This is a list of theorems, by Wikipedia page. See also

• list of fundamental theorems
• list of lemmas
• list of conjectures
• list of inequalities
• list of mathematical proofs

Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields. In mathematics, there are a number of fundamental theorems for different fields. ... Jump to: navigation, search This is a list of lemmas (i. ... This is a list of conjectures, by Wikipedia page. ... This page lists Wikipedia articles about particular mathematical inequalities. ... Wikipedia contains a number of articles with mathematical proofs: Theorems of which articles are primarily devoted to proving them Bertrands postulate and a proof Erdős-Ko-Rado theorem Estimation of covariance matrices Fermats little theorem and some proofs Gödels completeness theorem and its original proof Mathematical induction... Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ... Theoretical physics is physics that employs mathematical models and abstractions rather than experimental processes. ... U.S. Economic Calendar Economics at the Open Directory Project Economics textbooks on Wikibooks The Economists Economics A-Z Institutions and organizations Bureau of Labor Statistics - from the American Labor Department Center for Economic and Policy Research (USA) National Bureau of Economic Research (USA) - Economics material from the organization... Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. ...

A

• Abel's theorem (mathematical analysis)
• Abelian and tauberian theorems (mathematical analysis)
• Abel-Ruffini theorem (theory of equations, Galois theory)
• Ankeny-Artin-Chowla theorem (number theory)
• Arrow's impossibility theorem (game theory)
• Artin-Schreier theorem (real closed fields)
• Artin-Wedderburn theorem (abstract algebra)
• Arzelà-Ascoli theorem (functional analysis)
• Atiyah-Singer index theorem (elliptic differential operators, harmonic analysis)

In real analysis, Abels theorem for power series relates a limit of a power series to the sum of its coefficients. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... In mathematics, a large number of methods have been proposed for the summation of divergent series. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... The Abel-Ruffini theorem states that there is no general solution in radicals to polynomial equations of degree five or higher. ... In mathematics, the theory of equations comprises a major part of traditional algebra. ... In mathematics, Galois theory is a branch of abstract algebra. ... In number theory, the Ankeny-Artin-Chowla congruence is a result published in 1951 by N.C. Ankeny, Emil Artin and S. Chowla. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system meets all of a certain set of criteria when there are three or more choices. ... Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ... In mathematics, a real closed field is an ordered field F in which any of the following equivalent conditions are true: Every non-negative element of F has a square root in F, and any polynomial of odd degree with coefficients in F has at least one root in F... In mathematics, a real closed field is an ordered field F in which any of the following equivalent conditions are true: Every non-negative element of F has a square root in F, and any polynomial of odd degree with coefficients in F has at least one root in F... In abstract algebra, the Artin-Wedderburn theorem is a classification theorem for semisimple product of ni-by-ni matrix rings over division rings Di, for some integers ni, both of which are uniquely determined up to permutation of the index i. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... In mathematics, the Arzelà-Ascoli theorem of functional analysis is a criterion to decide whether a set of continuous functions from a compact metric space into a metric space is compact in the topology of uniform convergence. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In the mathematics of manifolds and differential operators, the Atiyah-Singer index theorem is an important unifying result that connects topology and analysis. ... In mathematics, an Elliptic operator is a major type of differential operator P defined on spaces of complex-valued functions, or some more general function-like objects, such that the coefficients of the highest-order derivatives satisfy a positivity condition. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ...

