Mathematics Subject Classification 1970 – 2010 compiled by Gabriele D¨orflinger Heidelberg, November 2013 Contents General 5 00 General . 5 History and foundations 5 01 History and biography . 5 02 Logic and foundations .................................... 6 03 Mathematical logic and foundations . 8 04 Set theory ........................................... 10 05 Combinatorics . 11 Algebra 12 06 Order, lattices, ordered algebraic structures . 12 08 General algebraic systems . 14 10 Number theory ........................................ 14 11 Number theory . 18 12 Field theory and polynomials . 24 13 Commutative rings and algebras . 26 14 Algebraic geometry . 28 15 Linear and multilinear algebra; matrix theory . 32 16 Associative rings and algebras . 33 17 Nonassociative rings and algebras . 37 18 Category theory; homological algebra . 39 19 K-theory . 41 20 Group theory and generalizations . 42 22 Topological groups, Lie groups . 46 2 Analysis 47 26 Real functions . 47 28 Measure and integration . 49 30 Functions of a complex variable . 51 31 Potential theory . 54 32 Several complex variables and analytic spaces . 55 33 Special functions . 59 34 Ordinary differential equations . 61 35 Partial differential equations . 65 37 Dynamical systems and ergodic theory . 71 39 Difference and functional equations . 74 40 Sequences, series, summability . 76 41 Approximations and expansions . 77 42 Fourier analysis . 77 43 Abstract harmonic analysis . 79 44 Integral transforms, operational calculus . 80 45 Integral equations . 80 46 Functional analysis . 82 47 Operator theory . 86 49 Calculus of variations and optimal control; optimization . 90 Geometry 95 50 Geometry ........................................... 95 51 Geometry . 96 52 Convex and discrete geometry . 98 53 Differential geometry . 99 54 General topology . 101 55 Algebraic topology . 103 57 Manifolds and cell complexes . 107 58 Global analysis, analysis on manifolds . 111 Probability and statistics 115 60 Probability theory and stochastic processes . 115 62 Statistics . 117 Numerical analysis and computer science 120 65 Numerical analysis . 120 68 Computer science . 123 3 Applications 127 70 Mechanics of particles and systems . 127 73 Mechanics of solids ...................................... 130 74 Mechanics of deformable solids . 134 76 Fluid mechanics . 136 78 Optics, electromagnetic theory . 139 80 Classical thermodynamics, heat transfer . 140 81 Quantum theory . 141 82 Statistical mechanics, structure of matter . 145 83 Relativity and gravitational theory . 147 85 Astronomy and astrophysics . 148 86 Geophysics . 148 90 Operations research, mathematical programming . 148 91 Game theory, economics, social and behavioral sciences . 151 92 Biology and other natural sciences . 152 93 Systems theory; control . 154 94 Information and communication, circuits . 156 Mathematical education 157 97 Mathematics education . 157 Education — Version 1970 160 4 00-XX General 00Bxx Conference proceedings and collec- tions of papers 00B05 Collections of abstracts of lectures 00-01 Instructional exposition (textbooks, tu- 00B10 Collections of articles of general interest torial papers, etc.) 00B15 Collections of articles of miscellaneous 00-02 Research exposition (monographs, sur- specific content vey articles) 00B20 Proceedings of conferences of general in- terest 00B25 Proceedings of conferences of miscella- neous specific interest 00Axx General and miscellaneous spe- 00B30 Festschriften cific topics 00B50 Volumes of selected translations 00A05 General mathematics 00B55 Miscellaneous volumes of translations 00A06 Mathematics for nonmathematicians 00B60 Collections of reprinted articles [See also (engineering, social sciences, etc.) 01A75] 00A07 Problem books 00B99 None of the above, but in this section 00A08 Recreational mathematics [See also 97A20] 00A09 Popularization of mathematics 00A10 (1980) Collections of papers; proceedings 01-XX History and biography [See also of conferences of general interest trans- the classification number -03 in the lation volumes, etc. other sections] → now 00Bxx 00A15 Bibliographies 00A17 External book reviews 01-00 General reference works (handbooks, 00A20 Dictionaries and other general reference dictionaries, bibliographies, etc.) works 01-01 Instructional exposition (textbooks, tu- 00A22 Formularies torial papers, etc.) 00A25 (1980) Methodology and philosophy of 01-02 Research exposition (monographs, sur- mathematics vey articles) → now 00A30, 00A35 01-06 Proceedings, conferences, collections, 00A30 Philosophy of mathematics [See also etc. 03A05] 01-08 Computational methods 00A35 Methodology of mathematics, didactics [See also 97Cxx, 97Dxx] 00A65 Mathematics and music 00A66 Mathematics and visual arts, visualiza- 01Axx History of mathematics and