CZ:Mathematics Workgroup: Difference between revisions

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imported>John Stephenson
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<!-- {{Workgroup|group=Mathematics|forum=http://forum.citizendium.org/index.php/board,29.0.html}} -->
{{WorkgroupTop|Mathematics}}


{{Tableheader}}
* Useful page for mathematics authors: [[CZ:Formatting mathematics]].
{{Naturalsciences|group=Mathematics|link=Mathematics|forum=http://forum.citizendium.org/index.php/board,29.0.html}}
* Is there any [http://en.citizendium.org/wiki/Special:Newpages new hot math-related stuff?] If so, let's mark it by inserting <nowiki>[[Category:Mathematics Workgroup]]</nowiki>.
 
==Core articles==
{{Core-articles-note}} ''Click [[CZ:Core Articles/Mathematics|here]] to edit this transcluded list.''
{{CZ:Core Articles/Mathematics}}
 
==Articles==
{{subtopics-note}}
{{r|Mathematics}}
{{:Mathematics/Related Articles}}
 
== Help plan Mathematics Week! ==
'''[[CZ:Mathematics_Workgroup/Workgroup_Week|Go here and sign up!]]'''


== Work plan white paper ==
== 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 and ZMATH, with some minor edits. Each of these top level topics is a big subject, and it is not 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.
The topics below are part of the division of mathematical knowledge to subdisciplines; they come from the 2000 Math. subject classification of the AMS <ref>[http://www.ams.org/msc/index.html#browse]</ref> and ZMATH <ref>[http://zmath.u-strasbg.fr/math-cgi-bin/zmscen?level=0&zb=/math-cgi-bin/zmen&maxdocs=300&type=zmath&form=/ZMATH/en/quick.html]</ref>, 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:
Remarks:
* We kept the original MSC numbering in places.
* 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.
* 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.
* In some places we really expect some other workgroups (usually the physicists) to do the work alongside - we state where.


Caveats:
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]]
* Do not copy articles from Wikipedia without carefully reading them, verifying both scope and focus. Besides, why not consider writing your article from scratch? Often this permits a better logical structure and more coherence. See [[CZ:How to convert Wikipedia articles to Citizendium articles]]
* 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 ===
==Most wanted math entries==
 
From the encyclopedic point of view, the "high priority" articles are probably listed below at the top level of the tree (or in the table of contents). These are, however, relatively wide syntheses. You may want to start with a bit smaller tasks. A collection of important entries to write (of both types) can be found on the '''[[CZ:Core_Articles/Natural_Sciences|Core Articles]]''' page (still to be reviewed and reorganized).
 
Most popular Wikipedia math entries are: [[Pi]], [[Mathematics]] , [[prime number]], [[computer]], [[trapezoid]]. These come from the list of 1000 most viewed  pages in March 2007.<ref>[http://hemlock.knams.wikimedia.org/%7Eleon/stats/wikicharts/index.php?wiki=enwiki&ns=articles&limit=1000&mode=view]</ref> This varies heavily over the time.
 
On [[Planet Math]],  the most popular (as of March 2007) were:<ref>see [http://planetmath.org/?op=enlist&mode=hits Planet Math] stats page</ref>
[[circle]],
[[proof of Markov's inequality]],
[[Cauchy-Schwarz inequality]],
[[matrix inverse]],
[[Banach fixed point theorem]],
[[metric space]],
[[invariant subspace]],
[[function]],
[[manifold]],
[[eigenvalue]],
[[quartic formula]],
[[Jensen's inequality]],
[[cross product]],
[[real number]],
[[differential equation]],
[[gradient]],
[[natural number]],
[[Jacobian matrix]],
[[Gram-Schmidt orthogonalization]],
[[rational number]].
 
