 2 MSC2010 Classification Codes->MSC2000 Classification Codes
MSC2010 | Description | MSC2000 |
|---|
| 00-XX | General | _ | ||
| 00A09 | Popularization of mathematics | 00A06 00A08 | ||
| 00A65 | Mathematics and music | 00A06 00A69 | ||
| 00A66 | Mathematics and visual arts, visualization | 00A06 00A08 | ||
| 00A67 | Mathematics and architecture | 00A06 00A08 | ||
| 00B99 | None of the above, but in this section | 00Bxx |
| 01-XX | History and biography [See also the classification number –03 in the other sections] | _ |
| 03-XX | Mathematical logic and foundations | _ | ||
| 03Axx | Philosophical aspects of logic and foundations | 03A05 | ||
| 03A10 | Logic in the philosophy of science | 03A05 | ||
| 03A99 | None of the above, but in this section | 03A05 | ||
| 03B62 | Combined logics | 03B60 68T27 | ||
| 03C48 | Abstract elementary classes and related topics [See also 03C45] | 03C45 | ||
| 03D32 | Algorithmic randomness and dimension [See also 68Q30] | 03D80 68Q30 | ||
| 03D78 | Computation over the reals For constructive aspects, see 03F60 | 03F60 68Q05 | ||
| 03E57 | Generic absoluteness and forcing axioms [See also 03E50] | 03E40 03E50 03E65 | ||
| 03G27 | Abstract algebraic logic | 03G25 |
| 05-XX | Combinatorics For finite fields, see 11Txx | _ | ||
| 05C21 | Flows in graphs | 05C15 05C20 | ||
| 05C31 | Graph polynomials | 05C15 05C50 | ||
| 05C42 | Density (toughness, etc.) | 05C40 | ||
| 05C51 | Graph designs and isomomorphic decomposition [See also 05B30] | 05B30 05B05 | ||
| 05C57 | Games on graphs [See also 91A43, 91A46] | 91A43 05C90 | ||
| 05C63 | Infinite graphs | 05C99 05C25 | ||
| 05C72 | Fractional graph theory, fuzzy graph theory | 05C99 05C15 05C69 05C70 | ||
| 05C76 | Graph operations (line graphs, products, etc.) | 05C62 | ||
| 05C81 | Random walks on graphs | 05C80 | ||
| 05C82 | Small world graphs, complex networks [See also 90Bxx, 91D30] | 05C80 05C90 91D30 | ||
| 05E18 | Group actions on combinatorial structures | 05E20 | ||
| 05E40 | Combinatorial aspects of commutative algebra | 05E15 05E20 05E25 | ||
| 05E45 | Combinatorial aspects of simplicial complexes | 05E25 05C25 05E99 |
| 06-XX | Order, lattices, ordered algebraic structures [See also 18B35] | _ | ||
| 06A75 | Generalizations of ordered sets | 06A06 | ||
| 06B75 | Generalizations of lattices | 06B05 06B99 | ||
| 06D75 | Other generalizations of distributive lattices | 06D05 06D99 | ||
| 06E75 | Generalizations of Boolean algebras | 06E05 06E99 |
| 08-XX | General algebraic systems | _ | ||
| 08C20 | Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30] | 08C05 08C99 |
| 11-XX | Number theory | _ | ||
| 11B30 | Arithmetic combinatorics; higher degree uniformity | 11B13 11B75 11P70 | ||
| 11D07 | The Frobenius problem | 11D04 11D45 | ||
| 11F68 | Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series | 11F66 11F67 | ||
| 11G32 | Dessins d'enfants, Bely? theory | 11G99 14G32 | ||
| 11G42 | Arithmetic mirror symmetry [See also 14J33] | 11G40 14J32 | ||
| 11J87 | Schmidt Subspace Theorem and applications | 11D75 11J25 | ||
| 11M32 | Multiple Dirichlet series and zeta functions and multizeta values | 11M41 | ||
| 11M50 | Relations with random matrices | 11M26 | ||
| 11M55 | Relations with noncommutative geometry | 11R56 58B34 | ||
| 11P84 | Partition identities; identities of Rogers-Ramanujan type | 11P81 11P82 | ||
| 11S82 | Non-Archimedean dynamical systems [See mainly 37Pxx] | 11S99 37Fxx | ||
| 11Zxx | Miscellaneous applications of number theory | 11Z05 | ||
| 11Z99 | None of the above, but in this section | 11Z05 |
| 12-XX | Field theory and polynomials | _ | ||
| 12Yxx | Computational aspects of field theory and polynomials | 12Y05 | ||
| 12Y99 | None of the above, but in this section | 12Y05 |
| 13-XX | Commutative rings and algebras | _ | ||
| 13C60 | Module categories | 13C99 | ||
| 13D09 | Derived categories | 13C99 | ||
| 13F35 | Witt vectors and related rings | 13K05 | ||
| 13F60 | Cluster algebras | 13A99 | ||
| 13Gxx | Integral domains | 13G05 | ||
| 13G99 | None of the above, but in this section | 13G05 | ||
| 13Lxx | Applications of logic to commutative algebra [See also 03Cxx, 03Hxx] | 13L05 | ||
| 13L99 | None of the above, but in this section | 13L05 | ||
| 13P15 | Solving polynomial systems; resultants | 13P99 | ||
| 13P20 | Computational homological algebra [See also 13Dxx] | 13P99 | ||
| 13P25 | Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) | 13P99 |
| 14-XX | Algebraic geometry | _ | ||
| 14D23 | Stacks and moduli problems | 14A20 14D20 | ||
| 14D24 | Geometric Langlands program: algebro-geometric aspects [See also 22E57] | 14L99 | ||
| 14E16 | McKay correspondence | 14B05 | ||
| 14E18 | Arcs and motivic integration | 14B05 | ||
| 14F18 | Multiplier ideals | 14F99 14C20 | ||
| 14G17 | Positive characteristic ground fields | 14G99 | ||
| 14H57 | Dessins d'enfants theory For arithmetic aspects, see 11G32 | 14H55 14G99 14H30 | ||
| 14J33 | Mirror symmetry [See also 11G42, 53D37] | 14J32 | ||
| 14M22 | Rationally connected varieties | 14M99 | ||
| 14M27 | Compactifications; symmetric and spherical varieties | 14M99 | ||
| 14Txx | Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] | 14P99 | ||
| 14T99 | None of the above, but in this section | 14P99 |
| 15-XX | Linear and multilinear algebra; matrix theory | _ | ||
| 15Axx | Basic linear algebra | 15-XX | ||
| 15A16 | Matrix exponential and similar functions of matrices | 15A99 | ||
| 15A80 | Max-plus and related algebras | 15A99 | ||
| 15A83 | Matrix completion problems | 15A99 | ||
| 15A86 | Linear preserver problems | 15A04 | ||
| 15Bxx | Special matrices | 15A57 | ||
| 15B05 | Toeplitz, Cauchy, and related matrices | 15A57 | ||
| 15B10 | Orthogonal matrices | 15A57 | ||
| 15B15 | Fuzzy matrices | 15A57 | ||
| 15B33 | Matrices over special rings (quaternions, finite fields, etc.) | 15A33 | ||
| 15B34 | Boolean and Hadamard matrices | 15A36 | ||
| 15B35 | Sign pattern matrices | 15A99 | ||
| 15B36 | Matrices of integers [See also 11C20] | 15A36 | ||
| 15B48 | Positive matrices and their generalizations; cones of matrices | 15A48 | ||
| 15B51 | Stochastic matrices | 15A51 | ||
| 15B52 | Random matrices | 15A52 | ||
| 15B57 | Hermitian, skew-Hermitian, and related matrices | 15A57 | ||
| 15B99 | None of the above, but in this section | 15A99 |
