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'''கணித இயல் வகைப்பாடு''' என்பது கணிதத்தின் உட்பிரிவுகளை வகைப்படுத்தி அமெரிக்க கணித சமூகத்தால் வெளியிடப்பட்ட வகை முறை ஆகும். இது கணித ஆய்வேடுகளின் தரவு தளத்தை பகுப்பாய்ந்து, அதன் அடிப்படையில் அமைந்தது.
== வகைப்பாடு ==
==== 00-XX பொது ====
==== 01-XX [[கணித வரலாறு|வரலாறு]], [[கணிதவியலாளர்|கணிதவியலாளர்கள்]] சுயசரிதம் ====
==== 03-XX கணித [[ஏரணம்]], அடிக்கட்டுமானம் (logic and foundations) ====
* [[கணக் கோட்பாடு]]
====05-XX [[சேர்வியல்]] ====
====06-XX Order, lattices, ordered algebraic structures====
* 06Axx [[Ordered set]]s
* 06Bxx [[Lattice (order)|Lattice]]s
* 06Cxx [[Modular lattice]]s, [[complemented lattice]]s
* 06Dxx [[Distributive lattice]]s
* 06Exx [[Boolean algebra]]s ([[Boolean ring]]s)
* 06Fxx [[Ordered structure]]s
====08-XX பொது இயற்கணித ஒருங்கியங்கள் (General algebraic systems) ====
====11-XX [[எண் கோட்பாடு]]====
*11Axx Elementary number theory {For analogues in number fields, see 11R04}
*11Bxx Sequences and sets
*11Cxx Polynomials and matrices
*11Dxx [[Diophantine equation]]s [See also 11Gxx, 14Gxx]
*11Exx Forms and [[linear algebraic group]]s [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}
*11Fxx Discontinuous groups and [[automorphic form]]s [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45}
*11Gxx [[Arithmetic algebraic geometry]] ([[Diophantine geometry]]) [See also 11Dxx, 14-xx, 14Gxx, 14Kxx]
*11Hxx [[Geometry of numbers]] {For applications in [[coding theory]], see 94B75}
*11Jxx [[Diophantine approximation]], [[transcendental number theory]] [See also 11K60]
*11Kxx Probabilistic theory: [[distribution modulo 1]]; metric theory of algorithms
*11Lxx [[Exponential sum]]s and [[character sum]]s {For [[finite field]]s, see 11Txx}
*11Mxx Zeta and <math>L</math>-functions: analytic theory
*11Nxx [[Multiplicative number theory]]
*11Pxx [[Additive number theory]]; [[partition]]s
*11Rxx [[Algebraic number theory]]: [[global field]]s {For [[complex multiplication]], see 11G15}
*11Sxx Algebraic number theory: [[local field|local]] and <math>p</math>-adic fields
*11Txx [[Finite field]]s and commutative rings (number-theoretic aspects)
*11Uxx Connections with logic
*11Yxx [[Computational number theory]] [See also 11-04]
====12-XX [[புலக் கோட்பாடு]], பல்லுறுப்புக் கோப்புகள் (Field theory and [[polynomial]]s) ====
