CZ:Core Articles/Mathematics: Difference between revisions

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imported>Peter Lyall Easthope
m (An algebra is an instance of a category; not _vice versa_.)
imported>John Stephenson
(→‎Calculus: missed e)
 
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This page lists links to entries identified as [[CZ:Core_Articles]] in mathematics.
{{col-begin}}
{{col-break}}
{{rpl|Exponentiation}}
 
===Geometry===
{{rpl|Angle}}
*[[Circle (disambiguation)]]
*[[Sphere (disambiguation)]]
{{rpl|Cone}}
{{rpl|Differential geometry}}
{{rpl|Homology}}
{{rpl|Poincaré conjecture}}
 
===Calculus===
{{rpl|Trigonometry}}
{{rpl|Polar coordinate}}
{{rpl|Limit}}
{{rpl|Differential calculus}}
{{rpl|Jacobian matrix}}
{{rpl|Fundamental Theorem of Calculus}}
{{rpl|Convolution}}
 
===Analysis===
*[[Analysis (disambiguation)]]
{{rpl|Mean value theorem}}
{{rpl|Taylor's theorem}}
{{rpl|Harmonic analysis}}
{{rpl|Harmonic function}}
{{rpl|Laplace transform}}
{{rpl|Jensen's inequality}}
{{rpl|Borel measure}}
{{rpl|Lebesgue measure}}
{{rpl|Lebesgue integral}}
{{rpl|Riemann integral}}
 
===Complex analysis===
{{rpl|de Moivre's identity}}
{{rpl|Euler formula}}
{{rpl|Complex logarithm}}
{{rpl|Complex exponentiation}}
{{rpl|Cauchy–Riemann equations}}
{{rpl|Pole (mathematics)}}
{{rpl|Meromorphic function}}
*[[Residue (disambiguation)]]
{{rpl|Cauchy's integral theorem}}
{{rpl|Cauchy's integral formula}}
{{rpl|Contour integral}}
{{rpl|Analytic continuation}}
{{rpl|Riemann hypothesis}}
 
===Functional analysis===
{{rpl|Functional analysis}}
{{rpl|Lp space|L<sub>''p''</sub> space}}
{{rpl|Hölder's inequality}}
{{rpl|Tempered distribution}}
{{rpl|Sobolev space}}
{{rpl|Operator theory}}
*[[Adjoint (disambiguation)]]
{{rpl|Riesz representation theorem}}
{{col-break}}
 
===Differential equations===
{{rpl|Ordinary differential equation}}
{{rpl|Linear differential equation}}
{{rpl|First order ordinary differential equation}}
{{rpl|Laplace equation}}
{{rpl|Poisson's equation}}
{{rpl|Wave equation}}
{{rpl|Poisson kernel}}
{{rpl|Dirichlet problem}}
{{rpl|Boundary value problem}}
{{rpl|K-theory}}
 
===Algebra===
{{rpl|Quadratic form}}
{{rpl|Group representation}}
{{rpl|Field theory}}
{{rpl|Abel–Ruffini theorem}}
{{rpl|Lie group}}
 
===Linear algebra===
{{rpl|System of linear equations}}
{{rpl|Basis (mathematics)}}
 
===Matrix theory===
{{rpl|Matrix multiplication}}
*[[Determinant (disambiguation)]]
{{rpl|Spectral theorem}}
{{rpl|Stochastic matrix}}


Current status on the CZ progress scale: [[CZ:Core_Articles#Stages_of_development|Stage 3]]
===Set theory===
{{rpl|Russell's paradox}}
{{rpl|Banach–Tarski paradox}}
{{rpl|Continuum}}
*[[Function (disambiguation)]]
{{rpl|Bijection}}


: (10) = worth this number of points &nbsp; * = external, to replace or rewrite &nbsp;  ** = micro-stub
===Logic===
{{col-begin}}
{{rpl|Mathematical logic}}
{{col-break|width=33%}}
{{rpl|Mathematical proof}}  
#                                    [[Mathematics]] (10) *
{{rpl|Proof by contradiction}}
# <small>''Elementary''</small>      [[Number]] (10)
{{rpl|Gödel's incompleteness theorem}}
# <small>''Elementary''</small>      [[Integer]] *
{{rpl|Philosophy of mathematics}}
# <small>''Elementary''</small>      [[Fraction (mathematics)|Fraction]] (2)
 