| 16-XX | Associative rings and algebras For the commutative case, see 13-XX | _ | ||
| 16E35 | Derived categories | 16E99 | ||
| 16Hxx | Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30 | 16H05 | ||
| 16H05 | Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | _ | ||
| 16H10 | Orders in separable algebras | 16H05 | ||
| 16H15 | Commutative orders | 16H05 | ||
| 16H20 | Lattices over orders | 16H05 | ||
| 16H99 | None of the above, but in this section | 16H05 | ||
| 16R60 | Functional identities | 16R99 | ||
| 16S85 | Rings of fractions and localizations [See also 13B30] | 16S90 | ||
| 16Txx | Hopf algebras, quantum groups and related topics | 16W30 16W35 | ||
| 16T05 | Hopf algebras and their applications [See also 16S40, 57T05] | 16W30 | ||
| 16T10 | Bialgebras | 16W30 | ||
| 16T15 | Coalgebras and comodules; corings | 16W30 | ||
| 16T20 | Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] | 16W35 | ||
| 16T25 | Yang-Baxter equations | 16W30 | ||
| 16T30 | Connections with combinatorics | 16W30 | ||
| 16T99 | None of the above, but in this section | 16W30 | ||
| 16Zxx | Computational aspects of associative rings | 16Z05 | ||
| 16Z99 | None of the above, but in this section | 16Z05 |
| 17-XX | Nonassociative rings and algebras | _ | ||
| 17B08 | Coadjoint orbits; nilpotent varieties | 14L30 17B20 | ||
| 17B22 | Root systems | 17B20 |
| 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 for algebraic topology | _ |
| 19-XX | $K$K -theory [See also 16E20, 18F25] | _ | ||
| 19L50 | Twisted $K$K -theory; differential $K$K -theory | 19L64 19L99 | ||
| 19Mxx | Miscellaneous applications of $K$K -theory | 19M05 | ||
| 19M99 | None of the above, but in this section | 19M05 |
| 20-XX | Group theory and generalizations | _ | ||
| 20F11 | Groups of finite Morley rank [See also 03C45, 03C60] | 20E32 | ||
| 20F70 | Algebraic geometry over groups; equations over groups | 20F99 | ||
| 20G07 | Structure theory | 20G99 | ||
| 20G41 | Exceptional groups | 20G99 | ||
| 20G43 | Schur and $q$q -Schur algebras | 16S99 20G99 | ||
| 20G44 | Kac-Moody groups | 20G99 | ||
| 20Lxx | Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05 | 20L05 | ||
| 20L99 | None of the above, but in this section | 20L05 | ||
| 20M13 | Arithmetic theory of monoids | 20M99 | ||
| 20M32 | Algebraic monoids | 20M99 | ||
| 20Pxx | Probabilistic methods in group theory [See also 60Bxx] | 20P05 | ||
| 20P99 | None of the above, but in this section | 20P05 |
| 22-XX | Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX | _ | ||
| 22Cxx | Compact groups | 22C05 | ||
| 22C99 | None of the above, but in this section | 22C05 | ||
| 22E57 | Geometric Langlands program: representation-theoretic aspects [See also 14D24] | 11R39 14D20 22E55 | ||
| 22E66 | Analysis on and representations of infinite-dimensional Lie groups | 22E65 | ||
| 22F99 | None of the above, but in this section | 22Fxx |
| 26-XX | Real functions [See also 54C30] | _ | ||
| 26E70 | Real analysis on time scales or measure chains For dynamic equations on time scales or measure chains see 34N05 | 39A10 |
| 28-XX | Measure and integration For analysis on manifolds, see 58-XX | _ |
| 30-XX | Functions of a complex variable For analysis on manifolds, see 58-XX | _ | ||
| 30Hxx | Spaces and algebras of analytic functions | 30H05 46Exx 46Jxx | ||
| 30H05 | Bounded analytic functions | 30D50 46Exx 46Jxx | ||
| 30H10 | Hardy spaces | 30D55 46E15 46E20 46E22 46E40 46J15 46J20 | ||
| 30H15 | Nevanlinna class and Smirnov class | 30D15 46E99 | ||
| 30H20 | Bergman spaces, Fock spaces | 30D60 46E20 46E22 46E40 | ||
| 30H25 | Besov spaces and $Q_p$Q_p -spaces | 30D60 46E15 46E20 46E22 46E35 | ||
| 30H30 | Bloch spaces | 30D45 46E15 | ||
| 30H35 | BMO-spaces | 30D60 46E15 | ||
| 30H50 | Algebras of analytic functions | 30H05 46J15 46J20 | ||
| 30H80 | Corona theorems | 30H05 46J15 | ||
| 30H99 | None of the above, but in this section | 30D99 | ||
| 30Jxx | Function theory on the disc | 30D50 | ||
| 30J05 | Inner functions | 30D50 | ||
| 30J10 | Blaschke products | 30D50 | ||
| 30J15 | Singular inner functions | 30D50 | ||
| 30J99 | None of the above, but in this section | 30D99 | ||
| 30Kxx | Universal holomorphic functions | 30B99 | ||
| 30K05 | Universal Taylor series | 30B99 30B10 | ||
| 30K10 | Universal Dirichlet series | 30B99 30B50 | ||
| 30K15 | Bounded universal functions | 30B99 | ||
| 30K20 | Compositional universality | 30B99 | ||
| 30K99 | None of the above, but in this section | 30B99 | ||
| 30Lxx | Analysis on metric spaces | 30C65 46E35 | ||
| 30L05 | Geometric embeddings of metric spaces | 30C65 46B20 | ||
| 30L10 | Quasiconformal mappings in metric spaces | 30C65 | ||
| 30L99 | None of the above, but in this section | 30C99 |
| 31-XX | Potential theory For probabilistic potential theory, see 60J45 | _ | ||
| 31Dxx | Axiomatic potential theory | 31D05 | ||
| 31D99 | None of the above, but in this section | 31D05 | ||
| 31Exx | Potential theory on metric spaces | 31Cxx 46E35 | ||
| 31E05 | Potential theory on metric spaces | 31C05 46E35 | ||
| 31E99 | None of the above, but in this section | 31C99 46E35 |
| 32-XX | Several complex variables and analytic spaces For infinite-dimensional holomorphy, see 46G20, 58B12 | _ | ||
| 32Pxx | Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) | 32P05 | ||
| 32P99 | None of the above, but in this section | 32P05 | ||
| 32Q26 | Notions of stability | 32Q15 32Q20 |
| 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 | _ | ||
| 34A07 | Fuzzy differential equations | 34A12 34A60 34G25 | ||
| 34A08 | Fractional differential equations | 34A12 34Bxx 26A33 | ||
| 34A33 | Lattice differential equations | 34A12 34B45 34C15 34A35 37K60 37L60 | ||
| 34A38 | Hybrid systems | 34A12 93C23 | ||
| 34C46 | Multifrequency systems | 34C15 34C29 70K43 | ||
| 34D06 | Synchronization | 34Dxx 34K20 34K05 | ||
| 34E17 | Canard solutions | 34C05 34E15 34C26 | ||
| 34Fxx | Equations and systems with randomness [See also 34K50, 60H10, 93E03] | 34F05 37H10 | ||
| 34F10 | Bifurcation | 34C23 34F05 34K18 37H20 | ||
| 34F15 | Resonance phenomena | 34F05 37J40 70J40 70K28 70K30 37H10 70L05 | ||
| 34F99 | None of the above, but in this section | 34F05 37H10 | ||
| 34Hxx | Control problems [See also 49J15, 49K15, 93C15] | 34H05 | ||