*12Dxx Real and complex fields
:: [[real number]]s
:: [[complex number]]s
*12Exx General field theory
** 12E05 [[Polynomial]]s (irreducibility, etc.)
** 12E10 Special polynomials
** 12E12 [[Equation]]s
** 12E15 [[Skew field]]s, [[division ring]]s
** 12E20 [[Finite field]]s (field-theoretic aspects)
** 12E25 [[Hilbertian field]]s; Hilbert's irreducibility theorem
** 12E30 Field arithmetic
*12Fxx [[Field extension]]s
*12Gxx Homological methods (field theory)
*12Hxx Differential and difference algebra
*12Jxx [[Topological field]]s
*12Kxx Generalizations of fields
*12Lxx Connections with logic
*12Yxx
**12Y05 Computational aspects of field theory and polynomials
====13-XX Commutative rings and algebras====
====14-XX [[Algebraic geometry]]====
*14Axx Foundations
**14A10 [[algebraic variety|Varieties]] and [[morphism]]s
**14A15 [[scheme (mathematics)|Schemes]] and morphisms
**14A20 Generalizations ([[algebraic space]]s, [[stack (algebraic geometry)|stacks]])
**14A22 [[Noncommutative algebraic geometry]]
*14Bxx Local theory
**14B05 [[Singularity (algebraic geomtetry|Singularities]] [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
**14B07 [[Deformations of singularities|Deformation of singularities]] [See also 14D15, 32S30]
**14B10 Infinitesimal methods [See also 13D10]
**14B12 [[Local deformation theory]], [[Artin approximation]], etc. [See also 13B40, 13D10]
**14B15 [[Local cohomology]] [See also 13D45, 32C36]
**14B20 [[Formal neighborhood]]s
**14B25 Local structure of morphisms: [[étale morphism]], [[flat morphism]], etc. [See also 13B40]
*14Cxx Cycles and [[subscheme]]s
**14C05 Parametrization ([[Chow scheme]]s and [[Hilbert scheme]]s)
**14C15 [[Chow group]]s and [[Chow ring|rings]]
**14C17 [[Intersection theory]], [[characteristic classes]], [[intersection multiplicities]] [See also 13H15]
**14C20 [[Divisor]]s, [[Linear system (algebraic geometry)|linear system]]s, [[invertible sheaf|invertible sheaves]]
**14C21 [[Pencil]]s, [[net]]s, [[web]]s [See also 53A60]
**14C22 [[Picard group]]s
**14C25 [[Algebraic cycle]]s
**14C30 Transcendental methods, [[Hodge theory]] [See also 14D07, 32G20, 32J25, 32S35], [[Hodge conjecture]]
**14C34 [[Torelli problem]] [See also 32G20]
**14C35 Applications of methods of algebraic K-theory [See also 19Exx]
**14C40 Riemann-Roch theorems [See also 19E20, 19L10]
*** [[Riemann-Roch theorem]]
*** [[Clifford's theorem]]
*** [[Grothendieck Riemann-Roch theorem]]
*14Dxx Families, fibrations
**14D05 Structure of families ([[Picard-Lefschetz]], monodromy, etc.)
**14D06 Fibrations, degenerations
**14D07 [[Variation of Hodge structures]] [See also 32G20]
**14D10 Arithmetic ground fields (finite, local, global)
**14D15 Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
**14D20 Algebraic moduli problems, [[moduli of vector bundles]] {For analytic moduli problems, see 32G13}
**14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
**14D22 [[Fine moduli space]]s and [[coarse moduli space]]s
*14Exx [[Birational geometry]]
**14E05 Rational and birational maps
**14E07 Birational automorphisms, [[Cremona group]] and generalizations
**14E08 Rationality questions
**14E15 Global theory and [[resolution of singularities]] [See also 14B05, 32S20, 32S45]
**14E20 Coverings [See also 14H30]
**14E22 [[Ramification]] problems [See also 11S15]
**14E25 Embeddings
**14E30 [[Minimal model program]] (Mori theory, [[extremal rays]])
*14Fxx (Co)homology theory [See also 13Dxx]
**14F05 [[Vector bundle]]s, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
**14F10 [[sheaf of Differentials]] and other special sheaves [See also 13Nxx, 32C38]
**14F17 [[Vanishing theorems]] [See also 32L20]
**14F20 [[Étale topology]] [[Etale cohomology]] and other [[Grothendieck topologies]] and [[Grothendieck cohomologies]]
**14F22 [[Brauer groups of schemes]] [See also 12G05, 16K50]
**14F25 Classical real and complex cohomology
**14F30 [[p-adic cohomology]], [[crystalline cohomology]]
**14F35 Homotopy theory; fundamental groups [See also 14H30]
**14F40 [[de Rham cohomology]] [See also 14C30, 32C35, 32L10]
**14F42 [[Motivic cohomology]]
**14F43 Other algebro-geometric (co)homologies (e.g., [[intersection cohomology]], [[equivariant cohomology]], Lawson, Deligne (co)homologies)
**14F45 Topological properties
*14Gxx Arithmetic problems. [[Diophantine geometry]] [See also 11Dxx, 11Gxx]
