CZ:Mathematics Workgroup
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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
- 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
- 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}
- 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 -theory
- 20-XX Group theory and generalizations
- 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
- 28Axx Classical 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
- 31Axx Two-dimensional 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)
- 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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