# <small>''Elementary''</small>      [[Addition]] (2)
===Probability===
# <small>''Elementary''</small>      [[Multiplication]]
{{rpl|Probability theory}}  
# <small>''Elementary''</small>      [[Exponentiation]]
{{rpl|Statistical hypothesis testing}}
# <small>''Elementary''</small>      [[Rational function]]
{{rpl|Mean}}
# <small>''Elementary''</small>      [[Linear equation]]
{{rpl|Variance}}
# <small>''Elementary''</small>      [[Quadratic equation]] (2)
{{rpl|Moment (mathematics)}}
# <small>''Elementary''</small>      [[Cubic equation]]
{{rpl|Moment-generating function}}
# <small>''Geometry''</small>        [[Angle]]
{{rpl|Central limit theorem}}
# <small>''Geometry''</small>        [[Triangle]]
{{rpl|Cauchy distribution}}
# <small>''Geometry''</small>        [[Circle]] (5)
{{rpl|Stochastic calculus}}
# <small>''Geometry''</small>        [[Pythagorean theorem|Pythagoras' theorem]]
{{rpl|Itô calculus}}
# <small>''Geometry''</small>        [[Conic sections]]
{{rpl|Stochastic differential equation}}
# <small>''Geometry''</small>        [[Parabola]]
{{rpl|Chapman–Kolmogorov equation}}
# <small>''Geometry''</small>        [[Sphere]]
{{rpl|Lévy process}}
# <small>''Geometry''</small>        [[Cone]]
{{rpl|Poisson process}}
# <small>''Geometry''</small>        [[Platonic solid]]
*[[Random walk (disambiguation)]]
# <small>''Geometry''</small>        [[Euclidean geometry]] (2) **
 