*14Hxx [[algebraic curve|Curves]]
**14H05 Algebraic functions; [[function fields]] [See also 11R58]
**14H10,14H15 [[moduli]] [See also 30F10, 32Gxx]
**14H20 Singularities, local rings [See also 13Hxx, 14B05]
**14H25 Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
**14H30 Coverings, fundamental group [See also 14E20, 14F35]
**14H37 Automorphisms
**14H40 [[Jacobians]], [[Prym varieties]] [See also 32G20]
**14H42 [[Theta functions]]; [[Schottky problem]] [See also 14K25, 32G20]
**14H45 Special curves and curves of low genus
:: [[hyperelliptic curve]]
**14H50 Plane and space curves
**14H51 Special divisors (gonality, Brill-Noether theory)
**14H52 [[Elliptic curves]] [See also 11G05, 11G07, 14Kxx]
**14H55 [[Riemann surfaces]]; [[Weierstrass points]]; [[gap sequences]] [See also 30Fxx]
**14H60 Vector bundles on curves and their moduli [See also 14D20, 14F05]
*14Jxx [[Algebraic surface|Surfaces]] and higher-dimensional varieties {For analytic theory, see 32Jxx}
**14J10 Families, moduli, classification: algebraic theory
**14J15 Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
**14J17 [[Singularities of surfaces]] [See also 14B05, 14E15]
**14J20 Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
**14J25 Special surfaces {For Hilbert modular surfaces, see 14G35}
**14J26 [[Rational surfaces]] and [[ruled surfaces]]
**14J27 [[Elliptic surfaces]]
**14J28 [[K3 surfaces]] and [[Enriques surfaces]]
:: [[Kummer surfaces]]
**14J29 [[Surfaces of general type]]
**14J30 [[3-folds]]
**14J32 [[Calabi-Yau manifolds]], [[mirror symmetry]]
**14J35 [[4-folds]]
**14J40 [[n-folds]] (''n'' > 4)
**14J45 [[Fano varieties]]
**14J50 Automorphisms of surfaces and higher-dimensional varieties
**14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
**14J70 Hypersurfaces
**14J80 Topology of surfaces ([[Donaldson polynomials]], [[Seiberg-Witten invariants]])
*14Kxx [[Abelian variety|Abelian varieties]] and schemes
*14Lxx Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}
*14Mxx Special varieties
*14Nxx Projective and enumerative geometry [See also 51-xx]
*14Pxx [[Real algebraic]] and real analytic geometry
*14Qxx Computational algebraic geometry [See also 12Y05, 13Pxx, 68W30]
*14Rxx Affine geometry
====15-XX நேரிய, பல்நேரிய இயற்கணிதம்; அணிக் கோட்பாடு (Linear and multilinear algebra; matrix theory) ====
* 15A03 [[Vector space]]s, [[linear dependence]], rank
* 15A04 [[Linear transformation]]s, [[semilinear transformation]]s
* 15A06 [[Linear equations]]
* 15A09 [[Matrix inversion]], [[generalized inverse]]s
* 15A12 Conditioning of matrices
* 15A15 [[Determinant]]s, [[permanent]]s, other special matrix functions
* 15A18 [[Eigenvalue]]s, [[singular value]]s, and [[eigenvector]]s
* 15A21 [[Canonical form]]s, reductions, classification
* 15A22 [[Matrix pencil]]s
* 15A23 Factorization of matrices
* 15A24 Matrix equations and identities
* 15A27 [[Commutativity]]
* 15A29 Inverse problems
* 15A30 Algebraic systems of matrices
* 15A33 Matrices over special rings (quaternions, finite fields, etc.)
* 15A36 Matrices of integers
* 15A39 Linear inequalities
* 15A42 Inequalities involving eigenvalues and eigenvectors
* 15A45 Miscellaneous inequalities involving matrices
* 15A48 Positive matrices and their generalizations; cones of matrices
* 15A51 [[Stochastic matrix|Stochastic matrices]]
* 15A52 [[Random matrix|Random matrices]]
* 15A54 Matrices over function rings in one or more variables
* 15A57 Other types of matrices ([[Hermitian matrix|Hermitian]], [[skew-Hermitian matrix|skew-Hermitian]], etc.)
