Lists of mathematics topics

Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions.The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.Processing of such signals includes filtering, storage and reconstruction, separation of information from noise, compression, and feature extraction.Statistics, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics).It has applications in a variety of fields, including economics, anthropology, political science, social psychology and military strategy.Operations research is the study and use of mathematical models, statistics, and algorithms to aid in decision-making, typically with the goal of improving or optimizing the performance of real-world systems.Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.
Mathematics
Fourier series approximation of square wave in five steps.
Ford circles —A circle rests upon each fraction in lowest terms. Each touches its neighbors without crossing.
Venn diagrams are illustrations of set theoretical, mathematical or logical relationships.
Phase portrait of a continuous-time dynamical system, the Van der Pol oscillator .
Ray tracing is a process based on computational mathematics .
The "bell curve"—the probability density function of the normal distribution .
mathematicsMathematics Subject ClassificationAmerican Mathematical SocietyMathematical ReviewsZentralblatt MATHlist of exponential topicslist of factorial and binomial topicsOutline of arithmeticOutline of discrete mathematicsList of calculus topicsList of geometry topicsOutline of geometryList of trigonometry topicsOutline of trigonometryList of trigonometric identitiesList of logarithmic identitiesList of integrals of logarithmic functionsList of set identities and relationsList of topics in logicAreas of mathematicsGlossary of areas of mathematicsPure mathematicsAlgebraOutline of algebraGlossary of field theoryGlossary of group theoryGlossary of linear algebraGlossary of ring theoryList of abstract algebra topicsList of algebraic structuresList of Boolean algebra topicsList of category theory topicsList of cohomology theoriesList of commutative algebra topicsList of homological algebra topicsList of group theory topicsList of representation theory topicsList of linear algebra topicsList of reciprocity lawsFourier seriesCalculusAnalysisGlossary of tensor theoryList of complex analysis topicsList of functional analysis topicsList of vector spaces in mathematicsList of integration and measure theory topicsList of harmonic analysis topicsList of Fourier analysis topicsList of mathematical seriesList of multivariable calculus topicsList of q-analogsList of real analysis topicsList of variational topicsFord circlesGeometryTopologyGlossary of differential geometry and topologyGlossary of general topologyGlossary of Riemannian and metric geometryGlossary of scheme theoryList of algebraic geometry topicsList of algebraic surfacesList of algebraic topology topicsList of circle topicsList of topics related to piList of curves topicsList of differential geometry topicsList of general topology topicsList of geometric shapesList of geometric topology topicsList of knot theory topicsList of Lie group topicsList of mathematical properties of pointsList of topology topicsList of topologiesTopological propertyList of triangle topicsCombinatoricsdiscretefiniteenumerative combinatoricscombinatorial designsmatroidextremal combinatoricscombinatorial optimizationalgebraicalgebraic combinatoricsOutline of combinatoricsGlossary of graph theoryList of graph theory topicsVenn diagramsmathematical logicList of first-order theoriesList of large cardinal propertiesList of mathematical logic topicsList of set theory topicsGlossary of order theoryNumber theoryprime numberList of algebraic number theory topicsList of number theory topicsList of recreational number theory topicsGlossary of arithmetic and Diophantine geometryList of prime numbersList of zeta functionsVan der Pol oscillatordifferential equationdynamical systemList of dynamical systems and differential equations topicsList of nonlinear partial differential equationsList of partial differential equation topicsMathematical physicsList of mathematical topics in classical mechanicsList of mathematical topics in quantum theoryList of mathematical topics in relativityList of string theory topicsIndex of wave articlesRay tracingcomputational mathematicscomputer sciencescientific computingList of algorithm general topicsList of computability and complexity topicsList of combinatorial computational geometry topicsList of computer graphics and descriptive geometry topicsList of numerical computational geometry topicsList of computer vision topicsList of formal language and literal string topicsList of numerical analysis topicsList of terms relating to algorithms and data structuresInformation theoryapplied mathematicssocial scienceinformationcommunicatingSignal processingsignalsimagesfilteringcompressionfeature extractionList of algebraic coding theory topicsList of information theory topicsnormal distributionLists of statistics topicsProbability theorymathematical statisticsstatistical theoryStatisticsCatalog of articles in probability theoryList of probability topicsList of stochastic processes topicsList of probability distributionsList of statistics topicsOutline of regression analysisGame theorymodelseconomicsanthropologypolitical sciencesocial psychologymilitary strategyGlossary of game theoryList of games in game theoryOperations researchList of knapsack problemsList of network theory topicsList of graphical methodsList of mathematics-based methodsList of rules of inferencepropositionList of algorithmsList of axiomsList of conjecturesList of conjectures by Paul ErdősCombinatorial principlesList of equationsList of formulae involving piList of representations of eList of inequalitiesList of lemmasList of mathematical identitiesList of mathematical proofsList of theoremsList of convexity topicsList of dualitiesList of exceptional set conceptsList of fractal topicsList of logarithm