| 34H10 | Chaos control | 34C28 37D45 37N35 | ||
| 34H15 | Stabilization | 34Dxx 93Dxx | ||
| 34H20 | Bifurcation control | 34C23 34K18 | ||
| 34H99 | None of the above, but in this section | 34H05 34C23 | ||
| 34K08 | Spectral theory of functional-differential operators | 34Lxx 47E05 47G20 | ||
| 34K09 | Functional-differential inclusions | 34A60 34G25 34K05 | ||
| 34K21 | Stationary solutions | 34Dxx 34K20 | ||
| 34K27 | Perturbations | 34D10 34E10 | ||
| 34K31 | Lattice functional-differential equations | 34C15 34B45 37K60 37L60 | ||
| 34K32 | Implicit equations | 34A09 34K05 | ||
| 34K33 | Averaging | 34C29 37J40 70K65 | ||
| 34K34 | Hybrid systems | 34A12 93C23 | ||
| 34K36 | Fuzzy functional-differential equations | 34K05 34K06 34A60 34G25 | ||
| 34K37 | Functional-differential equations with fractional derivatives | 34K05 34K06 | ||
| 34K38 | Functional-differential inequalities | 34A40 34K05 | ||
| 34M03 | Linear equations and systems | 34Mxx | ||
| 34M56 | Isomonodromic deformations | 34M55 37J35 | ||
| 34Nxx | Dynamic equations on time scales or measure chains For real analysis on time scales see 26E70 | 39A10 39A11 | ||
| 34N05 | Dynamic equations on time scales or measure chains For real analysis on time scales or measure chains, see 26E70 | 39A10 39A11 | ||
| 34N99 | None of the above, but in this section | 39A10 39A11 |
| 35-XX | Partial differential equations | _ | ||
| 35A01 | Existence problems: global existence, local existence, non-existence | 35A05 | ||
| 35A02 | Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness | 35A05 | ||
| 35A09 | Classical solutions | 35A05 | ||
| 35A16 | Topological and monotonicity methods | 35A25 | ||
| 35A23 | Inequalities involving derivatives and differential and integral operators, inequalities for integrals | 35A25 26D10 | ||
| 35A24 | Methods of ordinary differential equations | 35A25 | ||
| 35B06 | Symmetries, invariants, etc. | 35B05 58J70 | ||
| 35B07 | Axially symmetric solutions | 35B05 | ||
| 35B08 | Entire solutions | 35B05 | ||
| 35B09 | Positive solutions | 35B05 | ||
| 35B36 | Pattern formation | 35B34 | ||
| 35B44 | Blow-up | 35B40 | ||
| 35B51 | Comparison principles | 35B05 | ||
| 35B53 | Liouville theorems, Phragmén-Lindelöf theorems | 35B40 | ||
| 35C06 | Self-similar solutions | 35C05 | ||
| 35C07 | Traveling wave solutions | 35C05 | ||
| 35C08 | Soliton solutions | 35Q51 | ||
| 35C09 | Trigonometric solutions | 35C05 | ||
| 35C11 | Polynomial solutions | 35C05 | ||
| 35D30 | Weak solutions | 35D05 | ||
| 35D35 | Strong solutions | 35D05 | ||
| 35D40 | Viscosity solutions | 35D05 | ||
| 35F16 | Initial-boundary value problems for linear first-order equations | 35F15 | ||
| 35F21 | Hamilton-Jacobi equations | 35F20 | ||
| 35F31 | Initial-boundary value problems for nonlinear first-order equations | 35F30 | ||
| 35F35 | Linear first-order systems | 35F05 | ||
| 35F40 | Initial value problems for linear first-order systems | 35F10 | ||
| 35F45 | Boundary value problems for linear first-order systems | 35F15 | ||
| 35F46 | Initial-boundary value problems for linear first-order systems | 35F15 | ||
| 35F50 | Nonlinear first-order systems | 35F20 | ||
| 35F55 | Initial value problems for nonlinear first-order systems | 35F25 | ||
| 35F60 | Boundary value problems for nonlinear first-order systems | 35F30 | ||
| 35F61 | Initial-boundary value problems for nonlinear first-order systems | 35F30 | ||
| 35G16 | Initial-boundary value problems for linear higher-order equations | 35G05 | ||
| 35G31 | Initial-boundary value problems for nonlinear higher-order equations | 35G30 | ||
| 35G35 | Linear higher-order systems | 35G05 | ||
| 35G40 | Initial value problems for linear higher-order systems | 35G10 | ||
| 35G45 | Boundary value problems for linear higher-order systems | 35G15 | ||
| 35G46 | Initial-boundary value problems for linear higher-order systems | 35G15 | ||
| 35G50 | Nonlinear higher-order systems | 35G20 | ||
| 35G55 | Initial value problems for nonlinear higher-order systems | 35G25 | ||
| 35G60 | Boundary value problems for nonlinear higher-order systems | 35G30 | ||
| 35G61 | Initial-boundary value problems for nonlinear higher-order systems | 35G30 | ||
| 35J08 | Green's functions | 35A08 | ||
| 35J46 | First-order elliptic systems | 35F05 | ||
| 35J47 | Second-order elliptic systems | 35J15 35J45 | ||
| 35J48 | Higher-order elliptic systems | 35J30 35J45 | ||
| 35J56 | Boundary value problems for first-order elliptic systems | 35F15 | ||
| 35J57 | Boundary value problems for second-order elliptic systems | 35J25 | ||
| 35J58 | Boundary value problems for higher-order elliptic systems | 35J40 | ||
| 35J61 | Semilinear elliptic equations | 35J60 | ||
| 35J62 | Quasilinear elliptic equations | 35J60 | ||
| 35J66 | Nonlinear boundary value problems for nonlinear elliptic equations | 35J65 | ||
| 35J75 | Singular elliptic equations | 35J60 | ||
| 35J86 | Linear elliptic unilateral problems and linear elliptic variational inequalities [See also 35R35, 49J40] | 35J85 | ||
| 35J87 | Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40] | 35J85 | ||
| 35J88 | Systems of elliptic variational inequalities [See also 35R35, 49J40] | 35J85 | ||
| 35J91 | Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian | 35J60 | ||
| 35J92 | Quasilinear elliptic equations with $p$p -Laplacian | 35J60 | ||
| 35J93 | Quasilinear elliptic equations with mean curvature operator | 35J60 | ||
| 35J96 | Elliptic Monge-Ampère equations | 35J60 | ||
| 35K08 | Heat kernel | 35K05 | ||
| 35K41 | Higher-order parabolic systems | 35K25 35K40 | ||
| 35K45 | Initial value problems for second-order parabolic systems | 35K15 35K45 | ||
| 35K46 | Initial value problems for higher-order parabolic systems | 35K30 35K45 | ||
| 35K51 | Initial-boundary value problems for second-order parabolic systems | 35K20 35K35 | ||
| 35K52 | Initial-boundary value problems for higher-order parabolic systems | 35K35 35K45 | ||
| 35K58 | Semilinear parabolic equations | 35K55 | ||
| 35K59 | Quasilinear parabolic equations | 35K55 | ||
| 35K61 | Nonlinear initial-boundary value problems for nonlinear parabolic equations | 35K60 | ||
| 35K67 | Singular parabolic equations | 35K55 | ||
| 35K86 | Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40] | 35K85 | ||