* 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
* 15A63 [[Quadratic form|Quadratic]] and [[bilinear form]]s, [[inner product]]s [See mainly 11Exx]
* 15A66 [[Clifford algebra]]s, [[spinor]]s
* 15A69 [[Multilinear algebra]], [[tensor product]]s
* 15A72 Vector and tensor algebra, theory of invariants
* 15A75 [[Exterior algebra]], [[Grassmann algebra]]s
* 15A78 Other algebras built from modules
* 15A90 Applications of matrix theory to physics
====16-XX Associative rings and algebras ====
====17-XX Nonassociative rings and algebras====
====18-XX [[Category theory]]; [[homological algebra]] ====
*18Axx General theory of categories and functors
*18Bxx Special categories
*18Cxx Categories and theories
*18Dxx Categories with structure
*18Exx [[Abelian categories]]
*18Fxx Categories and geometry
*18Gxx Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]
**18G05 [[Projective objects]] and [[injective objects]] [See also 13C10, 13C11, 16D40, 16D50]
**18G10 [[Resolutions]]; [[derived functors]] [See also 13D02, 16E05, 18E25]
**18G15 [[Ext]] and [[Tor]], generalizations, [[Künneth formula]] [See also 55U25]
**18G20 [[Homological dimension]] [See also 13D05, 16E10]
**18G25 Relative homological algebra, projective classes
**18G30 [[Simplicial sets]], [[simplicial objects]] (in a category) [See also 55U10]
**18G35 [[Chain complexes]] [See also 18E30, 55U15]
**18G40 [[Spectral sequences]], [[hypercohomology]] [See also 55Txx]
**18G50 [[Nonabelian homological algebra]]
**18G55 [[Homotopical algebra]]
**18G60 Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]*20-XX [[Group theory]] and generalizations
====19-XX கே கோட்பாடு (K-theory) ====
==== 20-XX [[குலக் கோட்பாடு]] and generalizations ====
*20Axx Foundations
*20Bxx [[Permutation group]]s
*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 group]]s ([[classical group]]s) {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 group]]s
*20L05 [[Groupoid]]s (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 [[Semigroup]]s
*20Nxx Other generalizations of groups
*20P05 Probabilistic methods in group theory [See also 60Bxx]*22-XX [[Topological group]]s, [[Lie group]]s
====22-XX [[Topological groups]], [[Lie groups]] ====
For some useful suggestions see: [[/List of mathematical topics#Lie groups topics|Lie groups topics]]
====26-XX மெய் சார்புகள் (Real functions) ====
* [[Calculus]]
:: [[Mean value theorem]]
:: for some more suggestions of useful articles to write see also [[/List of mathematical topics|list of mathematical topics]]
====28-XX Measure and integration ====
* 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 measure]]s
:: [[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 ====
====31-XX [[Potential theory]] ====
*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 ====
====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 equation]]s ====
::see the current article on [[differential equation]]s
==== 35-XX [[Partial differential equation]]s ====
::[[Schrödinger equation]]
==== 37-XX [[Dynamical system]]s and [[ergodic theory]] ====
====39-XX Difference and functional equations ====
====40-XX [[Sequence]]s, [[series (mathematics)|series]], [[summability]]====
*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 ====
====42-XX Fourier analysis====
* 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 ====
====44-XX Integral transforms, operational calculus ====
====45-XX Integral equations ====
====46-XX Functional analysis ====
====47-XX Operator theory====
====49-XX [[Calculus of variations]] and optimal control; optimization ====
====51-XX [[Geometry]] ====
::for a list of possible suggestions see [[list of geometry topics]]
====52-XX Convex and discrete geometry====
====53-XX [[Differential geometry]] ====
====54-XX [[General topology]] ====
====55-XX [[Algebraic topology]] ====
====57-XX Manifolds and cell complexes ====
====58-XX Global analysis, analysis on manifolds ====
====60-XX [[Probability]] theory and stochastic processes ====
*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 [[Stochastic convergence|Limit theorems]] [See also 28Dxx, 60B12]
*60Gxx [[Stochastic process]]es
*60Hxx Stochastic analysis [See also 58J65]
*60Jxx [[Markov process]]es
*60Kxx Special processes
====62-XX [[Statistics]] ====
====65-XX [[Numerical analysis]]====
====68-XX Computer science====
''<small>(do we leave it for the computers Workgorup ?) </small> ''
====70-XX Mechanics of particles and systems====
''<small>(do we leave it for physics Workgroup??)</small>''
====74-XX Mechanics of deformable solids ====
''<small>(do we leave it for physics Workgroup??)</small>''
====76-XX Fluid mechanics====
''<small>(do we leave it for physics Workgroup??)</small>''
====78-XX Optics, electromagnetic theory ====
'' {For quantum optics, see 81V80} (do we leave it for physics Workgroup??)''
====80-XX Classical thermodynamics, heat transfer ====
''<small>(do we leave it for physics Workgroup??)</small>''
====81-XX Quantum theory ====
====82-XX Statistical mechanics, structure of matter ====
''<small>(do we leave it for physics Workgroup??)</small>''
====83-XX Relativity and gravitational theory ====
====85-XX Astronomy and astrophysics ====
''<small>(do we leave it for physics Workgroup??)</small>''
====86-XX Geophysics====
''<small>(do we leave it for physics Workgroup??)</small>''
====90-XX Operations research, mathematical programming ====
====91-XX Game theory, economics, social and behavioral sciences ====
''<small>(do we leave it for economy Workgroup??)</small>''
====92-XX Biology and other natural sciences ====
''<small>(do we leave it for biology Workgroup??)</small>''
====93-XX Systems theory; control====
==இவற்றையும் பார்க்கவும்==
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