CZ:Mathematics Workgroup

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 and elementary mathematics (for calculus see 26-XX Real functions below)
- high school mathematics
01-XX History and biography
- Euclid
- 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 $automorphicforms$ [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 sums and character sums {For finite fields, see 11Txx}
- 11Mxx Zeta and $L$ -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 $p$ -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
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
    - 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}
  - Kummer surfaces
- 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
19-XX $K$ -theory
20-XX Group theory and generalizations
22-XX Topological groups, Lie groups
26-XX Real functions
- Calculus
  - Mean Value Theorem
28-XX Measure and integration

 ** 28-02 Research exposition (monographs, survey articles)
 ** 28Axx Classical measure theory
  *** Lebesgu'e integral     
 ** 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
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
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
- 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 (we leave it for the computers Workgorup ?)
70-XX Mechanics of particles and systems (we leave it for physics Workgroup??)
74-XX Mechanics of deformable solids (we leave it for physics Workgroup??)
76-XX Fluid mechanics (we leave it for physics Workgroup??)
78-XX Optics, electromagnetic theory {For quantum optics, see 81V80} (we leave it for physics Workgroup??)
80-XX Classical thermodynamics, heat transfer (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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CZ:Mathematics Workgroup

Work plan white paper

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