 
 
__TOC__
 
== The classification ==
 
==== 00-XX General ====
''(for calculus see 26-XX Real functions below)''
* elementary mathematics (pre-university level) <!-- high school is not well known e.g. in continental europe-->
:: [[Elementary functions]]
:: [[trigonometric function]] <!-- just an example!-->
:: [[point]] [[line]] [[plane]] [[solid (geometry)|solid]] stubs
:: [[elementary algebra]]
:: for suggestions of useful articles to write see also [[/List of mathematical topics#calculus topics|here]]  (pre-calculus or geometry sections)
 
==== 01-XX History and biography ====
::[[Euclid]] <!-- just an example! feel free to change-->
::[[Euler]]
==== 03-XX Mathematical logic and foundations ====
[[Set (mathematics) | Set theory]]
 
====05-XX Combinatorics ====
====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 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 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 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


* 00-XX General and elementary mathematics
====15-XX Linear and multilinear algebra; matrix theory ====
** high school mathematics
* 15A03 [[Vector space]]s, [[linear dependence]], rank
** elementary calculus
* 15A04 [[Linear transformation]]s, [[semilinear transformation]]s
*01-XX History and biography
* 15A06 [[Linear equations]]
**[[Euclid]]
* 15A09 [[Matrix inversion]], [[generalized inverse]]s
**[[Euler]]
* 15A12 Conditioning of matrices
*03-XX Mathematical logic and foundations
* 15A15 [[Determinant]]s, [[permanent]]s, other special matrix functions
*05-XX Combinatorics
* 15A18 [[Eigenvalue]]s, [[singular value]]s, and [[eigenvector]]s
*06-XX Order, lattices, ordered algebraic structures [See also 18B35]
* 15A21 [[Canonical form]]s, reductions, classification
*08-XX General algebraic systems
* 15A22 [[Matrix pencil]]s
*11-XX [[Number theory]]
* 15A23 Factorization of matrices
**11Axx Elementary number theory {For analogues in number fields, see 11R04}
* 15A24 Matrix equations and identities
**11Bxx Sequences and sets
* 15A27 [[Commutativity]]
**11Cxx Polynomials and matrices  
* 15A29 Inverse problems
**11Dxx Diophantine equations [See also 11Gxx, 14Gxx]  
* 15A30 Algebraic systems of matrices
**11Exx Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}
* 15A33 Matrices over special rings (quaternions, finite fields, etc.)
**11Fxx Discontinuous groups and <math>automorphic forms</math> [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45}
* 15A36 Matrices of integers
**11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14-xx, 14Gxx, 14Kxx]
* 15A39 Linear inequalities
**11Hxx Geometry of numbers {For applications in coding theory, see 94B75}
* 15A42 Inequalities involving eigenvalues and eigenvectors
**11Jxx Diophantine approximation, transcendental number theory [See also 11K60]  
* 15A45 Miscellaneous inequalities involving matrices
**11Kxx Probabilistic theory: distribution modulo <math>1</math>; metric theory of algorithms
* 15A48 Positive matrices and their generalizations; cones of matrices
**11Lxx [[Exponential sums]] and character sums {For finite fields, see 11Txx}
* 15A51 [[Stochastic matrix|Stochastic matrices]]
**11Mxx Zeta and <math>L</math>-functions: analytic theory
* 15A52 [[Random matrix|Random matrices]]
**11Nxx Multiplicative number theory
* 15A54 Matrices over function rings in one or more variables
**11Pxx Additive number theory; [[partitions]]  
* 15A57 Other types of matrices ([[Hermitian matrix|Hermitian]], [[skew-Hermitian matrix|skew-Hermitian]], etc.)
**11Rxx Algebraic number theory: [[global fields]] {For complex multiplication, see 11G15}
* 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
**11Sxx Algebraic number theory: [[local and <math>p</math>-adic fields]]  
* 15A63 [[Quadratic form|Quadratic]] and [[bilinear form]]s, [[inner product]]s [See mainly 11Exx]
**11Txx [[Finite fields]] and commutative rings (number-theoretic aspects)
* 15A66 [[Clifford algebra]]s, [[spinor]]s
**11Uxx Connections with logic
* 15A69 [[Multilinear algebra]], [[tensor product]]s
**11Yxx Computational number theory [See also 11-04]
* 15A72 Vector and tensor algebra, theory of invariants
*12-XX Field theory and [[polynomials]]
* 15A75 [[Exterior algebra]], [[Grassmann algebra]]s
*13-XX Commutative rings and algebras
* 15A78 Other algebras built from modules
*14-XX [[Algebraic geometry]]
* 15A90 Applications of matrix theory to physics
**14Axx Foundations
 
