கணித இயல் வகைப்பாடு

கட்டற்ற கலைக்களஞ்சியமான விக்கிப்பீடியாவில் இருந்து.
தாவிச் செல்லவும்: வழிசெலுத்தல், தேடல்

கணித இயல் வகைப்பாடு என்பது கணிதத்தின் உட்பிரிவுகளை வகைப்படுத்தி அமெரிக்க கணித சமூகத்தால் வெளியிடப்பட்ட வகை முறை ஆகும். இது கணித ஆய்வேடுகளின் தரவு தளத்தை பகுப்பாய்ந்து, அதன் அடிப்படையில் அமைந்தது.

பொருளடக்கம்

வகைப்பாடு[தொகு]

00-XX பொது[தொகு]

01-XX வரலாறு, கணிதவியலாளர்கள் சுயசரிதம்[தொகு]

03-XX கணித ஏரணம், அடிக்கட்டுமானம் (logic and foundations)[தொகு]

05-XX சேர்வியல்[தொகு]

06-XX Order, lattices, ordered algebraic structures[தொகு]

08-XX பொது இயற்கணித ஒருங்கியங்கள் (General algebraic systems)[தொகு]

11-XX எண் கோட்பாடு[தொகு]

12-XX புலக் கோட்பாடு, பல்லுறுப்புக் கோப்புகள் (Field theory and polynomials)[தொகு]

  • 12Dxx Real and complex fields
real numbers
complex numbers
  • 12Exx General field theory
  • 12Fxx Field extensions
  • 12Gxx Homological methods (field theory)
  • 12Hxx Differential and difference algebra
  • 12Jxx Topological fields
  • 12Kxx Generalizations of fields
  • 12Lxx Connections with logic
  • 12Yxx
    • 12Y05 Computational aspects of field theory and polynomials

13-XX Commutative rings and algebras[தொகு]

14-XX Algebraic geometry[தொகு]

hyperelliptic curve
Kummer surfaces

15-XX நேரிய, பல்நேரிய இயற்கணிதம்; அணிக் கோட்பாடு (Linear and multilinear algebra; matrix theory)[தொகு]

16-XX Associative rings and algebras[தொகு]

17-XX Nonassociative rings and algebras[தொகு]

18-XX Category theory; homological algebra[தொகு]

19-XX கே கோட்பாடு (K-theory)[தொகு]

20-XX குலக் கோட்பாடு and generalizations[தொகு]

  • 20Axx Foundations
  • 20Bxx Permutation groups
  • 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
  • 20Dxx Abstract finite groups
  • 20Exx Structure and classification of infinite or finite groups
  • 20Fxx Special aspects of infinite or finite groups
  • 20Gxx Linear algebraic groups (classical groups) {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}
    • 20Hxx Other groups of matrices [See also 15A30]
  • 20Jxx Connections with homological algebra and category theory
  • 20Kxx Abelian groups
  • 20L05 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}
  • 20Mxx Semigroups
  • 20Nxx Other generalizations of groups
  • 20P05 Probabilistic methods in group theory [See also 60Bxx]*22-XX Topological groups, Lie groups

22-XX Topological groups, Lie groups[தொகு]

For some useful suggestions see: Lie groups topics

26-XX மெய் சார்புகள் (Real functions)[தொகு]

Mean value theorem
for some more suggestions of useful articles to write see also list of mathematical topics

28-XX Measure and integration[தொகு]

  • 28Axx Classical measure theory
    • 28A05 Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
    • 28A10 Real- or complex-valued set functions
    • 28A12 Contents, measures, outer measures, capacities
Lebesgue measure
    • 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24]
    • 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
    • 28A25 Integration with respect to measures and other set functions
Lebesgue integral
Bounded convergence theorem
Monotone convergence theorem
Fatou's lemma
    • 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
    • 28A35 Measures and integrals in product spaces
    • 28A50 Integration and disintegration of measures
    • 28A51 Lifting theory [See also 46G15]
    • 28A60 Measures on Boolean rings, measure algebras [See also 54H10]
    • 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
    • 28A78 Hausdorff and packing measures
Hausdorff measure
Hausdorff dimension
Packing dimension
    • 28A80 Fractals [See also 37Fxx]
    • 28A99 None of the above, but in this section
  • 28Bxx Set functions, measures and integrals with values in abstract spaces
  • 28Exx Miscellaneous topics in measure theory

30-XX Functions of a complex variable[தொகு]

31-XX Potential theory[தொகு]

