Wikipedia:WikiProject Wikislice/Mathematics

About mathematics

Mathematics is the study of patterns, including concepts such as quantity, structure, space, uncertainty, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of positions, shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.

General information

Mathematicians

History and Terminology

ABS - ARG - Abel Prize - Almost everywhere - Almost surely - Alternating group - Amplitude - Arithmetic - Array - Asterisk - BETA - Babylonian numerals - Backslash - Bar - Bar chart - Base - Basis - Belly - Bernoulli distribution - Beta - Beta distribution - Binomial - Binomial distribution - Bracket - CDF - CSC - Cartesian - Catalan number - Cauchy distribution - Ceiling - Cellular automaton - Characteristic - Cholesky decomposition - Circulant matrix - Circumflex - Class - Coefficient - Coker - Cole Prize - Colon - Comma - Complement - Composite number - Condition - Congruence - Conjecture - Conjugate transpose - Conjunctive normal form - Continued fraction - Contract - Corollary - Cos - Criterion - Cyclic group - Cylinder - DT - Dagger - Dash - Decade - Decimal - Decomposition - Definition - Degree - Del - Derivation - Derivative - Diagram - Diesis - Digit - Digit sum - Dihedral group - Discriminant - Domain - Dot - Dozen - Elements - Equality - Equation - Eternity - Euclidean algorithm - Euler's theorem - Exponential distribution - Exponentiation - Expression - Factor - Factorial - Family - Fermat's theorem - Fibonacci - Fields Medal - Flat - Floor function - Formula - Fourier - Gallows - Gamma - Gamma distribution - Gaussian elimination - Geometric distribution - Geometric mean - Golden ratio - Googol - Googolplex - Greek numerals - Growth - Hamiltonian path - Harmonic - Harmonic mean - Hat - Head - Heap - Hermitian matrix - Heuristic - Histogram - Homology - Huffman coding - Hyphen - Hypothesis - IFF - IM - Identity - Identity matrix - Index - Infimum - Infinity - Intersection - Interval - Inverse function - Irreducible polynomial - Ishango bone - Jacobi symbol - Jacobian - Kronecker delta - Kronecker product - Kurtosis - Laplace distribution - Life - Limit - Linear programming - Logistic distribution - Loop - MAX - Macron - Main diagonal - Mathematics - Matrix - Max - Mean - Median - Mega - Method - Method of exhaustion - Min - Minimal polynomial - Minor - Mnemonic - Mod - Modulus - Monad - Moser - Moving average - Multi-index notation - Multiplication sign - Multiplicative order - Multiplicity - ND - Nabla - Nest - Nevanlinna Prize - Newton's method - Nor - Norm - Normal distribution - Normal matrix - Not - Notation - O - Obelus - Octave - Order - Order of magnitude - Orthogonal matrix - Parallel - Parameter - Pareto distribution - Pascal's Wager - Percent sign - Permanent - Pi - Pie chart - Poisson distribution - Polyhedron - Polynomial - Power - Power set - Prime - Prime number - Principle - Problem - Procedure - Proposition - Q.E.D. - QR decomposition - Quadrature - Quadrivium - Quantity - Quarter - Quartet - Quaternion - Quintet - Quotient - Radical - Rayleigh distribution - Re - Reverse Polish notation - Roman numerals - Rotation matrix - Round - Rule - Run-length encoding - SIN - Scientific notation - Secant method - Semicolon - Sigma - Sign - Signature - Sin - Skewness - Sorites paradox - Spectrum - Sphere - Standard deviation - Star - Supremum - Symmetric difference - Symmetric group - Symmetric matrix - Symplectic group - Tail - Tan - Tau - Technique - Thue-Morse sequence - Tilde - Transpose - Triad - Triangular distribution - Trigonometry - Trivium - Truth table - Tuple - Turing machine - Underscore - Uniform distribution - Union - Unitary matrix - Universal Turing machine - Variable - Variance - Vertex - Vertical - Weibull distribution - Weight - Wolf Prize - Zeta