**14Bxx Local theory
====16-XX Associative rings and algebras ====
**14Cxx Cycles and subschemes
====17-XX Nonassociative rings and algebras====
**14Dxx Families, fibrations
====18-XX [[Category theory]]; [[homological algebra]] ====
**14Exx [[Birational geometry]]  
*18Axx General theory of categories and functors
**14Fxx (Co)homology theory [See also 13Dxx]  
*18Bxx Special categories
**14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]  
*18Cxx Categories and theories
**14Hxx [[algebraic curve|Curves]]
*18Dxx Categories with structure
***14H05 Algebraic functions; [[function fields]] [See also 11R58]
*18Exx [[Abelian categories]]
***14H10,14H15 [[moduli]]   [See also 30F10, 32Gxx]
*18Fxx Categories and geometry
***14H20 Singularities, local rings [See also 13Hxx, 14B05]
*18Gxx Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]
***14H25 Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
**18G05 [[Projective objects]] and [[injective objects]] [See also 13C10, 13C11, 16D40, 16D50]
***14H30 Coverings, fundamental group [See also 14E20, 14F35]  
**18G10 [[Resolutions]]; [[derived functors]] [See also 13D02, 16E05, 18E25]
***14H37 Automorphisms
**18G15 [[Ext]] and [[Tor]], generalizations, [[Künneth formula]] [See also 55U25]
***14H40 [[Jacobians]], [[Prym varieties]] [See also 32G20]
**18G20 [[Homological dimension]] [See also 13D05, 16E10]
***14H42 [[Theta functions]]; [[Schottky problem]] [See also 14K25, 32G20]
**18G25 Relative homological algebra, projective classes
***14H45 Special curves and curves of low genus
**18G30 [[Simplicial sets]], [[simplicial objects]] (in a category) [See also 55U10]
**** [[hyperelliptic curve]]
**18G35 [[Chain complexes]] [See also 18E30, 55U15]
***14H50 Plane and space curves
**18G40 [[Spectral sequences]], [[hypercohomology]] [See also 55Txx]
***14H51 Special divisors (gonality, Brill-Noether theory)
**18G50 [[Nonabelian homological algebra]]
***14H52 [[Elliptic curves]] [See also 11G05, 11G07, 14Kxx]
**18G55 [[Homotopical algebra]]
***14H55 Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
**18G60 Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]*20-XX [[Group theory]] and generalizations
***14H60 Vector bundles on curves and their moduli [See also 14D20, 14F05]
====19-XX ''K''-theory====
**14Jxx Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}
==== 20-XX [[Group theory]] and generalizations ====
*** [[Kummer surfaces]]
*20Axx Foundations
**14Kxx [[Abelian variety|Abelian varieties]] and schemes
*20Bxx [[Permutation group]]s
**14Lxx Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}  
*20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
**14Mxx Special varieties
*20Dxx Abstract finite groups
**14Nxx Projective and enumerative geometry [See also 51-xx]  
*20Exx Structure and classification of infinite or finite groups
**14Pxx [[Real algebraic]] and real analytic geometry
*20Fxx Special aspects of infinite or finite groups
**14Qxx Computational algebraic geometry [See also 12Y05, 13Pxx, 68W30]  
*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}
**14Rxx Affine geometry
**20Hxx Other groups of matrices [See also 15A30]
*15-XX Linear and multilinear algebra; matrix theory
*20Jxx Connections with homological algebra and category theory
*16-XX Associative rings and algebras
*20Kxx [[Abelian group]]s
*17-XX Nonassociative rings and algebras
*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}
*18-XX [[Category theory]]; [[homological algebra]]  
*20Mxx [[Semigroup]]s
*19-XX <math>K</math>-theory  
*20Nxx Other generalizations of groups
*20-XX [[Group theory]] and generalizations
*20P05 Probabilistic methods in group theory [See also 60Bxx]*22-XX [[Topological group]]s,  [[Lie group]]s
*22-XX [[Topological groups]][[Lie groups]]
 
*26-XX Real functions 
====22-XX [[Topological groups]],  [[Lie groups]] ====
** [[Calculus]]
For some useful suggestions see: [[/List of mathematical topics#Lie groups topics|Lie groups topics]]
*** [[Mean Value Theorem]]
 