math- tion ematicians 00A67 Mathematics and architecture 01A05 General histories, source books 00A69 General applied mathematics {For 01A07 Ethnomathematics, general physics, see 00A79 and Sections 70 01A10 Paleolithic, Neolithic through 86} 01A12 Indigenous cultures of the Americas 00A71 Theory of mathematical modeling 01A13 Other indigenous cultures (non- 00A72 General methods of simulation European) 00A73 Dimensional analysis 01A15 Indigenous European cultures (pre- 00A79 Physics (use more specific entries from Greek, etc.) Sections 70 through 86 when possible) 01A16 Egyptian 00A89 (1980) Physics 01A17 Babylonian → now 00A79 01A20 Greek, Roman 00A99 Miscellaneous topics 01A25 China 5 01A25 (1970) Far East 02Bxx (1970) Classical logical systems → now 01A25, 01A27, 01A29 → now 03Bxx 01A27 Japan 02B05 (1970) Propositional calculus 01A29 Southeast Asia → now 03B05 01A30 Islam (Medieval) 02B10 (1970) Predicate calculus 01A32 India → now 03B10 01A35 Medieval 02B15 (1970) Higher-order predicate calculus 01A40 15th and 16th centuries, Renaissance → now 03B15 01A45 17th century 02B20 (1970) Unusual qualifiers 01A50 18th century → now 03C80 01A55 19th century 02B25 (1970) Infinitely long sentences 01A60 20th century → now ..... 01A61 Twenty-first century 02B99 (1970) None of the above, but in this sec- 01A65 Contemporary tion 01A67 Future prospectives → now 03B99 01A70 Biographies, obituaries, personalia, bib- liographies 01A72 Schools of mathematics 02Cxx (1970) Nonclassical formal sys- 01A73 Universities tems 01A74 Other institutions and academies → now ..... 01A75 Collected or selected works; reprint- 02C05 (1970) Many-valued logic ings or translations of classics [See also → now 03B50 00B60] 02C10 (1970) Modal logic, etc. 01A80 Sociology (and profession) of mathemat- → now 03B45 ics 02C15 (1970) Formalizations of intuitionism, 01A85 Historiography etc. 01A90 Bibliographic studies → now ..... 01A99 Miscellaneous topics 02C20 (1970) Combinatory logic → now 03B40 02C99 (1970) None of the above, but in this sec- 02-XX Logic and foundations tion → now ..... This section has been deleted. [See now 03-XX] 02Dxx (1970) Proof theory 02-01 (1970) Elementary exposition → now 03Fxx → now 03-01 02D05 (1970) Proof theoretic ordinals 02-02 (1970) Advanced exposition → now 03F15 → now 03-02 02D99 (1970) Other proof theory 02-03 (1970) Historical → now ..... → now 03-03 02-04 (1970) Explicit machine computation and programs 02Exx (1970) Constructive mathematics → now 04-01 → now 03Fxx 02E05 (1970) Intuitionistic mathematics → now 03F55 02A05 (1970) Philosophical and critical 02E10 (1970) Algorithms → now 03A05 → now ..... 02E15 (1970) Computable functions → now ..... 6 02E99 (1970) None of the above, but in this sec- 02G20 (1970) Completeness, categoricity, etc. tion → now ..... → now ..... 02G99 (1970) None of the above, but in this sec- tion → now ..... 02Fxx (1970) Recursion theory → now 03Dxx 02F05 (1970) Thue and Post systems, etc. 02Hxx (1970) Model theory → now 03D03 → now 03Cxx 02F10 (1970) Automata 02H05 (1970) Models for theories in classical → now 03D05 predicate calculus 02F15 (1970) Turing machines → now ..... → now 03D10 02H10 (1970) Models for other theories 02F20 (1970) Classification of recursive func- → now ..... tions 02H13 (1970) Model construction → now 03D20 → now ..... 02F25 (1970) Recursively enumerable sets 02H15 (1970) Applications in algebra, number → now 03D25 theory, etc. 02F27 (1970) Recursion theory on ordinals and → now 03C98 sets and other abstract structures 02H20 (1970) Nonstandard models → now 03D60 → now 03Hxx 02F29 (1970) Recursion theory at higher type 02H25 (1970) Applications of nonstandard → now 03D65 models 02F30 (1970) Degrees of unsolvability → now 03H05, 03H10 → now ..... 02H99 (1970) None of the above, but in this sec- 02F35 (1970) Hierarchies tion → now 03D55 → now 03C99, 03H99 02F50 (1970) Recursive equivalence types → now 03D40 02F43 (1970) Formal systems for computability → now ..... 02Jxx (1970) Algebraic logic 02F45 (1970) Combinatorical functions → now 03Gxx → now ..... 02J05 (1970) Boolean algebras, lattices, topolo- 02F47 (1970) Word problems gies → now 03D40 → now 03G05 02F50 (1970) Applications 02J10 (1970) Algebra of relations → now 03D80 → now 03G15 02F99 (1970) None of the above, but in this sec- 02J15 (1970) Cylindric and polyadic algebras tion → now 03G15 → now 03D99 02J99 (1970) None of the above, but in this sec- tion → now 03G99 02Gxx (1970) Methodology of deductive systems → now ..... 02Kxx (1970) Set theory 02G05 (1970) Decidability and undecidability → now 03Exx → now ..... 02K05 (1970) Consistency and independence 02G10 (1970) Axiomatizability results → now ..... → now 03E35 02G15 (1970) Finite axiomatizability 02K10 (1970) Nonclassical set theories → now ..... → now 03E70