CZ:Mathematics Workgroup: Difference between revisions
imported>David Lehavi (added more pieces of classification tree) |
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* Keep in mind three audiences when writing an article: general readers, math students and professionals. | * Keep in mind three audiences when writing an article: general readers, math students and professionals. | ||
== The classification == | |||
==== 00-XX General ==== | |||
* | ''(for calculus see 26-XX Real functions below)'' | ||
* elementary mathematics | |||
:: [[trigonometric function]] <!-- just an example!--> | |||
==== 01-XX History and biography ==== | |||
::[[Euclid]] <!-- just an example! feel free to change--> | |||
::[[Euler]] | |||
==== 03-XX Mathematical logic and foundations ==== | |||
====05-XX Combinatorics ==== | |||
====06-XX Order, lattices, ordered algebraic structures==== | |||
''[See also 18B35]'' | |||
====08-XX General algebraic systems==== | |||
====11-XX [[Number theory]]==== | |||
*11Axx Elementary number theory {For analogues in number fields, see 11R04} | |||
*11Bxx Sequences and sets | |||
*11Cxx Polynomials and matrices | |||
*11Dxx Diophantine equations [See also 11Gxx, 14Gxx] | |||
*11Exx Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63} | |||
*11Fxx Discontinuous groups and automorphic forms [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 <math>1</math>; metric theory of algorithms | |||
*11Lxx [[Exponential sums]] and character sums {For finite fields, see 11Txx} | |||
*11Mxx Zeta and <math>L</math>-functions: analytic theory | |||
*11Nxx Multiplicative number theory | |||
*11Pxx Additive number theory; [[partitions]] | |||
*11Rxx Algebraic number theory: [[global fields]] {For complex multiplication, see 11G15} | |||
*11Sxx Algebraic number theory: [[local and <math>p</math>-adic fields]] | |||
*11Txx [[Finite fields]] and commutative rings (number-theoretic aspects) | |||
*11Uxx Connections with logic | |||
*11Yxx Computational number theory [See also 11-04] | |||
====12-XX Field theory and [[polynomials]] ==== | |||
*12Dxx Real and complex fields | |||
:: [[real numbers]] | |||
:: [[complex numbers]] | |||
*12Exx General field theory | |||
*12Fxx Field extensions | |||
*12Gxx Homological methods (field theory) | |||
**12Y05 Computational aspects of field theory and polynomials | *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==== | |||
====14-XX [[Algebraic geometry]]==== | |||
*14Axx Foundations | |||
*14Bxx Local theory | |||
*14Cxx Cycles and subschemes | |||
*14Dxx Families, fibrations | |||
*14Exx [[Birational geometry]] | |||
*14Fxx (Co)homology theory [See also 13Dxx] | |||
*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 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 Linear and multilinear algebra; matrix theory ==== | |||
====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 ''K''-theory==== | |||
==== 20-XX (name?) ==== | |||
*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] | **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]] ==== | |||
====26-XX Real functions ==== | |||
* [[Calculus]] | |||
:: [[Mean Value Theorem]] | |||
====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 equations]] ==== | |||
==== 35-XX [[Partial differential equations]] ==== | |||
::[[schrodinger equation]] | |||
==== 37-XX [[Dynamical systems]] and [[ergodic theory]] ==== | |||
====39-XX Difference and functional equations ==== | |||
====40-XX [[Sequences]], [[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 | |||
====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]] ==== | |||
====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 | **60C05 Combinatorial probability | ||
**60D05 Geometric probability, stochastic geometry, random sets [See also 52A22, 53C65] | **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]] ==== | |||
====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 ==== | |||
''(do we leave it for physics Workgroup??)'' | |||
====81-XX Quantum theory ==== | |||
====82-XX Statistical mechanics, structure of matter ==== | |||
''(we leave it for physics Workgroup??)'' | |||
====83-XX Relativity and gravitational theory ==== | |||
''(we leave it for physics Workgroup??) | |||
====85-XX Astronomy and astrophysics ==== | |||
''(we leave it for physics Workgroup??)'' | |||
====86-XX Geophysics==== | |||
''(we leave it for physics Workgroup??)'' | |||
====90-XX Operations research, mathematical programming ==== | |||
====91-XX Game theory, economics, social and behavioral sciences ==== | |||
''(we leave it for economy Workgroup??)'' | |||
====92-XX Biology and other natural sciences ==== | |||
''(we leave it for biology Workgroup??)'' | |||
====93-XX Systems theory; control==== |
Revision as of 04:31, 3 March 2007
Work plan white paper
The topics below are part of the division of mathematical knowledge to subdiciplines; they come from the 2000 Math. subject classification of the AMS [1] and ZMATH [2], with some minor edits. Each of these top level topics is a big subject, and it is not necessarily our first priority to write a long article on these entries. Our object with outlining this list is to establish a framework. We recommend that when you write a new article, you should try to find a proper node for it. Do not hesitate to put a link for an article you want to work on soon. Feel free to do the same to request a particular important topic to be covered.
