La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

Question : CC = Book
00-XX General

• 00-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 00A07 Problem books
• 00A17 External book reviews [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 00A99

01-XX History and biography

• 01-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 01-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 01A05 General histories, source books

03-XX Mathematical logic and foundations

• 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 03-01 Instructional exposition (textbooks, tutorial papers, etc.)

05-XX Combinatorics [For finite fields, see 11Txx]

• 05-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 05-01 Instructional exposition (textbooks, tutorial papers, etc.)

06-XX Order, lattices, ordered algebraic structures [See also 18B35]

• 06-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 06-01 Instructional exposition (textbooks, tutorial papers, etc.)

08-XX General algebraic systems

• 08-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 08-01 Instructional exposition (textbooks, tutorial papers, etc.)

11-XX Number theory

• 11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 11-01 Instructional exposition (textbooks, tutorial papers, etc.)

12-XX Field theory and polynomials

• 12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 12-01 Instructional exposition (textbooks, tutorial papers, etc.)

13-XX Commutative rings and algebras

• 13-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 13-01 Instructional exposition (textbooks, tutorial papers, etc.)

14-XX Algebraic geometry

• 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 14-01 Instructional exposition (textbooks, tutorial papers, etc.)

15-XX Linear and multilinear algebra; matrix theory

• 15-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 15-01 Instructional exposition (textbooks, tutorial papers, etc.)

16-XX Associative rings and algebras [For the commutative case, see 13-XX]

• 16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 16-01 Instructional exposition (textbooks, tutorial papers, etc.)

17-XX Nonassociative rings and algebras

• 17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 17-01 Instructional exposition (textbooks, tutorial papers, etc.)

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 55Nxx and 55Uxx for algebraic topology]

• 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 18-01 Instructional exposition (textbooks, tutorial papers, etc.)

19-XX $K$-theory [See also 16E20, 18F25]

• 19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 19-01 Instructional exposition (textbooks, tutorial papers, etc.)

20-XX Group theory and generalizations

• 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 20-01 Instructional exposition (textbooks, tutorial papers, etc.)

22-XX Topological groups, Lie groups [For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX]

• 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 22-01 Instructional exposition (textbooks, tutorial papers, etc.)

26-XX Real functions [See also 54C30]

• 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 26-01 Instructional exposition (textbooks, tutorial papers, etc.)

28-XX Measure and integration [For analysis on manifolds, see 58-XX]

• 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 28-01 Instructional exposition (textbooks, tutorial papers, etc.)

30-XX Functions of a complex variable [For analysis on manifolds, see 58-XX]

• 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 30-01 Instructional exposition (textbooks, tutorial papers, etc.)

31-XX Potential theory [For probabilistic potential theory, see 60J45]

• 31-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 31-01 Instructional exposition (textbooks, tutorial papers, etc.)

32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]

• 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 32-01 Instructional exposition (textbooks, tutorial papers, etc.)

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]

• 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 33-01 Instructional exposition (textbooks, tutorial papers, etc.)

34-XX Ordinary differential equations

• 34-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 34-01 Instructional exposition (textbooks, tutorial papers, etc.)

35-XX Partial differential equations

• 35-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 35-01 Instructional exposition (textbooks, tutorial papers, etc.)

37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]

• 37-00 General reference works (handbooks, dictionaries, bibliographies, etc.) [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 28-00, 34-00, 39-00, 54H20, 58-00
• 37-01 Instructional exposition (textbooks, tutorial papers, etc.) [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 28-01, 34-01, 39-01, 58-01

39-XX Difference and functional equations

• 39-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 39-01 Instructional expositions (textbooks, tutorial papers, etc.)

40-XX Sequences, series, summability

• 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 40-01 Instructional exposition (textbooks, tutorial papers, etc.)

41-XX Approximations and expansions [For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx]

• 41-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 41-01 Instructional exposition (textbooks, tutorial papers, etc.)

42-XX Fourier analysis

• 42-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 42-01 Instructional exposition (textbooks, tutorial papers, etc.)

43-XX Abstract harmonic analysis [For other analysis on topological and Lie groups, see 22Exx]

• 43-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 43-01 Instructional exposition (textbooks, tutorial papers, etc.)

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]

• 44-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 44-01 Instructional exposition (textbooks, tutorial papers, etc.)