Algebra

Abel's theorem - Abstract algebra - Algebra - Algebraic closure - Algebraic curve - Algebraic element - Algebraic equation - Algebraic extension - Algebraic geometry - Algebraic integer - Algebraic number - Algebraic number field - Alphabet - Artinian ring - Astroid - Binomial - CURL - Chain complex - Checksum - Cissoid of Diocles - Clifford algebra - Code - Coding theory - Coefficient - Column vector - Commutative diagram - Commutative ring - Completing the square - Cross - Cross product - Cubic equation - Curl (mathematics) - Cyclic redundancy check - Dedekind domain - Del - Direction - Directional derivative - Discriminant - Divergence - Divergence theorem - Dot product - Dual number - Eisenstein integer - Ellipse - Elliptic curve - Endomorphism - Euclidean domain - Exact sequence - Exterior algebra - Factorization - Field - Field of fractions - Filtration - Finite field - Free module - Galois theory - Global field - Gradient - Gray code - Green's theorem - Hadamard matrix - Hamming code - Hilbert's Nullstellensatz - Homogeneous polynomial - Homological algebra - Homology - Huffman coding - Hyperbola - Hypercomplex number - Ideal - Integral domain - Invariant - Inverse limit - Irreducible polynomial - Jerk - Kernel - Lemniscate - Letter - Linear algebra - Linear code - Linear equation - Linear independence - Local ring - Localization - Module - Monomial - Nabla - Noetherian ring - Noise - Null vector - Octonion - Orthogonal polynomials - PID - Parabola - Parallelogram law - Perpendicular - Polynomial - Polynomial ring - Prime ideal - Primorial - Principal ideal - Principal ideal domain - Pseudoscalar - Pseudovector - Quadratic equation - Quadratic form - Quartic equation - Quaternion - Quintic equation - Quotient ring - Rank-nullity theorem - Rational function - Ray - Regular local ring - Regulator - Resolution - Resultant - Riemann surface - Ring - Ring homomorphism - Root of unity - Scalar - Scalar field - Scheme - Semicubical parabola - Semiring - Separable extension - Simultaneous equations - Speed - Spinor - Split - Splitting field - Stochastic matrix - Surface integral - Symmetric polynomial - Syzygy - Term - Trinomial - Trivial ring - Turbine - UPC - Unit - Unit ring - Unit vector - Universal Product Code - Variable - Vector - Vector field - Vector potential - Vector space - Waring's problem - Wavelet - Zero divisor

Calculus and Analysis

Abel's theorem - Absolute value - Action - Additive function - Affine space - Algebraic element - Algebraic function - Almost surely - Analysis - Analytic continuation - Argument - Arithmetic function - Arithmetic-geometric mean - Atlas - Baire category theorem - Baire space - Banach algebra - Banach fixed point theorem - Banach space - Bifurcation - Bifurcation theory - Bilinear form - Binomial - Bounded operator - Bra - Brouwer fixed point theorem - Calculus of variations - Cantor set - Cascade - Catastrophe theory - Character - Closed graph theorem - Codimension - Codomain - Coefficient - Cohomology - Compact operator - Complete metric space - Complex system - Conjugate transpose - Convergence - Convolution - Cubic equation - Current - Derivation - Diffeomorphism - Differential - Differential form - Dirac delta function - Dissipative system - Domain - Dual space - Dynamical system - Egorov's theorem - Eigenfunction - Elementary function - Energy - Exact differential - Factorization - Fatou's lemma - Fourier series - Fractional calculus - Function - Function space - Functional analysis - Functional equation - Heaviside step function - Hilbert space - Homogeneous function - Homogeneous polynomial - Image - Implicit function - Inequality - Injection - Inner product space - Inverse function - Involution - Irreducible polynomial - Island - Jensen's inequality - Jordan measure - Ket - Lebesgue measure - Legendre transformation - Linear function - Linear functional - Logistic map - Lorenz attractor - Lusin's theorem - MAP - Manifold - Map - Markov's inequality - Maxima and minima - Measurable function - Measure - Monomial - Morse theory - Multiplicative function - Multiplicity - Multiplier algebra - Multivalued function - Newton's method - Norm - One-form - Open mapping theorem - Operand - Operation - Operator - Orthogonal polynomials - Oscillation - Partition of unity - Period - Periodic function - Phase space - Phase transition - Plateau's problem - Pointwise convergence - Pole - Polyhedron - Polynomial - Polynomial ring - Powers - Quartic equation - Quintic equation - ROOT - Rational function - Real analysis - Removable singularity - Resultant - Riemann hypothesis - Riemann sphere - Riemann zeta function - Riemannian geometry - Riemannian manifold - Root - SEED - Seed - Singularity - Smooth function - Spectral theorem - Spherical harmonics - Square wave - Stability - State - Step function - Stokes' theorem - Symmetric polynomial - Symplectic manifold - Tangent - Term - Topological manifold - Topological vector space - Transcendental function - Triangle inequality - Triangle wave - Trinomial - Unary operation - Value - Variable - Variation - Von Neumann algebra - World line - Young's inequality