topicsList of numeral system topicsList of order topicsList of partition topicsList of permutation topicsList of polynomial topicsList of properties of sets of realsList of transformsspacesList of mathematical examplesList of curvesList of complex reflection groupsList of complexity classesList of examples in general topologyList of finite simple groupsList of Fourier-related transformsList of manifoldsList of mathematical constantsList of mathematical functionsList of mathematical knots and linksList of mathematical shapesList of mathematical spacesList of matricesList of numbersList of polygons, polyhedra and polytopesList of regular polytopesList of simple Lie groupsList of small groupsList of special functions and eponymsList of surfacesTable of Lie groupsScientific equations named after peopleList of letters used in mathematics and scienceList of mathematical societiesList of mathematics competitionsList of mathematics history topicsList of publications in mathematicsList of mathematics journalsList of mathematiciansMathematicianstheoretical physicsList of films about mathematiciansList of game theoristsList of geometersList of logiciansList of mathematical probabilistsList of statisticiansList of things named after Niels Henrik AbelList of things named after George AiryList of things named after Jean d'AlembertList of things named after ArchimedesList of things named after Vladimir ArnoldList of things named after Emil ArtinList of things named after Stefan BanachList of things named after Thomas BayesList of things named after members of the Bernoulli familyList of things named after Jakob BernoulliList of things named after Friedrich BesselList of things named after Élie CartanList of things named after Augustin-Louis CauchyList of things named after Arthur CayleyList of things named after Pafnuty ChebyshevList of things named after John Horton ConwayList of things named after Richard DedekindList of things named after Pierre DeligneList of things named after Peter Gustav Lejeune DirichletList of things named after Albert EinsteinList of things named after EuclidList of things named after Leonhard EulerList of things named after Paul ErdősList of things named after Pierre de FermatList of things named after FibonacciList of things named after Joseph FourierList of things named after Erik FredholmList of things named after Ferdinand Georg FrobeniusList of things named after Carl Friedrich GaussList of things named after Évariste GaloisList of things named after Hermann GrassmannList of things named after Alexander GrothendieckList of things named after Jacques HadamardList of things named after William Rowan HamiltonList of things named after Erich HeckeList of things named after Eduard HeineList of things named after Charles HermiteList of things named after David HilbertList of things named after W. V. D. HodgeList of things named after Carl Gustav Jacob JacobiList of things named after Johannes KeplerList of things named after Felix KleinList of things named after Joseph-Louis LagrangeList of things named after Johann LambertList of things named after Pierre-Simon LaplaceList of things named after Adrien-Marie LegendreList of things named after Gottfried LeibnizList of things named after Sophus LieList of things named after Joseph LiouvilleList of things named after Andrey MarkovList of things named after John MilnorList of things named after Hermann MinkowskiList of things named after John von NeumannList of things named after Isaac NewtonList of things named after Emmy NoetherList of things named after Henri PoincaréList of things named after Siméon Denis PoissonList of things named after PythagorasList of things named after Srinivasa RamanujanList of things named after Bernhard RiemannList of things named after Issai SchurList of things named after Anatoliy SkorokhodList of things named after George Gabriel StokesList of things named after Jean-Pierre SerreList of things named after James Joseph SylvesterList of things named after Alfred TarskiList of things named after Alan TuringList of things named after Stanislaw UlamList of things named after Karl WeierstrassList of things named after André WeilList of things named after Hermann WeylList of things named after Norbert WienerList of things named after Ernst WittList of mathematical reference tablesList of moments of inertiaTable of derivativesintegralLists of integralsList of integrals of exponential functionsList of integrals of hyperbolic functionsList of integrals of inverse hyperbolic functionsList of integrals of inverse trigonometric functionsList of integrals of irrational functionsList of integrals of rational functionsList of integrals of trigonometric functionsList of mathematics education journalsGlossary of mathematical symbolsList of important publications in mathematicsList of important publications in statisticsList of mathematical theoriesList of mathematics categoriesList of mathematical symbols by subjectTable of logic symbolsTable of mathematical symbolsOutline of mathematicsTimeline of women in mathematicsLists of unsolved problems in mathematicsList of order theory topicsList of topics related to πHistoryTimelineFutureGlossaryFoundationsCategory theoryPhilosophy of mathematicsSet theoryType theoryAbstractCommutativeElementaryGroup theoryLinearMultilinearUniversalHomologicalReal analysisComplex analysisHypercomplex analysisDifferential equationsFunctional analysisHarmonic analysisMeasure theoryGraph theoryOrder theoryAnalyticArithmeticDifferentialEuclideanAlgebraic number theoryAnalytic number theoryDiophantine geometryGeneralGeometricHomotopy theoryAppliedEngineering mathematicsMathematical biologyMathematical chemistryMathematical economicsMathematical financeMathematical psychologyMathematical sociologyProbabilitySystems scienceControl theoryComputationalTheory of computationComputational complexity theoryNumerical analysisOptimizationComputer algebraInformal mathematicsFilms about mathematiciansRecreational mathematicsMathematics and artMathematics education