B

• Baire category theorem (topology, metric spaces)
• Banach-Alaoglu theorem (functional analysis)
• Banach fixed point theorem (metric spaces, differential equations)
• Banach-Steinhaus theorem (functional analysis)
• Barbier's theorem (geometry)
• Bass's theorem (group theory)
• Bayes' theorem (probability)
• Beatty's theorem (diophantine approximation)
• Beck's monadicity theorem (category theory)
• Beck's theorem (incidence geometry)
• Bell's theorem (quantum theory - physics)
• Bendixson-Dulac theorem (dynamical systems)
• Berry-Esséen theorem (probability theory)
• Bertrand's ballot theorem (probability theory, combinatorics)
• Bertrand's postulate (prime numbers)
• Bézout's theorem (algebraic curves)
• Binomial theorem (algebra, combinatorics)
• Birkhoff's theorem (ergodic theory)
• Bohr-Mollerup theorem (gamma function)
• Bolyai-Gerwien theorem (geometry)
• Bolzano-Weierstrass theorem (real analysis, calculus)
• Boolean prime ideal theorem (mathematical logic)
• Borel-Bott-Weil theorem (representation theory)
• Bott periodicity theorem (homotopy theory)
• Borsuk-Ulam theorem (topology)
• Brouwer fixed point theorem (topology)
• Brown's representability theorem (homotopy theory)
• Bruck-Chowla-Ryser theorem (combinatorics)
• Buckingham Pi theorem (dimensional analysis)

The Baire category theorem is an important tool in general topology and functional analysis. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ... The Banach-Alaoglu theorem (also known as Alaoglus Theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the product of compact sets with the product topology. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... The Banach fixed point theorem is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps of metric spaces, and provides a constructive method to find those fixed points. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In mathematics, the uniform boundedness principle (sometimes known as the Banach-Steinhaus Theorem) is one of the fundamental results of functional analysis. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... Barbiers theorem is a basic result on curves of constant width first proved by Joseph Emile Barbier. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, Gromovs theorem on groups of polynomial growth, named for Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups which have nilpotent subgroups of finite index. ... Group theory is that branch of mathematics concerned with the study of groups. ... Bayes theorem is a result in probability theory. ... The word probability derives from the Latin probare (to prove, or to test). ... In mathematics, Beattys theorem states that if p and q are two positive irrational numbers with then the positive integers are all pairwise distinct, and each positive integer occurs precisely once in the list. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... In category theory, a branch of mathematics, Becks monadicity theorem asserts that a functor is monadic if and only if U has a left adjoint; U reflects isomorphisms; and C has co-equalizers of U-split co-equalizer pairs, and U preserves those co-equalizers. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... In incidence geometry, Becks theorem is a more quantitative form of the more classical Sylvester-Gallai theorem. ... Incidence geometry is a mathematical structure composed of objects of various types and an incidence relation between them. ... It has been suggested that Bells original inequality be merged into this article or section. ... Fig. ... In mathematics, the Bendixson-Dulac theorem on dynamical systems states that if there exists φ(x,y) almost everywhere in the region of interest, then the plane autonomous system has no periodic solutions. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ... The central limit theorem in probability theory and statistics states that under certain circumstances the sample mean, considered as a random quantity, becomes more normally distributed as the sample size is increased. ... Probability theory is the mathematical study of probability. ... In combinatorics, Bertrands ballot theorem is the solution to the question: In an election where one candidate receives p votes and the other q votes with p≥q, what is the probability that the first candidate will be strictly ahead of the second candidate throughout the count? The answer... Probability theory is the mathematical study of probability. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... Bertrands postulate states that if n>3 is an integer, then there always exists at least one prime number p with n < p < 2n-2. ... Jump to: navigation, search In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ... This article refers to Bézouts theorem in algebraic geometry. ... In algebraic geometry, an algebraic curve is an algebraic variety of dimension equal to 1. ... In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ... Algebra is a branch of mathematics, which studies structure and quantity. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... This term Birkhoffs theorem is used for several theorems fundamental to different areas of mathematics and physics: The ergodic theorem of George David Birkhoff relates averages over time and space; see ergodic theory. ... In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ... In mathematical analysis, the Bohr_Mollerup theorem, named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it, characterizes the gamma function, defined for x > 0 by as the only function f on the interval x > 0 that simultaneously has the three properties and and is a convex function. ... The Gamma function along an interval In mathematics, the Gamma function extends the factorial function to the complex numbers. ... In geometry, the Bolyai-Gerwien theorem states that if two simple polygons of equal area are given, one can cut the first into finitely many polygonal pieces and rearrange the pieces to obtain the second polygon. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... The Bolzano-Weierstrass theorem in real analysis states that every bounded sequence of real numbers contains a convergent subsequence. ... Real analysis is that branch of mathematical analysis dealing with the set of real numbers and functions of real numbers. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... In mathematics, a number of prime ideal theorems for guaranteeing the existence of certain subsets of an abstract algebra can be stated. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematics, the Borel-Bott-Weil theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... In mathematics, the Bott periodicity theorem is a result from homotopy theory which was discovered by Raoul Bott during the latter part of the 1950s, and proved to be of foundational significance for much further research, in particular in K-theory. ... An illustration of a homotopy between the two bold paths In topology, two continuous functions from one topological space to another are called homotopic (Greek homeos = identical and topos = place) if one can be continuously deformed into the other, such a deformation being called a homotopy between the two functions. ... The Borsuk-Ulam theorem states that any continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematics, the Brouwer fixed point theorem states that every continuous function from the closed unit ball D n to itself has a fixed point. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematics, Browns representability theorem in homotopy theory gives necessary and sufficient conditions on a contravariant functor F on the homotopy category Hot of pointed CW complexes, to the category of sets Sets, to be a representable functor. ... An illustration of a homotopy between the two bold paths In topology, two continuous functions from one topological space to another are called homotopic (Greek homeos = identical and topos = place) if one can be continuously deformed into the other, such a deformation being called a homotopy between the two functions. ... The Bruck-Chowla-Ryser theorem is a result on the combinatorics of block designs. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... The Buckingham Ï€ theorem is a key theorem in dimensional analysis. ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...