# <small>''Geometry''</small>        [[Differential geometry]]
===Applied===
# <small>''Geometry''</small>        [[Algebraic geometry]]
{{rpl|Dynamical system}}
# <small>''Geometry''</small>        [[Homology]]
{{rpl|Ergodic theory}}
# <small>''Geometry''</small>        [[Poincaré conjecture]] (2)
{{rpl|Mathematical model}}
#                                    [[Topology]] (5)
{{rpl|Variational calculus}}
# <small>''Topology''</small>        [[Borel set]]
# <small>''Topology''</small>        [[Cantor set]] (2)
# <small>''Calculus''</small>        [[Trigonometry]]
# <small>''Calculus''</small>        [[Trigonometric function]] *
# <small>''Calculus''</small>        [[Inverse trigonometric function]]
# <small>''Calculus''</small>        [[Cartesian coordinates]]
# <small>''Calculus''</small>        [[Polar coordinate]]
# <small>''Calculus''</small>        [[e (mathematics)|e]]
# <small>''Calculus''</small>        [[Exponential function]]
# <small>''Calculus''</small>        [[Special functions]]
# <small>''Calculus''</small>        [[Limit]] (5)
# <small>''Calculus''</small>        [[Differential calculus]]
# <small>''Calculus''</small>        [[Derivative]] (5)
# <small>''Calculus''</small>        [[Chain rule]]
# <small>''Calculus''</small>        [[Partial derivative]]
# <small>''Calculus''</small>        [[Jacobian matrix]]
# <small>''Calculus''</small>        [[Fundamental Theorem of Calculus]]
# <small>''Calculus''</small>        [[Convolution]]
#                                    [[Analysis]] (2)
# <small>''Analysis''</small>        [[Mean value theorem]]
# <small>''Analysis''</small>        [[Taylor's theorem]]
# <small>''Analysis''</small>        [[Harmonic analysis]]
# <small>''Analysis''</small>        [[Harmonic function]]
# <small>''Analysis''</small>        [[Fourier transform]]
# <small>''Analysis''</small>        [[Laplace transform]]
# <small>''Analysis''</small>        [[Jensen's inequality]]
# <small>''Analysis''</small>        [[Approximation theory]]
# <small>''Analysis''</small>        [[Borel measure]]
# <small>''Analysis''</small>        [[Lebesgue measure]]
# <small>''Analysis''</small>        [[Lebesgue integral]]
# <small>''Analysis''</small>        [[Riemann integral]] (2)
# <small>''Compl. anal.''</small>    [[de Moivre's identity]]
# <small>''Compl. anal.''</small>    [[Euler formula]] (5)
# <small>''Compl. anal.''</small>    [[Complex logarithm]]
# <small>''Compl. anal.''</small>    [[Complex exponentiation]]
# <small>''Compl. anal.''</small>    [[Holomorphic function]] (2)
# <small>''Compl. anal.''</small>    [[Cauchy–Riemann equations]]
# <small>''Compl. anal.''</small>    [[Pole (mathematics)]]
# <small>''Compl. anal.''</small>    [[Meromorphic function]]
# <small>''Compl. anal.''</small>    [[Residue]]
{{col-break|width=33%}}
# <small>''Compl. anal.''</small>    [[Cauchy's integral theorem]]
# <small>''Compl. anal.''</small>    [[Cauchy's integral formula]]
# <small>''Compl. anal.''</small>    [[Contour integral]]
# <small>''Compl. anal.''</small>    [[Analytic continuation]]
# <small>''Compl. anal.''</small>    [[Riemann hypothesis]] (2)
#                                    [[Functional analysis]] (2)
# <small>''Func. anal.''</small>      [[Banach space]]
# <small>''Func. anal.''</small>      [[Hilbert space]]
# <small>''Func. anal.''</small>      [[Lp space|L<sub>''p''</sub> space]]
# <small>''Func. anal.''</small>      [[Hölder's inequality]]
# <small>''Func. anal.''</small>      [[Dirac delta function]]
# <small>''Func. anal.''</small>      [[Distribution (mathematics)]]
# <small>''Func. anal.''</small>      [[Tempered distribution]]
# <small>''Func. anal.''</small>      [[Sobolev space]]
# <small>''Func. anal.''</small>      [[Operator theory]]
# <small>''Func. anal.''</small>      [[Dual space]]
# <small>''Func. anal.''</small>      [[Adjoint]]
# <small>''Func. anal.''</small>      [[Self-adjoint operator]]
# <small>''Func. anal.''</small>      [[Riesz representation theorem]]
# <small>''Func. anal.''</small>      [[Baire category theorem]]
# <small>''Diff. eqns''</small>      [[Ordinary differential equation]] (5)
# <small>''Diff. eqns''</small>      [[Linear differential equation]]
# <small>''Diff. eqns''</small>      [[First order ordinary differential equation]]
# <small>''Diff. eqns''</small>      [[Partial differential equation]] (2)
# <small>''Diff. eqns''</small>      [[Laplace equation]]
# <small>''Diff. eqns''</small>      [[Poisson's equation]]
# <small>''Diff. eqns''</small>      [[Wave equation]]
# <small>''Diff. eqns''</small>      [[Poisson kernel]]
# <small>''Diff. eqns''</small>      [[Dirichlet problem]]
# <small>''Diff. eqns''</small>      [[Boundary value problem]]
#                                    [[K-theory]]
#                                    [[Category theory]]
#                                    [[Algebra]] (2)
# <small>''Algebra''</small>          [[Cauchy-Schwarz inequality]]
# <small>''Algebra''</small>          [[Quadratic form]]
# <small>''Algebra''</small>          [[Group (mathematics)]] (5) *
# <small>''Algebra''</small>          [[Permutation group]]
# <small>''Algebra''</small>          [[Group representation]]
# <small>''Algebra''</small>          [[Abelian group]] -- [[User:Barry R. Smith|Barry R. Smith]]
# <small>''Algebra''</small>          [[Field theory]]
# <small>''Algebra''</small>          [[Galois theory]]
# <small>''Algebra''</small>          [[Abel–Ruffini theorem]]
# <small>''Algebra''</small>          [[Lie group]]
# <small>''Algebra''</small>          [[Lie algebra]]
#                                    [[Linear algebra]]
# <small>''Linear alg.''