User:Arael2/wikislice-math

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 History of mathematics - Philosophy of mathematics - Mathematical notation - Mathematical beauty - Mathematics education - Areas of mathematics - Foundations of mathematics - Set theory - Naive set theory - Axiomatic set theory - Mathematical logic - Proof theory - Model theory - Category theory - Topos theory - Gödel's incompleteness theorems - Absorption law - Allegory - Axiom - Axiom of choice - Axiom of extensionality - Axiom of infinity - Borel measure - Boundary - Bounded set - Category - Category theory - Closed set - Commutative diagram - Complete metric space - Concave - Connected space - Continuous function - Convex - Convex function - Convex set - Covering space - De Morgan's laws - Direct product - Domain - Endomorphism - Epimorphism - Fiber - Functor - Fuzzy logic - Half-space (geometry) - Heredity - Hilbert's axioms - Homomorphism - Initial object - Injection - Interval - Isomorphism - Metric space - Model theory - Monomorphism - Morphism - NET - Object - Open - Open set - Parallel postulate - Postulate - Probability axioms - Region - Species - Topos - Trivial topology - Zariski topology Mathematicians Shatapatha Brahmana - Pythagoras - Aristotle - Euclid - Pingala - Archimedes - Zu Chongzhi - Surya Siddhanta - Abu Bakr al-Karaji - Scipione del Ferro - Bartholomaeus Pitiscus - Regiomontanus - François Vieta - René Descartes - John Napier - Gottfried Wilhelm Leibniz - Isaac Newton - Pierre de Fermat - Blaise Pascal - Leonhard Euler - Bernhard Riemann - Augustin-Louis Cauchy - Joseph_Fourier - Karl Weierstrass - George Boole - Niels Henrik Abel - Évariste Galois - Georg Cantor - David Hilbert - Srinivasa Aiyangar Ramanujan - Kurt Gödel 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 - 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 - 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 Action - Alpha-beta pruning - Anti-aliasing - Approximation theory - Auction - Bar chart - Bifurcation - Bifurcation theory - Carrying capacity - Cascade - Catastrophe theory - Chaos - Circulant matrix - Codimension - Complex system - Contour line - Control theory - Conway's Game of Life - Decision theory - Dissipative system - Duel - Dynamical system - Economics - Election - Electrical engineering - Endomorphism - Entropy - Ergodic theory - Filter - Finance - Game - Game theory - Generation - Genetic algorithm - Genetic programming - Growth - Hough transform - Information theory - Inverse problem - Island - Kalman filter - Life expectancy - Linear programming - Logistic map - Lorenz attractor - Mixed strategy - Monty Hall problem - Mutual information - Nash equilibrium - Nelder-Mead method - Noise - Nonlinear programming - Numerical integration - Nyquist frequency - Operations research - Optimization - Perfect information - Phase space - Phase transition - Pie chart - Population growth - Prisoner's dilemma - SEED - Safe - Sampling - Seed - Signal-to-noise ratio - Simulated annealing - Stability - Stochastic - Stochastic resonance - Strategy - Surreal number - Synergetics - Tabu search - Transfer function - Ultrafilter - Vector field - Vickrey auction - Voting - World line Discrete Mathematics Discrete mathematics - Combinatorics - Graph theory - Game theory - Discrete geometry - Theoretical computer science - Computability theory - Complexity theory - Information theory - Abstract machine - Alphabet - Alternating group - Ant - Automata theory - Automaton - Bracketing - Bravais lattice - Busy beaver - Catalan number - Catalan's constant - Cellular automaton - Checksum - Cluster - Code - Coding theory - Combinatorial optimization - Complex system - Concatenation - Cyclic group - Cyclic redundancy check - Dihedral group - Discrete mathematics - Encryption - Entropy - Enumeration - Experimental mathematics - Fibonacci number - Filter - Finite group - Galois group - General linear group - Graph coloring - Gray code - Hadamard matrix - Hamming code - Huffman coding - Information theory - Klein four-group - Langton's ant - Lattice - Letter - Life - Linear code - Logistic map - Machine - Monster group - Mutual information - Noise - Nyquist frequency - Oracle - PEG - Pell number - Permutation group - Pi - Pick's theorem - Ramsey theory - Recurrence relation - Sampling - Signal-to-noise ratio - Simple group - Stochastic resonance - Subset sum problem - Sylow theorems - Symbolic computation - Symmetric group - Theory of computation - Turing machine - UPC - Ultrafilter - Universal Product Code - Universal Turing machine - Virtual machine - Wireworld - Zero Geometry Analytic geometry - Angles - Antiquity - Arbelos - Axis - Azimuth - Bode plot - Brianchon's theorem - Cartesian - Center - Cissoid of Diocles - Concentric - Coordinate system - Cover - Dissection - Distance - Dual polyhedron - Elliptic geometry - Endomorphism - Ergodic theory - Eternity - Euclidean geometry - Geodesic - Geometry - Heptadecagon - Homogeneous coordinates - Hyperbolic geometry - Kepler conjecture - Locus - Midpoint - Non-Euclidean geometry - Noncommutative geometry - Origami - Perfect square - Pick's theorem - Planes - Point - Point at infinity - Quadrant - Quadrature - Real line - Reciprocal - Right-hand rule - Simplicity - Soma cube - Spherical trigonometry - Subset sum problem - Surveying - Symmetry - Tangram - Tomahawk - Triangulation - Visibility - Volume - Zenith 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 - 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 Absolute deviation - Almost surely - Analysis of variance - Bar chart - Bayes' theorem - Benford's law - Bernoulli trial - Birthday problem - Borel-Cantelli lemma - Central moment - Characteristic function - Class - Cluster analysis - Coin flipping - Coincidence - Conditional probability - Confidence interval - Correlation - Covariance - Domain - Error - Estimator - Event - Expected value - Experiment - Failure rate - Fence - Fisher information - Fisher's exact test - Frequency distribution - Hinge - Histogram - Hypothesis - Indicator - Jitter - Kolmogorov-Smirnov test - Kurtosis - Linear regression - Logistic regression - Markov chain - Markov process - Markov's inequality - Maximum likelihood - Mean - Median - Mode - Moment - Moving average - Multivariate normal distribution - NET - Neyman-Pearson lemma - Null hypothesis - Odds - Ogive - P-value - Percentile - Population - Precision - Probability - Probability axioms - Probability space - Quantile - Quartile - RMS - Random variable - Random walk - Redundancy - Regression - Run - Run-length encoding - Russian roulette - SEED - Sample - Sample size - Sample space - Sampling - Seed - Simpson's paradox - Skewness - Standard deviation - Statistic - Statistical dispersion - Statistical power - Statistics - Step - Stochastic - Stochastic matrix - Stochastic process - Tail - Time series - Variance - Wiener process - Zipf's law Recreational Mathematics Abelian group - Aliquot sequence - Banach space - Baseball - Bernoulli number - Bertrand's postulate - Bowling - Brun's constant - Busy beaver - Carmichael number - Constant - Cross product - Cube - Curve of constant width - Cylinder - Derivative - Dihedral group - Dissection - Eigenfunction - Epsilon - Eternity - Euler number - Fibonacci number - Finite group - Fraction - Geometry - Gilbreath's conjecture - Golf ball - Golomb ruler - Hadamard matrix - Hilbert space - Illusion - Jastrow illusion - Khinchin's constant - Latin square - Lemma - Limit - Mean - Mersenne prime - Milliard - Necker cube - Numerology - Optical illusion - Origami - Palindromic prime - Penrose triangle - Perfect number - Perfect square - Pi - Point - Pole - Prime number - Proof - Puzzle - Real line - Repunit - Ring - Rubik's Cube - Simple group - Smith number - Soma cube - Sophie Germain prime - Square number - Statistics - Sudoku - Tangram - Theorem - Topology - Tower of Hanoi - Triskaidekaphobia - Wall-Sun-Sun prime - Wieferich prime - Wilson prime - Zeno's paradoxes - Zorn's lemma Topology Algebraic topology - Anchor - Atlas - Baire category theorem - Baire space - Banach space - Borel measure - Boundary - Bounded set - CAP - Cap - Closed graph theorem - Closed set - Cohomology - Column space - Commutative diagram - Compact space - Compactness theorem - Complete metric space - Concave - Connected space - Continuous function - Continuum - Convex - 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 - Free - Function space - Fundamental group - Gadget - Genus - Geometric topology - Global - Half-space (geometry) - Heredity - Hilbert space - Hole - Homeomorphism - Homology - Homotopy - Injection - Interval - Isotope - Jordan curve theorem - Klein bottle - Lift - Local - Low-dimensional topology - Machine - Manifold - Metric space - Minkowski space - Morse theory - Mutation - NET - Nerve - Normal space - Open - Open set - Parallel transport - Partition of unity - Path - Phase space - Plumbing - Principal bundle - Product topology - Projective space - Quotient space - Region - Riemann sphere - Riemannian geometry - Riemannian manifold - Row space - Separable space - Sigma-algebra - Simplicial complex - 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 - Zip