C

• Cantor-Bernstein-Schroeder theorem (Set theory, cardinal numbers)
• Cantor's theorem (Set theory, Cantor's diagonal argument)
• Carathéodory's theorem (conformal mapping)
• Carathéodory's theorem (convex hull)
• Carathéodory's theorem (measure theory)
• Cartan's theorem (Lie group)
• Cartan's theorems A and B (several complex variables)
• Cauchy integral theorem (Complex analysis)
• Cayley-Hamilton theorem (Linear algebra)
• Cayley's theorem (group theory)
• Central limit theorem (probability)
• Ceva's theorem (geometry)
• Chebotarev's density theorem (number theory)
• Chen's theorem (number theory)
• Chern-Gauss-Bonnet theorem (differential geometry)
• Chinese remainder theorem (number theory)
• Chowla-Mordell theorem (number theory)
• Church-Rosser theorem (lambda calculus)
• Closed graph theorem (functional analysis)
• Cluster decomposition theorem (quantum field theory)
• Coase theorem (economics)
• Cochran's theorem (statistics)
• Compactness theorem (mathematical logic)
• Conservativity theorem (mathematical logic)
• Convolution theorem (Fourier transforms)
• Cook's theorem (computational complexity theory)
• Cox's theorem (probability foundations)
• Crystallographic restriction theorem (group theory, crystallography)
• Cut-elimination theorem (proof theory)