</small>      [[System of linear equations]] (2)
# <small>''Linear alg.''</small>      [[Gaussian elimination]]
# <small>''Linear alg.''</small>      [[Gram-Schmidt orthogonalization]]
# <small>''Linear alg.''</small>      [[Basis (mathematics)]] (2)
# <small>''Matrix theory''</small>    [[Matrix]]
# <small>''Matrix theory''</small>    [[Matrix multiplication]]
# <small>''Matrix theory''</small>    [[Matrix inverse]]
# <small>''Matrix theory''</small>    [[Determinant]]
# <small>''Matrix theory''</small>    [[Eigenvalue]]
# <small>''Matrix theory''</small>    [[Spectral theorem]]
# <small>''Matrix theory''</small>    [[Stochastic matrix]]
#                                    [[Set theory]] (2)
# <small>''Set theory''</small>      [[Union]]
# <small>''Set theory''</small>      [[Intersection]]
# <small>''Set theory''</small>      [[Cartesian product]]
# <small>''Set theory''</small>      [[Equivalence relation]] (10)
# <small>''Set theory''</small>      [[Supremum]] and [[infimum]]
# <small>''Set theory''</small>      [[Russell's paradox]]
# <small>''Set theory''</small>      [[Banach–Tarski paradox]]
# <small>''Set theory''</small>      [[Continuum]]
# <small>''Set theory''</small>      [[Continuum hypothesis]]
{{col-break|width=33%}}
# <small>''Set theory''</small>      [[Axiom of choice]]
# <small>''Set theory''</small>      [[Cardinality]] - [[User:Ashley J. Ballard|Ashley J. Ballard]]
# <small>''Set theory''</small>      [[Aleph-0]]
# <small>''Set theory''</small>      [[Function]] (5)
# <small>''Set theory''</small>      [[Bijection]]
# <small>''Set theory''</small>      [[Function composition]]
# <small>''Set theory''</small>      [[Inverse function]]
#                                    [[Mathematical logic]]
# <small>''Logic''</small>            [[Mathematical proof]] (10)
# <small>''Logic''</small>            [[Proof by contradiction]]
# <small>''Logic''</small>            [[Gödel's incompleteness theorem]]
# <small>''Logic''</small>            [[Boolean algebra]]
# <small>''Logic''</small>            [[Philosophy of mathematics]] (2)
#                                    [[Probability theory]] (5)
# <small>''Probability''</small>      [[Statistics]] (2)
# <small>''Probability''</small>      [[Statistical hypothesis testing]]
# <small>''Probability''</small>      [[Mean]] (2)
# <small>''Probability''</small>      [[Variance]]
# <small>''Probability''</small>      [[Covariance]]
# <small>''Probability''</small>      [[Moment (mathematics)]]
# <small>''Probability''</small>      [[Moment-generating function]]
# <small>''Probability''</small>      [[Bayes Theorem]]
# <small>''Probability''</small>      [[Central limit theorem]]
# <small>''Probability''</small>      [[Cauchy distribution]]
# <small>''Probability''</small>      [[Normal distribution]] *
# <small>''Probability''</small>      [[Stochastic calculus]]
# <small>''Probability''</small>      [[Itô calculus]]
# <small>''Probability''</small>      [[Stochastic differential equation]]
# <small>''Probability''</small>      [[Chapman–Kolmogorov equation]]
# <small>''Probability''</small>      [[Stochastic process]] *
# <small>''Probability''</small>      [[Martingale]]
# <small>''Probability''</small>      [[Lévy process]]
# <small>''Probability''</small>      [[Markov chain]]
# <small>''Probability''</small>      [[Poisson process]]
# <small>''Probability''</small>      [[Random walk]]
# <small>''Applied''</small>          [[Dynamical system]]
# <small>''Applied''</small>          [[Ergodic theory]]
# <small>''Applied''</small>          [[Game theory]]
# <small>''Applied''</small>          [[Mathematical model]] (5)
# <small>''Applied''</small>          [[Numerical analysis]]
# <small>''Applied''</small>          [[Optimization (mathematics)]]
# <small>''Applied''</small>          [[Variational calculus]]
#                                    [[Discrete mathematics]]
# <small>''Discr. maths''</small>    [[Graph theory]] (2)
# <small>''Discr. maths''</small>    [[Four color theorem]]
# <small>''Discr. maths''</small>    [[Binomial coefficient]]
# <small>''Discr. maths''</small>    [[Ramsey theory]]
# <small>''Number theory''</small>    [[Perfect number]] -- [[User:Barry R. Smith|Barry R. Smith]]
# <small>''Number theory''</small>    [[Modular arithmetic]] -- [[User:Barry R. Smith|Barry R. Smith]]
# <small>''Number theory''</small>    [[Chinese remainder theorem]]
# <small>''Number theory''</small>    [[Fermat's last theorem]] (2) -- [[User:Barry R. Smith|Barry R. Smith]]
#                                    [[History of mathematics]] (10)
# <small>''History''</small>          [[Augustin Louis Cauchy]]
# <small>''History''</small>          [[Pierre-Simon Laplace]]
# <small>''History''</small>          [[Joseph Fourier]]
# <small>''History''</small>          [[Euclid]]
# <small>''History''</small>          [[Leonhard Euler]]
# <small>''History''</small>          [[Carl Friedrich Gauss]]
# <small>''History''</small>          [[David Hilbert]]
# <small>''History''</small>          [[Gottfried Leibniz]]
# <small>''History''</small>          [[Bernhard Riemann]]
# <small>''History''</small>          [[John von Neumann]]
# <small>''History''</small>          [[Blaise Pascal]]
# <small>''History''</small>          [[Siméon Denis Poisson]]
# <small>''History''</small>          [[Henri Poincaré]]
# <small>''History''</small>          [[Fields medal]]
{{col-end}}