45-XX Integral equations

• 45-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 45-01 Instructional expositions (textbooks, tutorial papers, etc.)

46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]

• 46-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 46-01 Instructional exposition (textbooks, tutorial papers, etc.)

47-XX Operator theory

• 47-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 47-01 Instructional exposition (textbooks, tutorial papers, etc.)

49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]

• 49-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 49-01 Instructional exposition (textbooks, tutorial papers, etc.)

51-XX Geometry [For algebraic geometry, see 14-XX]

• 51-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 51-01 Instructional exposition (textbooks, tutorial papers, etc.)

52-XX Convex and discrete geometry

• 52-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 52-01 Instructional exposition (textbooks, tutorial papers, etc.)

53-XX Differential geometry [For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx]

• 53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 53-01 Instructional exposition (textbooks, tutorial papers, etc.)

54-XX General topology [For the topology of manifolds of all dimensions, see 57Nxx]

• 54-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 54-01 Instructional exposition (textbooks, tutorial papers, etc.)

55-XX Algebraic topology

• 55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 55-01 Instructional exposition (textbooks, tutorial papers, etc.)

57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]

• 57-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 57-01 Instructional exposition (textbooks, tutorial papers, etc.)

58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]

• 58-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 58-01 Instructional exposition (textbooks, tutorial papers, etc.)

60-XX Probability theory and stochastic processes [For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX]

• 60-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 60-01 Instructional exposition (textbooks, tutorial papers, etc.)

62-XX Statistics

• 62-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 62-01 Instructional exposition (textbooks, tutorial papers, etc.)

65-XX Numerical analysis

• 65-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 65-01 Instructional exposition (textbooks, tutorial papers, etc.)

68-XX Computer science [For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area]

• 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 68-01 Instructional exposition (textbooks, tutorial papers, etc.)

70-XX Mechanics of particles and systems [For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX]

• 70-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 70-01 Instructional exposition (textbooks, tutorial papers, etc.)

74-XX Mechanics of deformable solids

• 74-00 General reference works (handbooks, dictionaries, bibliographies, etc.) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 73-00
• 74-01 Instructional expositions (textbooks, tutorial papers, etc.) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 73-01

76-XX Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX]

• 76-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 76-01 Instructional exposition (textbooks, tutorial papers, etc.)

78-XX Optics, electromagnetic theory [For quantum optics, see 81V80]

• 78-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 78-01 Instructional exposition (textbooks, tutorial papers, etc.)

80-XX Classical thermodynamics, heat transfer [For thermodynamics of solids, see 74A15]

• 80-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 80-01 Instructional exposition (textbooks, tutorial papers, etc.)

81-XX Quantum theory

• 81-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 81-01 Instructional exposition (textbooks, tutorial papers, etc.)

82-XX Statistical mechanics, structure of matter

• 82-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 82-01 Instructional exposition (textbooks, tutorial papers, etc.)

83-XX Relativity and gravitational theory

• 83-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 83-01 Instructional exposition (textbooks, tutorial papers, etc.)

85-XX Astronomy and astrophysics [For celestial mechanics, see 70F15]

• 85-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 85-01 Instructional exposition (textbooks, tutorial papers, etc.)

86-XX Geophysics [See also 76U05, 76V05]

• 86-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 86-01 Instructional exposition (textbooks, tutorial papers, etc.)

90-XX Operations research, mathematical programming

• 90-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 90-01 Instructional exposition (textbooks, tutorial papers, etc.)

91-XX Game theory, economics, social and behavioral sciences

• 91-00 General reference works (handbooks, dictionaries, bibliographies, etc.) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 90-00
• 91-01 Instructional exposition (textbooks, tutorial papers, etc.) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 90-01

92-XX Biology and other natural sciences

• 92-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 92-01 Instructional exposition (textbooks, tutorial papers, etc.)

93-XX Systems theory; control [For optimal control, see 49-XX]

• 93-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 93-01 Instructional exposition (textbooks, tutorial papers, etc.)

94-XX Information and communication, circuits

• 94-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 94-01 Instructional exposition (textbooks, tutorial papers, etc.)

97-XX Mathematics education

• 97-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 97-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 97U20 Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom
• 97U40 Problem books; student competitions, examination questions

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