| 35K87 | Systems of parabolic variational inequalities [See also 35R35, 49J40] | 35K85 | ||
| 35K91 | Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian | 35K55 | ||
| 35K92 | Quasilinear parabolic equations with $p$p -Laplacian | 35K55 | ||
| 35K93 | Quasilinear parabolic equations with mean curvature operator | 35K55 53C44 | ||
| 35K96 | Parabolic Monge-Ampère equations | 35K55 | ||
| 35L02 | First-order hyperbolic equations | 35L40 | ||
| 35L03 | Initial value problems for first-order hyperbolic equations | 35L45 | ||
| 35L04 | Initial-boundary value problems for first-order hyperbolic equations | 35L50 | ||
| 35L51 | Second-order hyperbolic systems | 35L10 | ||
| 35L52 | Initial value problems for second-order hyperbolic systems | 35L15 | ||
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems | 35L20 | ||
| 35L56 | Initial value problems for higher-order hyperbolic systems | 35L30 | ||
| 35L57 | Initial-boundary value problems for higher-order hyperbolic systems | 35L35 | ||
| 35L71 | Semilinear second-order hyperbolic equations | 35L70 | ||
| 35L72 | Quasilinear second-order hyperbolic equations | 35L70 | ||
| 35L76 | Semilinear higher-order hyperbolic equations | 35L75 | ||
| 35L77 | Quasilinear higher-order hyperbolic equations | 35L75 | ||
| 35L81 | Singular hyperbolic equations | 35L70 | ||
| 35L86 | Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40] | 35L85 | ||
| 35L87 | Unilateral problems and variational inequalities for hyperbolic systems [See also 35R35, 49J40] | 35L85 | ||
| 35M11 | Initial value problems for equations of mixed type | 35M10 | ||
| 35M12 | Boundary value problems for equations of mixed type | 35M10 | ||
| 35M13 | Initial-boundary value problems for equations of mixed type | 35M10 | ||
| 35M30 | Systems of mixed type | 35M10 | ||
| 35M31 | Initial value problems for systems of mixed type | 35M10 | ||
| 35M32 | Boundary value problems for systems of mixed type | 35M10 | ||
| 35M33 | Initial-boundary value problems for systems of mixed type | 35M10 | ||
| 35M85 | Linear unilateral problems and variational inequalities of mixed type [See also 35R35, 49J40] | 35M10 | ||
| 35M86 | Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also 35R35, 49J40] | 35M10 | ||
| 35M87 | Systems of variational inequalities of mixed type [See also 35R35, 49J40] | 35M10 | ||
| 35N20 | Overdetermined initial value problems | 35N05 | ||
| 35N25 | Overdetermined boundary value problems | 35N05 | ||
| 35N30 | Overdetermined initial-boundary value problems | 35N05 | ||
| 35Q20 | Boltzmann equations | 35F20 76P05 82C40 | ||
| 35Q31 | Euler equations [See also 76D05, 76D07, 76N10] | 35Q35 | ||
| 35Q41 | Time-dependent Schrödinger equations, Dirac equations | 35Q40 | ||
| 35Q56 | Ginzburg-Landau equations | 35Q60 | ||
| 35Q61 | Maxwell equations | 35Q60 | ||
| 35Q62 | PDEs in connection with statistics | 35Q80 | ||
| 35Q68 | PDEs in connection with computer science | 35Q80 | ||
| 35Q70 | PDEs in connection with mechanics of particles and systems | 35Q72 | ||
| 35Q74 | PDEs in connection with mechanics of deformable solids | 35Q72 | ||
| 35Q76 | Einstein equations | 35Q75 | ||
| 35Q82 | PDEs in connection with statistical mechanics | 35Q80 | ||
| 35Q83 | Vlasov-like equations | 35F20 | ||
| 35Q84 | Fokker-Planck equations | 35K55 | ||
| 35Q85 | PDEs in connection with astronomy and astrophysics | 35Q80 | ||
| 35Q86 | PDEs in connection with geophysics | 35Q80 | ||
| 35Q90 | PDEs in connection with mathematical programming | 35Q80 | ||
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences | 35Q80 | ||
| 35Q92 | PDEs in connection with biology and other natural sciences | 35Q80 | ||
| 35Q93 | PDEs in connection with control and optimization | 35B37 | ||
| 35Q94 | PDEs in connection with information and communication | 35Q80 | ||
| 35R01 | Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] | 35R99 31C12 58Jxx | ||
| 35R02 | Partial differential equations on graphs and networks (ramified or polygonal spaces) | 35R99 31C20 | ||
| 35R03 | Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc. | 35R99 | ||
| 35R06 | Partial differential equations with measure | 35R05 | ||
| 35R09 | Integro-partial differential equations [See also 45Kxx] | 35R10 | ||
| 35R11 | Fractional partial differential equations | 35R10 26A33 | ||
| 35R13 | Fuzzy partial differential equations | 35R99 | ||
| 35R37 | Moving boundary problems | 35R35 | ||
| 35S11 | Initial-boundary value problems for pseudodifferential operators | 35S15 |
| 37-XX | Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] | _ | ||
| 37Pxx | Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45] | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P05 | Polynomial and rational maps | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P10 | Analytic and meromorphic maps | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P15 | Global ground fields | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P20 | Non-Archimedean local ground fields | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P25 | Finite ground fields | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P30 | Height functions; Green functions; invariant measures [See also 11G50, 14G40] | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P35 | Arithmetic properties of periodic points | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P40 | Non-Archimedean Fatou and Julia sets | 37F50 | ||
| 37P45 | Families and moduli spaces | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P50 | Dynamical systems on Berkovich spaces | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P55 | Arithmetic dynamics on general algebraic varieties | 11S99 37A45 37B10 37B99 37F10 | ||
| 37P99 | None of the above, but in this section | 11S99 37A45 37B10 37B99 37F10 |
| 39-XX | Difference and functional equations | _ | ||
| 39A06 | Linear equations | 39A10 39A11 | ||
| 39A14 | Partial difference equations | 39A10 39A11 39A20 | ||
| 39A21 | Oscillation theory | 39A10 39A11 | ||
| 39A22 | Growth, boundedness, comparison of solutions | 39A10 39A11 | ||
| 39A23 | Periodic solutions | 39A10 39A11 37C25 37E05 | ||
| 39A24 | Almost periodic solutions | 39A10 39A11 | ||
| 39A28 | Bifurcation theory | 39A10 39A11 37E05 37Gxx | ||
| 39A30 | Stability theory | 39A10 39A11 37B25 37C75 | ||