'''Already-written core articles in this workgroup'''
===History===
:(Core Article points not available for these articles.)
{{rpl|History of mathematics}}
{{col-begin}}
{{rpl|Augustin Louis Cauchy}}
{{col-break|width=33%}}
{{rpl|Pierre-Simon Laplace}}
# <small>''Elementary''</small>      [[Logarithm]]
{{rpl|David Hilbert}}
# <small>''Elementary''</small>      [[Real number]]
{{rpl|Gottfried Leibniz}}
# <small>''Elementary''</small>      [[Polynomial]]
{{rpl|John von Neumann}}
# [[Geometry]]
{{rpl|Siméon Denis Poisson}}
# <small>''Geometry''</small>        [[Line (geometry)]]
{{rpl|Henri Poincaré}}
# <small>''Geometry''</small>        [[Manifold (geometry)]]
{{rpl|Fields medal}}
# <small>''Geometry''</small>        [[Elliptic curve]]
{{col-break}}
# <small>''Topology''</small>        [[Open set]]
# <small>''Topology''</small>        [[Compact set]]
# <small>''Topology''</small>        [[Continuity]]
{{col-break|width=33%}}
# <small>''Topology''</small>        [[Topological space]]
# <small>''Calculus''</small>        [[Integral]]
# <small>''Calculus''</small>        [[Pi]]
# <small>''Analysis''</small>        [[Sequence]]
# <small>''Analysis''</small>        [[Series (mathematics)]]
# <small>''Analysis''</small>        [[Fundamental Theorem of Algebra]]
# <small>''Analysis''</small>        [[Measure (mathematics)]]
# [[Complex analysis]]
# <small>''Compl. anal.''</small>    [[Complex number]]
{{col-break|width=33%}}
# [[Differential equation]]
# <small>''Algebra''</small>          [[Ring (mathematics)]]
# <small>''Linear alg.''</small>      [[Vector space]]
# <small>''Set theory''</small>      [[Set]]
# <small>''Logic''</small>            [[Mathematical induction]]
# [[Number theory]]
# <small>''Number theory''</small>    [[Prime number]]
# <small>''Applied''</small>          [[Cryptography]]
# <small>''Applied''</small>          [[Fractal]]
{{col-break|width=33%}}
{{col-end}}
{{col-end}}

Latest revision as of 14:25, 31 October 2014

Geometry

Calculus

Analysis

Complex analysis

Functional analysis

Differential equations

Algebra

Linear algebra

Matrix theory

Set theory

Logic

Probability

Applied

History