  • 31Axx Two-dimensional theory
    • 31A05 Harmonic, subharmonic, superharmonic functions
    • 31A10 Integral representations, integral operators, integral equations methods
    • 31A15 Potentials and capacity, harmonic measure, extremal length [See also 30C85]
    • 31A20 Boundary behavior (theorems of Fatou type, etc.)
    • 31A25 Boundary value and inverse problems
    • 31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation
    • 31A35 Connections with differential equations
    • 31A99 None of the above, but in this section
  • 31Bxx Higher-dimensional theory
    • 31B05 Harmonic, subharmonic, superharmonic functions
    • 31B10 Integral representations, integral operators, integral equations methods
    • 31B15 Potentials and capacities, extremal length
    • 31B20 Boundary value and inverse problems
    • 31B25 Boundary behavior
    • 31B30 Biharmonic and polyharmonic equations and functions
    • 31B35 Connections with differential equations
    • 31B99 None of the above, but in this section
  • 31Cxx Other generalizations
  • 31D05 Axiomatic potential theory

32-XX Several complex variables and analytic spaces[தொகு]

33-XX Special functions[தொகு]

(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[தொகு]

see the current article on differential equations

35-XX Partial differential equations[தொகு]

Schrödinger equation

37-XX Dynamical systems and ergodic theory[தொகு]

39-XX Difference and functional equations[தொகு]

40-XX Sequences, series, summability[தொகு]

  • 40Axx Convergence and divergence of infinite limiting processes
  • 40B05 Multiple sequences and series {(should also be assigned at least one other classification number in this section)}
  • 40Cxx General summability methods
  • 40Dxx Direct theorems on summability
  • 40Exx Inversion theorems
  • 40F05 Absolute and strong summability
  • 40Gxx Special methods of summability
  • 40H05 Functional analytic methods in summability
  • 40J05 Summability in abstract structures [See also 43A55, 46A35, 46B15]

41-XX Approximations and expansions[தொகு]

42-XX Fourier analysis[தொகு]

  • 42-04 Explicit machine computation and programs (not the theory of computation or programming)
Fourier series
  • 42Axx Fourier analysis in one variable
  • 42Bxx Fourier analysis in several variables {For automorphic theory, see mainly 11F30}
  • 42Cxx Nontrigonometric Fourier analysis

43-XX Abstract harmonic analysis[தொகு]

44-XX Integral transforms, operational calculus[தொகு]

45-XX Integral equations[தொகு]

46-XX Functional analysis[தொகு]

47-XX Operator theory[தொகு]

49-XX Calculus of variations and optimal control; optimization[தொகு]

51-XX Geometry[தொகு]

for a list of possible suggestions see list of geometry topics

52-XX Convex and discrete geometry[தொகு]

53-XX Differential geometry[தொகு]

54-XX General topology[தொகு]

55-XX Algebraic topology[தொகு]

57-XX Manifolds and cell complexes[தொகு]

58-XX Global analysis, analysis on manifolds[தொகு]

60-XX Probability theory and stochastic processes[தொகு]

  • 60Axx Foundations of probability theory
  • 60Bxx Probability theory on algebraic and topological structures
    • 60C05 Combinatorial probability
    • 60D05 Geometric probability, stochastic geometry, random sets [See also 52A22, 53C65]
  • 60Exx Distribution theory [See also 62Exx, 62Hxx]
  • 60Fxx Limit theorems [See also 28Dxx, 60B12]
  • 60Gxx Stochastic processes
  • 60Hxx Stochastic analysis [See also 58J65]
  • 60Jxx Markov processes
  • 60Kxx Special processes

62-XX Statistics[தொகு]

65-XX Numerical analysis[தொகு]

68-XX Computer science[தொகு]

(do we leave it for the computers Workgorup ?)

70-XX Mechanics of particles and systems[தொகு]

(do we leave it for physics Workgroup??)

74-XX Mechanics of deformable solids[தொகு]

(do we leave it for physics Workgroup??)

76-XX Fluid mechanics[தொகு]

(do we leave it for physics Workgroup??)

78-XX Optics, electromagnetic theory[தொகு]

{For quantum optics, see 81V80} (do we leave it for physics Workgroup??)

80-XX Classical thermodynamics, heat transfer[தொகு]

(do we leave it for physics Workgroup??)

81-XX Quantum theory[தொகு]

82-XX Statistical mechanics, structure of matter[தொகு]

(do we leave it for physics Workgroup??)

83-XX Relativity and gravitational theory[தொகு]

85-XX Astronomy and astrophysics[தொகு]

(do we leave it for physics Workgroup??)

86-XX Geophysics[தொகு]

(do we leave it for physics Workgroup??)

90-XX Operations research, mathematical programming[தொகு]

91-XX Game theory, economics, social and behavioral sciences[தொகு]

(do we leave it for economy Workgroup??)

92-XX Biology and other natural sciences[தொகு]

(do we leave it for biology Workgroup??)

93-XX Systems theory; control[தொகு]

இவற்றையும் பார்க்கவும்[தொகு]

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