In set theory, the Cantor-Bernstein-Schroeder theorem, named after Georg Cantor, Felix Bernstein, and Ernst Schröder, states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In linguistics, cardinal numbers is the name given to number words that are used for quantity (one, two, three), as opposed to ordinal numbers, words that are used for order (first, second, third). ... Note: in order to fully understand this article you may want to refer to the set theory portion of the table of mathematical symbols. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Cantors diagonal argument is a proof devised by Georg Cantor to demonstrate that the real numbers are not countably infinite. ... In mathematics, Carathéodorys theorem in complex analysis states that if U is a simply connected open subset of the complex plane C, whose boundary is a Jordan curve Γ then the Riemann map f: U → D from U to the unit disk D extends continuously to the boundary, giving... An illustration of Carathéodorys theorem for a square in R2 In mathematics Carathéodorys theorem on convex sets states that if a point x of Rd lies in the convex hull of a set P, there is a subset P′ of P consisting of no more than... In mathematics, in particular in measure theory, an outer measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. ... In mathematics, there are two basic results in Lie group theory that go by the name Cartans theorem. ... In mathematics, a Lie group (IPA ) is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... In mathematics, Cartans theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X. They are significant both as applied to several complex variables, and in the general development of sheaf cohomology. ... The theory of functions of several complex variables is the branch of mathematics dealing with functions f(z1, z2, ... , zn) on the space Cn of n-tuples of complex numbers. ... In mathematics, the Cauchy integral theorem in complex analysis, named after Augustin Louis Cauchy, is an important statement about path integrals for holomorphic functions in the complex plane. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In linear algebra, the Cayley-Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field, satisfies its own characteristic equation. ... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ... In group theory, Cayleys theorem, named in honor of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a... Group theory is that branch of mathematics concerned with the study of groups. ... Central limit theorems are a set of weak-convergence results in probability theory. ... The word probability derives from the Latin probare (to prove, or to test). ... Cevas Theorem (pronounced Cheva) is a very popular theorem in elementary geometry. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, Chebotarevs density theorem in algebraic number theory is a generalisation to algebraic number fields that are Galois extensions, of Dirichlets theorem on arithmetic progressions. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Chens theorem was first stated by Chinese mathematician Chen Jingrun in 1966, with further details of the proof in 1973. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematics, the generalized-Gauss-Bonnet theorem presents the Euler characteristic of a closed Riemannian manifold as an integral of a certain polynomial derived from its curvature. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... The Chinese remainder theorem is the name for several related results in abstract algebra and number theory. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematics, the Chowla-Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... The Church-Rosser theorem states that if there are two distinct reductions starting from some term in the lambda calculus, then there exists a term that is reachable via reduction from both sequences. ... The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ... In mathematics, the closed graph theorem is a basic result of functional analysis. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In physics, the cluster decomposition theorem guarantees locality in quantum field theory. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In law and economics, the Coase theorem, attributed to Ronald Coase, is a theorem relating to the economic efficiency of a governments allocation of property rights. ... U.S. Economic Calendar Economics at the Open Directory Project Economics textbooks on Wikibooks The Economists Economics A-Z Institutions and organizations Bureau of Labor Statistics - from the American Labor Department Center for Economic and Policy Research (USA) National Bureau of Economic Research (USA) - Economics material from the organization... In statistics, Cochrans theorem is used in the analysis of variance. ... Jump to: navigation, search Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... The compactness theorem is a basic fact in symbolic logic and model theory and asserts that a set (possibly infinite) of first-order sentences is satisfiable, i. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematical logic, the conservativity theorem states the following: Suppose that a closed formula is a theorem of a first-order theory . ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematics, the convolution theorem states that the Fourier transform of a convolution is the point-wise product of Fourier transforms. ... The Fourier transform, named after Joseph Fourier, is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i. ... In computational complexity theory, Cooks theorem, proved by Stephen Cook in his 1971 paper The Complexity of Theorem Proving Procedures, states that the Boolean satisfiability problem is NP-complete. ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... Coxs theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. ... The word probability derives from the Latin probare (to prove, or to test). ... The crystallographic restriction theorem in its basic form is the observation that the rotational symmetries of a crystal are limited to 2-fold, 3-fold, 4-fold, and 6-fold. ... Group theory is that branch of mathematics concerned with the study of groups. ... Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. ... The Cut-elimination theorem is the central result establishing the significance of the sequent calculus. ... Proof theory, studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ...