Remarks:
- We kept the original MSC numbering in places.
- No, of course its not the whole MSC tree - not even close to it. We should eventually put as much of it as appropriate.
- In some places we really expect some otherwork group (usually the physicsits) to do the work for us - we state where.
Caveats:
- Do not copy articles from wikipedia without carefully reading them, verifying both scope and focus. See Citizendium Pilot:How to convert Wikipedia articles to Citizendium articles
- Keep in mind three audiences when writing an article: general readers, math students and professionals.
The classification
00-XX General
(for calculus see 26-XX Real functions below)
- elementary mathematics
01-XX History and biography
03-XX Mathematical logic and foundations
05-XX Combinatorics
06-XX Order, lattices, ordered algebraic structures
[See also 18B35]
08-XX General algebraic systems
11-XX Number theory
- 11Axx Elementary number theory {For analogues in number fields, see 11R04}
- 11Bxx Sequences and sets
- 11Cxx Polynomials and matrices
- 11Dxx Diophantine equations [See also 11Gxx, 14Gxx]
- 11Exx Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}
- 11Fxx Discontinuous groups and automorphic forms [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 ; metric theory of algorithms
- 11Lxx Exponential sums and character sums {For finite fields, see 11Txx}
- 11Mxx Zeta and -functions: analytic theory
- 11Nxx Multiplicative number theory
- 11Pxx Additive number theory; partitions
- 11Rxx Algebraic number theory: global fields {For complex multiplication, see 11G15}
- 11Sxx Algebraic number theory: [[local and -adic fields]]
- 11Txx Finite fields and commutative rings (number-theoretic aspects)
- 11Uxx Connections with logic
- 11Yxx Computational number theory [See also 11-04]
12-XX Field theory and polynomials
- 12Dxx Real and complex fields
- 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
14-XX Algebraic geometry
- 14Axx Foundations
- 14Bxx Local theory
- 14Cxx Cycles and subschemes
- 14Dxx Families, fibrations
- 14Exx Birational geometry
- 14Fxx (Co)homology theory [See also 13Dxx]
- 14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
- 14Hxx 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
- 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 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
- 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 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 Linear and multilinear algebra; matrix theory
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 K-theory
20-XX (name?)
- 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
26-XX Real functions
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
- 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
- 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
- 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 equations
35-XX Partial differential equations
37-XX Dynamical systems and ergodic theory
39-XX Difference and functional equations
40-XX Sequences, 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
41-XX Approximations and expansions
42-XX Fourier analysis
- 42-04 Explicit machine computation and programs (not the theory of computation or programming)
- 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
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 Limit theorems [See also 28Dxx, 60B12]
- 60Gxx Stochastic processes
- 60Hxx Stochastic analysis [See also 58J65]
- 60Jxx Markov processes
- 60Kxx Special processes
62-XX Statistics
65-XX Numerical analysis
68-XX Computer science
(do we leave it for the computers Workgorup ?)
70-XX Mechanics of particles and systems
(do we leave it for physics Workgroup??)
74-XX Mechanics of deformable solids
(do we leave it for physics Workgroup??)
76-XX Fluid mechanics
(do we leave it for physics Workgroup??)
78-XX Optics, electromagnetic theory
{For quantum optics, see 81V80} (do we leave it for physics Workgroup??)
80-XX Classical thermodynamics, heat transfer
(do we leave it for physics Workgroup??)
81-XX Quantum theory
82-XX Statistical mechanics, structure of matter
(we leave it for physics Workgroup??)
83-XX Relativity and gravitational theory
(we leave it for physics Workgroup??)
85-XX Astronomy and astrophysics
(we leave it for physics Workgroup??)
86-XX Geophysics
(we leave it for physics Workgroup??)
90-XX Operations research, mathematical programming
91-XX Game theory, economics, social and behavioral sciences
(we leave it for economy Workgroup??)
92-XX Biology and other natural sciences
(we leave it for biology Workgroup??)
93-XX Systems theory; control
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