| 39A33 | Complex (chaotic) behavior of solutions | 39A10 39A11 37E05 37D45 | ||
| 39A45 | Equations in the complex domain | 39A10 39A11 | ||
| 39A50 | Stochastic difference equations | 39A10 39A11 37H10 | ||
| 39A60 | Applications | 39Axx |
| 40-XX | Sequences, series, summability | _ | ||
| 40A35 | Ideal and statistical convergence [See also 40G15] | 40G99 | ||
| 40Bxx | Multiple sequences and series | 40B05 | ||
| 40B99 | None of the above, but in this section | 40B05 | ||
| 40Fxx | Absolute and strong summability (should also be assigned at least one other classification number in Section 40) | 40F05 | ||
| 40F99 | None of the above, but in this section | 40F05 | ||
| 40G15 | Summability methods using statistical convergence [See also 40A35] | 40G99 | ||
| 40Hxx | Functional analytic methods in summability | 46A35 46A45 46B15 46B45 | ||
| 40H99 | None of the above, but in this section | 40H05 | ||
| 40Jxx | Summability in abstract structures [See also 43A55, 46A35, 46B15] | 40J05 | ||
| 40J99 | None of the above, but in this section | 40J05 |
| 41-XX | Approximations and expansions For all approximation theory in the complex domain, see~; for numerical approximation, see~65Dxx | _ | ||
| 41Axx | Approximations and expansions For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx | 41-XX |
| 42-XX | Fourier analysis | _ | ||
| 42B37 | Harmonic analysis and PDE [See also 35-XX] | 32D50 35A25 35S30 43A85 |
| 43-XX | Abstract harmonic analysis For other analysis on topological and Lie groups, see 22Exx | _ | ||
| 43Axx | Abstract harmonic analysis For other analysis on topological and Lie groups, see 22Exx | 43-XX |
| 44-XX | Integral transforms, operational calculus For fractional derivatives and integrals, see 26A33. For Fourier transforms, see . For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10 | _ | ||
| 44Axx | 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-XX |
| 45-XX | Integral equations | _ | ||
| 45Axx | Linear integral equations | 45-XX | ||
| 45A99 | None of the above, but in this section | 45A05 | ||
| 45Bxx | Fredholm integral equations | 45B05 | ||
| 45B99 | None of the above, but in this section | 45B05 | ||
| 45Cxx | Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75] | 47A75 47G10 47N20 | ||
| 45C99 | None of the above, but in this section | 45C05 | ||
| 45Dxx | Volterra integral equations [See also 34A12] | 45D05 | ||
| 45D99 | None of the above, but in this section | 45D05 | ||
| 45G99 | None of the above, but in this section | 45G15 | ||
| 45Hxx | Miscellaneous special kernels [See also 44A15] | 45H05 | ||
| 45H99 | None of the above, but in this section | 45H05 | ||
| 45Jxx | Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] | 47G20 | ||
| 45J99 | None of the above, but in this section | 45J05 | ||
| 45Kxx | Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] | 45K05 | ||
| 45K99 | None of the above, but in this section | 45K05 | ||
| 45Lxx | Theoretical approximation of solutions For numerical analysis, see 65Rxx | 45L05 | ||
| 45L99 | None of the above, but in this section | 45L05 | ||
| 45Nxx | Abstract integral equations, integral equations in abstract spaces | 47N20 | ||
| 45N99 | None of the above, but in this section | 45N05 47N20 | ||
| 45Pxx | Integral operators [See also 47B38, 47G10] | 45P05 47G10 | ||
| 45P99 | None of the above, but in this section | 45P05 47G10 | ||
| 45Qxx | Inverse problems | 45Q05 | ||
| 45Q99 | None of the above, but in this section | 45Q05 | ||
| 45Rxx | Random integral equations [See also 60H20] | 45R05 | ||
| 45R99 | None of the above, but in this section | 45R05 |
| 46-XX | Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx | _ | ||
| 46B06 | Asymptotic theory of Banach spaces [See also 52A23] | 46B07 46B20 46B99 | ||
| 46B80 | Nonlinear classification of Banach spaces; nonlinear quotients | 46B03 46B20 46B99 46T99 | ||
| 46B85 | Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] | 46B07 46B20 | ||
| 46L36 | Classification of factors | 46L10 46L35 |
| 47-XX | Operator theory | _ | ||
| 47Exx | Ordinary differential operators [See also 34Bxx, 34Lxx] | 47E05 | ||
| 47E99 | None of the above, but in this section | 47E05 | ||
| 47Fxx | Partial differential operators [See also 35Pxx, 58Jxx] | 47F05 | ||
| 47F99 | None of the above, but in this section | 47F05 | ||
| 47G40 | Potential operators [See also 31-XX] | 47H50 | ||
| 47H08 | Measures of noncompactness and condensing mappings, $K$K -set contractions, etc. | 46A50 46B50 47H09 | ||
| 47H25 | Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35] | 47A35 47H09 47H10 47H20 | ||
| 47J22 | Variational and other types of inclusions [See also 34A60, 49J21, 49K21] | 47J20 49J40 | ||
| 47L22 | Ideals of polynomials and of multilinear mappings | 46G25 47H60 |
| 49-XX | Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] | _ | ||
| 49J21 | Optimal control problems involving relations other than differential equations | 49J22 49J24 | ||
| 49K21 | Problems involving relations other than differential equations | 49K22 49K24 | ||
| 49Rxx | Variational methods for eigenvalues of operators [See also 47A75] | 49R50 | ||
| 49R99 | None of the above, but in this section | 49R50 | ||
| 49Sxx | Variational principles of physics | 49S05 | ||
| 49S99 | None of the above, but in this section | 49S05 |
| 51-XX | Geometry For algebraic geometry, see 14-XX | _ | ||
| 51Cxx | Ring geometry (Hjelmslev, Barbilian, etc.) | 51C05 | ||
| 51C99 | None of the above, but in this section | 51C05 | ||
| 51Gxx | Ordered geometries (ordered incidence structures, etc.) | 51G05 | ||
| 51G99 | None of the above, but in this section | 51G05 | ||
| 51Pxx | Geometry and physics (should also be assigned at least one other classification number from Sections 70–86) | 51P05 | ||
| 51P99 | None of the above, but in this section | 51P05 |
| 52-XX | Convex and discrete geometry | _ | ||
| 52A23 | Asymptotic theory of convex bodies [See also 46B06] | 52A20 52A27 52A40 46B07 46B20 |
| 53-XX | Differential geometry For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx | _ | ||
| 53C08 | Gerbes, differential characters: differential geometric aspects | 53C05 55R65 | ||
| 53D18 | Generalized geometries (à la Hitchin) | 53C26 53D17 | ||
| 53D37 | Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33] | 14J32 52D35 | ||
