數學科目分類各本之異

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'''數學科目分類'''者,乃[[亞美利堅數學協會]]所定之數位分類法。
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(from http://www.ams.org/msc/)
 
眾數學雜誌皆以之為據,令研究報告及釋文著者為其文附分類號。夫分類號之列,乃為二大數據庫所需也,即[[數學評論]]及[[數學文摘]]。
以下為 2000年以來[[亞美利堅數學協會]]所編之[[數學回顧]](''Mathematical Reviews'')
與歐洲眾數學協會所編之[[中央數學報]] (''Zentralblatt MATH'')
通用之分類系統:
 
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2000 數學科目分類
*00-xx General
*01-xx History and biography [See also the classification number -03 in the other sections]
*03-xx Mathematical logic and foundations
*04-xx This section has been deleted {For set theory see 03Exx}
*05-xx Combinatorics {For finite fields, see 11Txx}
*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
*13-xx Commutative rings and algebras
*14-xx Algebraic geometry
*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 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology}
*19-xx $K$-theory [See also 16E20, 18F25]
*20-xx Group theory and generalizations
*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 {For analysis on manifolds, see 58-xx}
*31-xx Potential theory {For probabilistic potential theory, see 60J45}
*32-xx Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12}
*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
*35-xx Partial differential equations
*37-xx Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-xx]
*39-xx Difference and functional equations
*40-xx Sequences, series, summability
*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}
*42-xx Fourier analysis
*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 57N20, 58Bxx}
47-xx Operator theory
49-xx Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-xx]
51-xx Geometry {For algebraic geometry, see 14-xx}
52-xx Convex and discrete geometry
53-xx Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}
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 32Qxx}
58-xx Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-xx, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}
60-xx Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-xx, 90-xx, 91-xx,92-xx, 93-xx, 94-xx]
62-xx Statistics
65-xx Numerical analysis
68-xx Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area}
70-xx Mechanics of particles and systems {For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-xx}
73-xx This section has been deleted {For mechanics of solids, see 74-xx}
74-xx Mechanics of deformable solids
76-xx Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-xx}
78-xx Optics, electromagnetic theory {For quantum optics, see 81V80}
80-xx Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15}
81-xx Quantum theory
82-xx Statistical mechanics, structure of matter
83-xx Relativity and gravitational theory
85-xx Astronomy and astrophysics {For celestial mechanics, see 70F15}
86-xx Geophysics [See also 76U05, 76V05]
90-xx Operations research, mathematical programming
91-xx Game theory, economics, social and behavioral sciences
92-xx Biology and other natural sciences
93-xx Systems theory; control {For optimal control, see 49-xx}
94-xx Information and communication, circuits
97-xx Mathematics education
 
[[de:Mathematics Subject Classification]]
二七七二七