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:

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
  • 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
  • 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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