| 53D42 | Symplectic field theory; contact homology | 53D35 | ||
| 53Zxx | Applications to physics | 53Z05 | ||
| 53Z99 | None of the above, but in this section | 53Z05 |
| 54-XX | General topology For the topology of manifolds of all dimensions, see 57Nxx | _ | ||
| 54Jxx | Nonstandard topology [See also 03H05] | 54J05 | ||
| 54J99 | None of the above, but in this section | 54J05 |
| 55-XX | Algebraic topology | _ | ||
| 55N32 | Orbifold cohomology | 55N35 57R19 | ||
| 55P50 | String topology | 55P35 57R19 |
| 57-XX | Manifolds and cell complexes For complex manifolds, see 32Qxx | _ | ||
| 57R18 | Topology and geometry of orbifolds | 57R19 |
| 58-XX | Global analysis, analysis on manifolds [See also FullScheme49Q15] | _ | ||
| 58J51 | Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity | 37A25 58J50 | ||
| 58Zxx | Applications to physics | 58Z05 | ||
| 58Z99 | None of the above, but in this section | 58Z05 |
| 60-XX | Probability theory and stochastic processes For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX | _ | ||
| 60A86 | Fuzzy probability | 03E72 28E10 60A05 60A10 60F99 | ||
| 60B20 | Random matrices (probabilistic aspects; for algebraic aspects see 15B52) | 15A52 46L53 60B11 82B44 82C44 | ||
| 60Cxx | Combinatorial probability | 60C05 | ||
| 60C99 | None of the above, but in this section | 60C05 | ||
| 60Dxx | Geometric probability and stochastic geometry [See also 52A22, 53C65] | 60D05 | ||
| 60D99 | None of the above, but in this section | 60D05 | ||
| 60G22 | Fractional processes, including fractional Brownian motion | 60G15 60G18 | ||
| 60J28 | Applications of continuous-time Markov processes on discrete state spaces | 60J27 60J20 | ||
| 60J67 | Stochastic (Schramm-)Loewner evolution (SLE) | 60J65 60K35 82B31 82C31 | ||
| 60J68 | Superprocesses | 60J80 60G57 60J55 60J25 |
| 62-XX | Statistics | _ | ||
| 62Axx | Foundational and philosophical topics | 62A01 | ||
| 62A86 | Fuzzy analysis in statistics | 28A99 62A01 94D05 | ||
| 62A99 | None of the above, but in this section | 62A01 | ||
| 62B86 | Fuzziness, sufficiency, and information | 62B05 62B10 62B15 62B99 94D05 | ||
| 62C86 | Decision theory and fuzziness | 62C05 62C99 | ||
| 62Dxx | Sampling theory, sample surveys | 62D05 | ||
| 62D99 | None of the above, but in this section | 62D05 | ||
| 62E86 | Fuzziness in connection with the topics on distributions in this section | 62E15 62E99 | ||
| 62F86 | Parametric inference and fuzziness | 62F03 62F10 62F12 62F15 62F99 | ||
| 62G86 | Nonparametric inference and fuzziness | 62G99 62G05 62G07 62G08 62G09 62G10 62G20 | ||
| 62H86 | Multivariate analysis and fuzziness | 03E72 60E05 62H05 62H20 62H25 62H30 68T10 | ||
| 62J86 | Fuzziness, and linear inference and regression | 03E72 62J02 62J05 62J99 | ||
| 62K86 | Fuzziness and design of experiments | 62K99 | ||
| 62L86 | Fuzziness and sequential methods | 62L99 | ||
| 62M86 | Inference from stochastic processes and fuzziness | 03E72 26E50 62M10 62M30 62M45 62M99 | ||
| 62N86 | Fuzziness, and survival analysis and censored data | 62N01 62N02 62N03 62N99 | ||
| 62Qxx | Statistical tables | 62Q05 | ||
| 62Q99 | None of the above, but in this section | 62Q05 |
| 65-XX | Numerical analysis | _ | ||
| 65Axx | Tables | 65A05 | ||
| 65A99 | None of the above, but in this section | 65A05 | ||
| 65D19 | Computational issues in computer and robotic vision | 65D18 68T45 | ||
| 65Exx | Numerical methods in complex analysis (potential theory, etc.) For numerical methods in conformal mapping, see also 30C30 | 65E05 | ||
| 65E99 | None of the above, but in this section | 65E05 | ||
| 65F08 | Preconditioners for iterative methods | 65F10 | ||
| 65F60 | Matrix exponential and similar matrix functions | 65F30 | ||
| 65H04 | Roots of polynomial equations | 65H05 | ||
| 65J08 | Abstract evolution equations | 65J10 | ||
| 65K15 | Numerical methods for variational inequalities and related problems | 65K10 | ||
| 65L03 | Functional-differential equations | 65L05 | ||
| 65L04 | Stiff equations | 65L05 | ||
| 65L11 | Singularly perturbed problems | 65L10 | ||
| 65M08 | Finite volume methods | 65M06 | ||
| 65M22 | Solution of discretized equations [See also 65Fxx, 65Hxx] | 65M99 | ||
| 65M38 | Boundary element methods | 65M99 | ||
| 65M75 | Probabilistic methods, particle methods, etc. | 65M99 | ||
| 65M80 | Fundamental solutions, Green's function methods, etc. | 65M99 | ||
| 65M85 | Fictitious domain methods | 65M99 | ||
| 65N08 | Finite volume methods | 65N06 | ||
| 65N20 | Ill-posed problems | 65J20 | ||
| 65N75 | Probabilistic methods, particle methods, etc. | 65N99 | ||
| 65N80 | Fundamental solutions, Green's function methods, etc. | 65N99 | ||
| 65N85 | Fictitious domain methods | 65N99 | ||
| 65Qxx | Difference and functional equations, recurrence relations | 65Q05 | ||
| 65Q10 | Difference equations | 65Q05 | ||
| 65Q20 | Functional equations | 65Q05 | ||
| 65Q30 | Recurrence relations | 65Q05 | ||
| 65Q99 | None of the above, but in this section | 65Q05 | ||
| 65Sxx | Graphical methods | 65S05 | ||
| 65S99 | None of the above, but in this section | 65S05 | ||
| 65Y04 | Algorithms for computer arithmetic, etc. [See also 68M07] | 65Y99 | ||
| 65Zxx | Applications to physics | 65Z05 | ||
| 65Z99 | None of the above, but in this section | 65Z05 |
| 68-XX | Computer science For papers involving machine computations and programs in a specific mathematical area, see Section –04 in that area | _ | ||
| 68M11 | Internet topics [See also 68U35] | 68M10 68U35 | ||
| 68Q12 | Quantum algorithms and complexity [See also 68Q05, 81P68] | 68Q05 68Q15 81P68 68Q10 | ||
| 68Q87 | Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40] | 68Q25 68W20 68W40 | ||
| 68T42 | Agent technology | 68T20 68T99 | ||
| 68W27 | Online algorithms | 68Q10 68W40 68W05 | ||
| 68W32 | Algorithms on strings | 68W05 |
| 70-XX | Mechanics of particles and systems For relativistic mechanics, see~; for statistical mechanics, see~82-XX | _ | ||
| 70Axx | Axiomatics, foundations | 70A05 | ||
| 70A99 | None of the above, but in this section | 70A05 | ||
| 70Cxx | Statics | 70C20 | ||
| 70C99 | None of the above, but in this section | 70C20 | ||
| 70Lxx | Random vibrations [See also 74H50] | 70L05 | ||
| 70L99 | None of the above, but in this section | 70L05 | ||
| 70Mxx | Orbital mechanics | 70M20 | ||