D

• Dandelin's theorem (geometry)
• De Branges' theorem (complex analysis)
• De Finetti's theorem (probability)
• De Rham's theorem (differential topology)
• Deduction theorem (logic)
• Desargues' theorem (geometry)
• Descartes' theorem (geometry)
• Dilworth's theorem (combinatorics, order theory)
• Dimension theorem for vector spaces (vector spaces, linear algebra)
• Dirichlet's theorem on arithmetic progressions (number theory)
• Dirichlet's unit theorem (algebraic number theory)
• Divergence theorem (vector calculus)
• Dominated convergence theorem (Lebesgue integration)

Dandelin Spheres—graphics by Hop David In geometry, a nondegenerate conic section formed by a plane intersecting a cone has one or two Dandelin spheres characterized thus: Each Dandelin sphere touches, but does not cross, both the plane and the cone. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In complex analysis, de Branges theorem, named after Louis de Branges, formerly called the Bieberbach conjecture, after Ludwig Bieberbach, states a necessary condition on an analytic function to map the unit disk injectively to the complex plane. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In probability theory, de Finettis theorem explains why exchangeable observations are conditionally independent given some (usually) unobservable quantity to which an epistemic probability distribution would then be assigned. ... The word probability derives from the Latin probare (to prove, or to test). ... In mathematics, de Rham cohomology is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematical logic, the deduction theorem states that if a formula F is deducible from E then the implication E → F is demonstrable (i. ... Logic (from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... In projective geometry, Desargues theorem, named in honor of Girard Desargues, states: In a projective space, two triangles are in perspective axially if and only if they are in perspective centrally. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In geometry, Descartes theorem, named after René Descartes, establishes a relationship between four kissing, or mutually tangent, circles. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In the mathematical area of order theory, an antichain in a partially ordered set S is a subset A of S such that every pair of members of A is incomparable, i. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering. ... In mathematics, the dimension theorem for vector spaces states that a vector space has a definite, well-defined number of dimensions. ... Jump to: navigation, search A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra. ... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ... In number theory, Dirichlets theorem states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n > 0, or in other words: there are infinitely many primes which are congruent to a modulo d. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In algebraic number theory, Dirichlets unit theorem determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The statement is that the rank is r + s − 1 where r is the number of real embeddings and 2s the number... In mathematics, an algebraic number field (or simply number field) is a finite field extension of the rational numbers Q. That is, it is a field which contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and these days... In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky-Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... In mathematics, Henri Lebesgues dominated convergence theorem states that if a sequence { fn : n = 1, 2, 3, ... } of real-valued measurable functions on a measure space S converges almost everywhere, and is dominated (explained below) by some measurable function g whose integral is finite, then To say that the... The integral can be interpreted as the area under a curve. ...

E

• Earnshaw's theorem (electrostatics)
• Ehresmann's theorem (differential topology)
• Equipartition theorem (ergodic theory)
• Erdős-Ko-Rado theorem (combinatorics)
• Euler's rotation theorem (geometry)
• Euler's theorem (number theory)
• Euler's theorem on homogeneous functions (multivariate calculus)
• Extreme value theorem

Earnshaws theorem states that a collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges. ... It has been suggested that this article or section be merged with static electricity. ... In mathematics, Ehresmanns fibration theorem states that a smooth mapping f:M → N where M and N are smooth manifolds, such that f is a submersion, and f is a proper map, is a locally trivial fibration. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... The Equipartition Theorem is a principle of classical (non-quantum) statistical mechanics which states that the internal energy of a system composed of a large number of particles will distribute itself evenly among each of the degrees of freedom allowed to the particles of the system. ... In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ... In combinatorial mathematics, the ErdÅ‘s-Ko-Rado theorem of Paul ErdÅ‘s, Chao Ko, and Richard Rado is the following. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... In mathematics, Eulers rotation theorem states that any rotation has an axis. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In number theory, Eulers theorem (also known as the Fermat-Euler theorem) states that if n is a positive integer and a is coprime to n, then aφ(n) ≡ 1 (mod n) where φ(n) denotes Eulers totient function. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematics, a homogeneous function is a function with nice scaling behaviour: if the argument is multiplied by some factor, then the result is multiplied by some power of this factor. ... Multivariate calculus is a means of analyzing deterministic systems with multiple degrees of freedom. ... In calculus, the extreme value theorem states that if a function f(x) is continuous in the closed interval [a,b] then f(x) must attain its maximum and minimum value, each at least once. ...