*28-XX Measure and integration
====26-XX Real functions  ====
*30-XX Functions of a complex variable  
* [[Calculus]]
*31-XX [[Potential theory]]  
:: [[Mean value theorem]]
*32-XX Several complex variables and analytic spaces  
:: for some more suggestions of useful articles to write see also [[/List of mathematical topics|list of mathematical topics]]
*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]]
====28-XX Measure and integration ====
*35-XX [[Partial differential equations]]
* 28Axx Classical measure theory
*37-XX [[Dynamical systems]] and [[ergodic theory]]  
**28A05 Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
*39-XX Difference and functional equations
** 28A10 Real- or complex-valued set functions
*40-XX [[Sequences]], [[series]], [[summability]]
** 28A12 Contents, measures, outer measures, capacities
*41-XX Approximations and expansions  
:: [[Lebesgue measure]]
*42-XX Fourier analysis
** 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24]
** [[Fourier series]]
** 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
*43-XX Abstract harmonic analysis  
** 28A25 Integration with respect to measures and other set functions
*44-XX Integral transforms, operational calculus  
:: [[Lebesgue integral]]
*45-XX Integral equations
:: [[Bounded convergence theorem]]
*46-XX Functional analysis  
:: [[Monotone convergence theorem]]
*47-XX Operator theory
:: [[Fatou's lemma]]
*49-XX [[Calculus of variations]] and optimal control; optimization  
** 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
*51-XX [[Geometry]]  
** 28A35 Measures and integrals in product spaces
*52-XX Convex and discrete geometry
** 28A50 Integration and disintegration of measures
*53-XX [[Differential geometry]]  
** 28A51 Lifting theory [See also 46G15]
*54-XX [[General topology]]  
** 28A60 Measures on Boolean rings, measure algebras [See also 54H10]
*55-XX [[Algebraic topology]]
** 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
*57-XX Manifolds and cell complexes  
** 28A78 Hausdorff and [[packing measure]]s
*58-XX Global analysis, analysis on manifolds  
:: [[Hausdorff measure]]
*60-XX [[Probability]] theory and stochastic processes  
:: [[Hausdorff dimension]]
**60Axx Foundations of probability theory  
:: [[Packing dimension]]
**60Bxx Probability theory on algebraic and topological structures  
** 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|Sequences]], [[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  
**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]  
*60Exx Distribution theory [See also 62Exx, 62Hxx]  
**60Fxx Limit theorems [See also 28Dxx, 60B12]  
*60Fxx [[Stochastic convergence|Limit theorems]] [See also 28Dxx, 60B12]  
**60Gxx Stochastic processes
*60Gxx [[Stochastic process]]es
**60Hxx Stochastic analysis [See also 58J65]  
*60Hxx Stochastic analysis [See also 58J65]  
**60Jxx [[Markov processes]]  
*60Jxx [[Markov process]]es
**60Kxx Special processes
*60Kxx Special processes
*62-XX [[Statistics]]
 
*65-XX [[Numerical analysis]]
====62-XX [[Statistics]] ====
*68-XX Computer science                       (we leave it for the computers Workgorup ?)  
====65-XX [[Numerical analysis]]====
*70-XX Mechanics of particles and systems     (we leave it for physics Workgroup??)
====68-XX Computer science====
*74-XX Mechanics of deformable solids           (we leave it for physics Workgroup??)
''<small>(do we leave it for the computers Workgorup ?) </small> ''
*76-XX Fluid mechanics                                     (we leave it for physics Workgroup??)
====70-XX Mechanics of particles and systems====
*78-XX Optics, electromagnetic theory {For quantum optics, see 81V80}          (we leave it for physics Workgroup??)
''<small>(do we leave it for physics Workgroup??)</small>''
*80-XX Classical thermodynamics, heat transfer                                             (we leave it for physics Workgroup??)
====74-XX Mechanics of deformable solids ====
*81-XX Quantum theory                                                       (at the beginning we leave it for physics Workgroup??)
''<small>(do we leave it for physics Workgroup??)</small>''
*82-XX Statistical mechanics, structure of matter                       (we leave it for physics Workgroup??)
====76-XX Fluid mechanics====
*83-XX Relativity and gravitational theory                                 (we leave it for physics Workgroup??)
''<small>(do we leave it for physics Workgroup??)</small>''
*85-XX Astronomy and astrophysics                                         (we leave it for physics Workgroup??)
====78-XX Optics, electromagnetic theory ====
*86-XX Geophysics                                       (we leave it for physics Workgroup??)
'' {For quantum optics, see 81V80}          (do we leave it for physics Workgroup??)''
*90-XX Operations research, mathematical programming
====80-XX Classical thermodynamics, heat transfer ====
*91-XX Game theory, economics, social and behavioral sciences   (we leave it for economy Workgroup??)
''<small>(do we leave it for physics Workgroup??)</small>''
*92-XX Biology and other natural sciences                                 (we leave it for biology Workgroup??)
====81-XX Quantum theory ====
*93-XX Systems theory; control
====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====
 