| 70M99 | None of the above, but in this section | 70M20 | ||
| 70Pxx | Variable mass, rockets | 70P05 | ||
| 70P99 | None of the above, but in this section | 70P05 | ||
| 70Qxx | Control of mechanical systems [See also 60Gxx, 60Jxx] | 70Q05 | ||
| 70Q99 | None of the above, but in this section | 70Q05 |
| 74-XX | Mechanics of deformable solids | _ | ||
| 74S60 | Stochastic methods | 74G15 74H15 74S30 | ||
| 74S70 | Complex variable methods | 74G05 74G15 74H05 74H15 74S30 |
| 76-XX | Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XX | _ | ||
| 76Gxx | General aerodynamics and subsonic flows | 76G25 | ||
| 76G99 | None of the above, but in this section | 76G25 | ||
| 76Hxx | Transonic flows | 76H05 | ||
| 76H99 | None of the above, but in this section | 76H05 | ||
| 76Jxx | Supersonic flows | 76J20 | ||
| 76J99 | None of the above, but in this section | 76J20 | ||
| 76Kxx | Hypersonic flows | 76K05 | ||
| 76K99 | None of the above, but in this section | 76K05 | ||
| 76Lxx | Shock waves and blast waves [See also 35L67] | 76L05 | ||
| 76L99 | None of the above, but in this section | 76L05 | ||
| 76Pxx | Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] | 76P05 | ||
| 76P99 | None of the above, but in this section | 76P05 | ||
| 76Qxx | Hydro- and aero-acoustics | 76Q05 | ||
| 76Q99 | None of the above, but in this section | 76Q05 | ||
| 76Sxx | Flows in porous media; filtration; seepage | 76S05 | ||
| 76S99 | None of the above, but in this section | 76S05 | ||
| 76Uxx | Rotating fluids | 76U05 | ||
| 76U99 | None of the above, but in this section | 76U05 | ||
| 76Vxx | Reaction effects in flows [See also 80A32] | 76V05 | ||
| 76V99 | None of the above, but in this section | 76V05 | ||
| 76Wxx | Magnetohydrodynamics and electrohydrodynamics | 76W05 | ||
| 76W99 | None of the above, but in this section | 76W05 | ||
| 76Xxx | Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] | 76X05 | ||
| 76X99 | None of the above, but in this section | 76X05 | ||
| 76Yxx | Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] | 76Y05 | ||
| 76Y99 | None of the above, but in this section | 76Y05 |
| 78-XX | Optics, electromagnetic theory For quantum optics, see 81V80 | _ | ||
| 78A37 | Ion traps | 78A55 | ||
| 78A57 | Electrochemistry | 92E10 92E99 | ||
| 78M12 | Finite volume methods, finite integration techniques | 78M25 | ||
| 78M16 | Multipole methods | 78M25 | ||
| 78M22 | Spectral methods | 78M25 | ||
| 78M31 | Monte Carlo methods | 78M25 | ||
| 78M32 | Neural and heuristic methods | 78M25 | ||
| 78M34 | Model reduction | 78M25 78M99 |
| 80-XX | Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15 | _ |
| 81-XX | Quantum theory | _ | ||
| 81P13 | Contextuality | 81P15 | ||
| 81P16 | Quantum state spaces, operational and probabilistic concepts | 81P15 81S25 | ||
| 81P40 | Quantum coherence, entanglement, quantum correlations | 81P15 | ||
| 81P45 | Quantum information, communication, networks [See also 94A15, 94A17] | 81P68 | ||
| 81P50 | Quantum state estimation, approximate cloning | 46L60 46N50 81P15 | ||
| 81P70 | Quantum coding (general) | 81P68 94B60 | ||
| 81P94 | Quantum cryptography [See also 94A60] | 81P68 94A60 | ||
| 81Q12 | Non-selfadjoint operator theory in quantum theory | 47N50 | ||
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. | 34B45 | ||
| 81Q37 | Quantum dots, waveguides, ratchets, etc. | 81Q50 81Q99 | ||
| 81Q65 | Alternative quantum mechanics | 81Q05 81Q99 | ||
| 81Q80 | Special quantum systems, such as solvable systems | 81Q05 81Q10 | ||
| 81Q93 | Quantum control | 81Q99 | ||
| 81S22 | Open systems, reduced dynamics, master equations, decoherence [See also 82C31] | 82C10 | ||
| 81T28 | Thermal quantum field theory [See also 82B30] | 81T99 | ||
| 81T55 | Casimir effect | 81T10 81T99 | ||
| 81U35 | Inelastic and multichannel scattering | 81U10 81U99 | ||
| 81V65 | Quantum dots [See also 82D20] | 81Q99 |
| 82-XX | Statistical mechanics, structure of matter | _ | ||
| 82D77 | Quantum wave guides, quantum wires [See also 78A50] | 81Q99 82B10 82D20 | ||
| 82D80 | Nanostructures and nanoparticles | 74A25 74A60 74A99 |
| 83-XX | Relativity and gravitational theory | _ | ||
| 83Axx | Special relativity | 70H40 83A05 | ||
| 83A99 | None of the above, but in this section | 70H40 83A05 | ||
| 83Bxx | Observational and experimental questions | 83B05 | ||
| 83B99 | None of the above, but in this section | 83B05 | ||
| 83Dxx | Relativistic gravitational theories other than Einstein's, including asymmetric field theories | 83D05 | ||
| 83D99 | None of the above, but in this section | 83D05 | ||
| 83Fxx | Cosmology | 83F05 | ||
| 83F99 | None of the above, but in this section | 83F05 |
| 85-XX | Astronomy and astrophysics For celestial mechanics, see 70F15 | _ | ||
| 85Axx | Astronomy and astrophysics For celestial mechanics, see 70F15 | 85-XX |
| 86-XX | Geophysics [See also 76U05, 76V05] | _ | ||
| 86Axx | Geophysics [See also 76U05, 76V05] | 86-XX |
| 90-XX | Operations research, mathematical programming | _ |
| 91-XX | Game theory, economics, social and behavioral sciences | _ | ||
| 91B15 | Welfare economics | 91B14 91B18 | ||
| 91B25 | Asset pricing models | 91B28 | ||
| 91B51 | Dynamic stochastic general equilibrium theory | 91B50 91B52 91A15 | ||
| 91B55 | Economic dynamics | 91B62 91B64 91A25 | ||
| 91B69 | Heterogeneous agent models | 91B28 91B62 91B64 | ||
| 91B80 | Applications of statistical and quantum mechanics to economics (econophysics) | 91B99 91B82 | ||
| 91Gxx | Mathematical finance | 91B28 | ||
| 91G10 | Portfolio theory | 91B28 | ||
| 91G20 | Derivative securities | 91B28 | ||
| 91G30 | Interest rates (stochastic models) | 91B28 91B70 | ||
| 91G40 | Credit risk | 91B30 91B28 | ||
| 91G50 | Corporate finance | 91B28 | ||
| 91G60 | Numerical methods (including Monte Carlo methods) | 91B28 | ||
| 91G70 | Statistical methods, econometrics | 91B82 91B84 | ||
| 91G80 | Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) | 91B28 | ||
| 91G99 | None of the above, but in this section | 91B28 91B99 |
| 92-XX | Biology and other natural sciences | _ | ||
| 92B25 | Biological rhythms and synchronization | 92C20 92C30 | ||
| 92C42 | Systems biology, networks | 92B05 92B20 | ||
| 92Fxx | Other natural sciences (should also be assigned at least one other classification number in this section) | 92F05 | ||