Applied Mathematics

Discrete Mathematics

Geometry

Number Theory

Number theory -

Algebraic number theory -

Analytic number theory -

Arithmetic -

Numbers -

Natural numbers -

Prime numbers -

Rational numbers -

Algebraic numbers -

Fundamental theorem of arithmetic -

Algebraic integer - Algebraic number - Algebraic number theory - Analytic number theory - Associative array - Cantor set - Casting out nines - Cauchy sequence - Chinese remainder theorem - Class field theory - Congruence - Continued fraction - Coprime - Dedekind domain - Digit - Diophantine equation - Diophantine set - Discrete logarithm - Divisor - Divisor function - Dragon curve - Elliptic curve - Endomorphism - Ergodic theory - Euclidean algorithm - Fermat's last theorem - Fermat's little theorem - Fermat's theorem - Gelfond's constant - Generating function - Global field - Golden ratio - Greatest common divisor - Integer - Integer sequence - Irrational number - Khinchin's constant - Knapsack problem - Large numbers - Least common multiple - Least significant bit - Legendre symbol - Liouville number - Lychrel number - Markov number - Mod - Modular arithmetic - Modulus - Multiplicative order - Normal number - Number theory - Parity (mathematics) - Pi - Prime number theorem - Pythagorean triple - Quadratic residue - Quotient - Rational number - Real number - Rounding - Semicubical parabola - Sequence - Square root of 2 - Square root of 3 - Subsequence - Subset sum problem - Thue-Morse sequence - Transcendental number - Waring's problem - Wilson's theorem - Wolstenholme's theorem - Zero

Probability and Statistics

Recreational Mathematics

Topology

Algebraic topology - Atlas - Baire category theorem - Baire space - Banach space - Borel measure - Boundary - Bounded set - Closed graph theorem - Closed set - Cohomology - Column space - Commutative diagram - Compact space - Compactness theorem - Complete metric space - Concave set - Connected space - Continuous function - Continuum - Convex function - Convex set - Cotangent bundle - Covering space - De Rham cohomology - Deformation - Deformation retract - Dendrite - Diffeomorphism - Dimension - Domain - Embedding - Euclidean space - Euler characteristic - Euler number - Fiber - Fiber bundle - Flat - Function space - Fundamental group - Genus - Geometric topology - Global field - Half-space (geometry) - Hilbert space - Homeomorphism - Homology - Homotopy - Injection - Interval - Isotope - Jordan curve theorem - Klein bottle - Lift - Local property - Low-dimensional topology - Manifold - Metric space - Minkowski space - Morse theory - Mutation - Net - Nerve - Normal space - Open set - Parallel transport - Partition of unity - Path - Phase space - Principal bundle - Product topology - Projective space - Quotient space - Region - Riemann sphere - Riemannian geometry - Riemannian manifold - Row space - Separable space - Sigma-algebra - Simplicial complex - n-skeleton - Sobolev space - Space - Species - Spectral theorem - Stokes' theorem - Stone-Weierstrass theorem - Surgery - Suspension - Symplectic manifold - Tangent bundle - Tangent space - Topological group - Topological manifold - Topological space - Topological vector space - Topology - Trivial topology - Urysohn's lemma - Vector bundle - Vector field - Vector space - Zariski topology