==References==
{{reflist}}

Latest revision as of 07:58, 23 March 2021

Workgroups are no longer used for group communications, but they still are used to group articles into fields of interest. Each article is assigned to 1-3 Workgroups via the article's Metadata.

Mathematics Workgroup
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The Mathematics Workgroup will organize and coordinate efforts to create and improve articles relating to Mathematics. If you are interested in participating, you may add yourself to Category:Mathematics Authors, then simply dive in and begin contributing!

Please note that information below may be out-of-date.



Core articles

Core articles are those that are as-yet unwritten and so should be prioritised. Please start articles on the topics below. Click here to edit this transcluded list.

Geometry

Calculus

Analysis

Complex analysis

Functional analysis

Differential equations

Algebra

Linear algebra

Matrix theory

Set theory

Logic

Probability

Applied

History

Articles

Click on the [r] after the first definition below to edit this list of transcluded subtopics.


Help plan Mathematics Week!

Go here and sign up!

Work plan white paper

The topics below are part of the division of mathematical knowledge to subdisciplines; 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 other workgroups (usually the physicists) to do the work alongside - we state where.

Caveats:

  • Do not copy articles from Wikipedia without carefully reading them, verifying both scope and focus. Besides, why not consider writing your article from scratch? Often this permits a better logical structure and more coherence. See CZ:How to convert Wikipedia articles to Citizendium articles
  • Keep in mind three audiences when writing an article: general readers, math students and professionals.

Most wanted math entries

From the encyclopedic point of view, the "high priority" articles are probably listed below at the top level of the tree (or in the table of contents). These are, however, relatively wide syntheses. You may want to start with a bit smaller tasks. A collection of important entries to write (of both types) can be found on the Core Articles page (still to be reviewed and reorganized).

Most popular Wikipedia math entries are: Pi, Mathematics , prime number, computer, trapezoid. These come from the list of 1000 most viewed pages in March 2007.[3] This varies heavily over the time.

On Planet Math, the most popular (as of March 2007) were:[4] circle, proof of Markov's inequality, Cauchy-Schwarz inequality, matrix inverse, Banach fixed point theorem, metric space, invariant subspace, function, manifold, eigenvalue, quartic formula, Jensen's inequality, cross product, real number, differential equation, gradient, natural number, Jacobian matrix, Gram-Schmidt orthogonalization, rational number.



The classification

00-XX General

(for calculus see 26-XX Real functions below)

  • elementary mathematics (pre-university level)
Elementary functions
trigonometric function
point line plane solid stubs
elementary algebra
for suggestions of useful articles to write see also here (pre-calculus or geometry sections)

01-XX History and biography

Euclid
Euler

03-XX Mathematical logic and foundations

Set theory

05-XX Combinatorics

06-XX Order, lattices, ordered algebraic structures

08-XX General algebraic systems

11-XX Number theory

12-XX Field theory and polynomials

  • 12Dxx Real and complex fields
real numbers
complex numbers

13-XX Commutative rings and algebras

14-XX Algebraic geometry

hyperelliptic curve
Kummer surfaces

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

19-XX K-theory

20-XX Group theory and generalizations

  • 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

For some useful suggestions see: Lie groups topics

26-XX Real functions

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

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

see the current article on differential equations

35-XX Partial differential equations

Schrödinger 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

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 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

(do we leave it for physics Workgroup??)

83-XX Relativity and gravitational theory

85-XX Astronomy and astrophysics

(do we leave it for physics Workgroup??)

86-XX Geophysics

(do we leave it for physics Workgroup??)

90-XX Operations research, mathematical programming

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

(do we leave it for economy Workgroup??)

92-XX Biology and other natural sciences

(do we leave it for biology Workgroup??)

93-XX Systems theory; control

References

  1. [1]
  2. [2]
  3. [3]
  4. see Planet Math stats page