| 92F99 | None of the above, but in this section | 92F05 |
| 93-XX | Systems theory; control For optimal control, see 49-XX | _ |
| 94-XX | Information and communication, circuits | _ | ||
| 94Dxx | Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10] | 94D05 | ||
| 94D99 | None of the above, but in this section | 94D05 |
| 97-XX | Mathematics education | _ | ||
| 97A10 | Comprehensive works, reference books | 97-99 | ||
| 97A30 | History of mathematics and mathematics education [See also 01-XX] | 01-XX | ||
| 97A50 | Bibliographies [See also 01-00] | 01A70 | ||
| 97A70 | Theses and postdoctoral theses | 97-02 | ||
| 97A99 | None of the above, but in this section | 97-99 | ||
| 97C10 | Comprehensive works | 97-99 | ||
| 97Exx | Foundations of mathematics | 03A05 03Bxx 03Exx | ||
| 97E10 | Comprehensive works | 97-99 | ||
| 97E20 | Philosophy and mathematics | 03A05 | ||
| 97E30 | Logic | 03Bxx | ||
| 97E40 | Language of mathematics | 97-99 | ||
| 97E50 | Reasoning and proving in the mathematics classroom | 97-99 | ||
| 97E60 | Sets, relations, set theory | 03Exx | ||
| 97E99 | None of the above, but in this section | 97-99 | ||
| 97Fxx | Arithmetic, number theory | 11-XX | ||
| 97F10 | Comprehensive works | 97-99 | ||
| 97F20 | Pre-numerical stage, concept of numbers | 97-99 | ||
| 97F30 | Natural numbers | 97-99 | ||
| 97F40 | Integers, rational numbers | 97-99 | ||
| 97F50 | Real numbers, complex numbers | 97-99 | ||
| 97F60 | Number theory | 11Axx | ||
| 97F70 | Measures and units | 97-99 | ||
| 97F80 | Ratio and proportion, percentages | 97-99 | ||
| 97F90 | Real life mathematics, practical arithmetic | 00A69 | ||
| 97F99 | None of the above, but in this section | 97-99 | ||
| 97Gxx | Geometry | 97-99 | ||
| 97G10 | Comprehensive works | 97-99 | ||
| 97G20 | Informal geometry | 97-99 | ||
| 97G30 | Areas and volumes | 97-99 | ||
| 97G40 | Plane and solid geometry | 97-99 | ||
| 97G50 | Transformation geometry | 97-99 | ||
| 97G60 | Plane and spherical trigonometry | 97-99 | ||
| 97G70 | Analytic geometry. Vector algebra | 15-XX | ||
| 97G80 | Descriptive geometry | 97-99 | ||
| 97G99 | None of the above, but in this section | 97-99 | ||
| 97Hxx | Algebra | 15-XX | ||
| 97H10 | Comprehensive works | 97-99 | ||
| 97H20 | Elementary algebra | 97-99 | ||
| 97H30 | Equations and inequalities | 97-99 | ||
| 97H40 | Groups, rings, fields | 20-XX | ||
| 97H50 | Ordered algebraic structures | 97-99 | ||
| 97H60 | Linear algebra | 15-XX | ||
| 97H99 | None of the above, but in this section | 97-99 | ||
| 97Ixx | Analysis | 97-99 | ||
| 97I10 | Comprehensive works | 97-99 | ||
| 97I20 | Mappings and functions | 97-99 | ||
| 97I30 | Sequences and series | 11Bxx 40Axx | ||
| 97I40 | Differential calculus | 26A24 | ||
| 97I50 | Integral calculus | 26B15 | ||
| 97I60 | Functions of several variables | 26Bxx | ||
| 97I70 | Functional equations | 39Bxx | ||
| 97I80 | Complex analysis | 30-XX | ||
| 97I99 | None of the above, but in this section | 97-99 | ||
| 97Kxx | Combinatorics, graph theory, probability theory, statistics | 05-XX 60-XX 62-XX | ||
| 97K10 | Comprehensive works | 97-99 | ||
| 97K20 | Combinatorics | 05-XX | ||
| 97K30 | Graph theory | 05Cxx | ||
| 97K40 | Descriptive statistics | 62-XX | ||
| 97K50 | Probability theory | 60-XX | ||
| 97K60 | Distributions and stochastic processes | 60Exx 60Gxx | ||
| 97K70 | Foundations and methodology of statistics | 62-XX | ||
| 97K80 | Applied statistics | 62Pxx | ||
| 97K99 | None of the above, but in this section | 97-99 | ||
| 97Mxx | Mathematical modeling, applications of mathematics | 93A30 00A69 | ||
| 97M10 | Modeling and interdisciplinarity | 97-99 | ||
| 97M20 | Mathematics in vocational training and career education | 97-99 | ||
| 97M30 | Financial and insurance mathematics | 91Bxx | ||
| 97M40 | Operations research, economics | 91Bxx | ||
| 97M50 | Physics, astronomy, technology, engineering | 70-XX 74-XX 76-XX 78-XX 80-XX 81-XX 83-XX 85-XX 86-XX 90-XX 93-XX | ||
| 97M60 | Biology, chemistry, medicine | 92-XX | ||
| 97M70 | Behavioral and social sciences | 91-XX | ||
| 97M80 | Arts, music, language, architecture | 00A06 00A69 | ||
| 97M99 | None of the above, but in this section | 07-99 | ||
| 97Nxx | Numerical mathematics | 65Nxx | ||
| 97N10 | Comprehensive works | 97-99 | ||
| 97N20 | Rounding, estimation, theory of errors | 97-99 | ||
| 97N30 | Numerical algebra | 97-99 | ||
| 97N40 | Numerical analysis | 65Nxx | ||
| 97N50 | Interpolation and approximation | 65Dxx | ||
| 97N60 | Mathematical programming | 90Cxx | ||
| 97N70 | Discrete mathematics | 05Cxx 68Rxx | ||
| 97N80 | Mathematical software, computer programs | 90Cxx | ||
| 97N99 | None of the above, but in this section | 97-99 | ||
| 97Pxx | Computer science | 68-XX | ||
| 97P10 | Comprehensive works | 97-99 | ||
| 97P20 | Theory of computer science | 68Pxx 68Qxx | ||
| 97P30 | System software | 68Nxx | ||
| 97P40 | Programming languages | 68N15 | ||
| 97P50 | Programming techniques | 68N17 68N18 68N19 | ||
| 97P60 | Hardware | 68Mxx | ||
| 97P70 | Computer science and society | 68-99 | ||
| 97P99 | None of the above, but in this section | 68-99 | ||
| 97Qxx | Computer science education | 68-99 | ||
| 97Q10 | Comprehensive works | 68-99 | ||
| 97Q20 | Affective aspects in teaching computer science | 68-99 | ||
| 97Q30 | Cognitive processes | 68-99 | ||
| 97Q40 | Sociological aspects | 68-99 | ||
| 97Q50 | Objectives | 68-99 | ||
| 97Q60 | Teaching methods and classroom techniques | 68-99 | ||
| 97Q70 | Student assessment | 68-99 | ||
| 97Q80 | Teaching units | 68-99 | ||
| 97Q99 | None of the above, but in this section | 68-99 | ||
| 97Rxx | Computer science applications | 68Uxx | ||
| 97R10 | Comprehensive works, collections of programs | 97-99 | ||
| 97R20 | Applications in mathematics | 68U99 | ||
| 97R30 | Applications in sciences | 68U99 | ||
| 97R40 | Artificial intelligence | 68Txx | ||
| 97R50 | Data bases, information systems | 68U35 | ||
| 97R60 | Computer graphics | 68U05 | ||
| 97R70 | User programs, administrative applications | 97-99 | ||
| 97R80 | Recreational computing | 97-99 | ||
| 97R99 | None of the above, but in this section | 97-99 |
| MSC2010 | Description | MSC2000 |
|---|
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