F

• Faltings' theorem (diophantine geometry)
• Feit-Thompson theorem (finite groups)
• Fermat's last theorem (number theory)
• Fermat's little theorem (number theory)
• Fisher separation theorem (economics)
• Five color theorem (graph theory)
• Fixed point theorems in infinite-dimensional spaces
• Fluctuation dissipation theorem (physics)
• Fluctuation theorem
• Four color theorem (graph theory)
• Fourier inversion theorem (harmonic analysis)
• Frobenius reciprocity theorem (group representations)
• Frobenius theorem (foliations)
• Fubini's theorem (integration)
• Fuglede's theorem (functional analysis)
• Fundamental theorem of algebra (complex analysis)
• Fundamental theorem of arbitrage-free pricing (financial mathematics)
• Fundamental theorem of arithmetic (number theory)
• Fundamental theorem of calculus (calculus)
• Fundamental theorem on homomorphisms (abstract algebra)

In number theory, the Mordell conjecture stated a basic result regarding the rational number solutions to Diophantine equations. ... In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ... In mathematics, the Feit-Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. ... In mathematics, a finite group is a group which has finitely many elements. ... Pierre de Fermat Fermats last theorem (sometimes abbreviated as FLT and also called Fermats great theorem) is one of the most famous theorems in the history of mathematics. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Fermats little theorem (not to be confused with Fermats last theorem) states that if p is a prime number, then for any integer a, This means that if you take some number a, multiply it by itself p times and subtract a, the result is divisible by p... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... The Fisher separation theorem in economics asserts that the objective of a firm will be the maximization of its present value, regardless of the preferences of its owners. ... U.S. Economic Calendar Economics at the Open Directory Project Economics textbooks on Wikibooks The Economists Economics A-Z Institutions and organizations Bureau of Labor Statistics - from the American Labor Department Center for Economic and Policy Research (USA) National Bureau of Economic Research (USA) - Economics material from the organization... The five color theorem in graph theory states that any map can be colored with no more than five colors. ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics, a number of fixed point theorems in infinite-dimensional spaces generalise the Brouwer fixed point theorem. ... In statistical physics, the fluctuation dissipation theorem states that if a thermodynamic system responds linearly to an external perturbation, then the amount by which it responds is simply related to the fluctuation properties of the thermodynamic system. ... Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ... The Second Law of Thermodynamics stands in apparent contradiction with the time reversible equations of motion for classical and quantum systems. ... Example of a four color map The four color theorem states that any plane separated into regions, such as a political map of the counties of a state, can be colored using no more than four colors in such a way that no two adjacent regions receive the same color. ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics, Fourier inversion recovers a function from its Fourier transform. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ... In mathematics, and in particular group representation theory, the induced representation is one of the major general operations for passing from a representation of a subgroup H to a representation of the (whole) group G itself. ... Representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. ... In mathematics, the Frobenius theorem states, in its smooth version of degree 1, the following: Let U be an open set in Rn and F a submodule of Ω1(U) of constant rank r in U. Then F is integrable if and only if for every p ∈ U the stalk... In mathematics, informally speaking, a foliation is a kind of clothing worn on a manifold, cut from a stripy fabric. ... In mathematical analysis, Fubinis theorem, named in honor of Guido Fubini, states that if the integral being taken with respect to a product measure on the space over , then the first two integrals being iterated integrals, and the third being an integral with respect to a product measure. ... Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ... In mathematics, Fugledes theorem is a result in functional analysis. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, the fundamental theorem of algebra states that every complex polynomial of degree n has exactly n roots (zeroes), counted with multiplicity. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematical finance, a risk-neutral measure is a probability measure in which todays fair (i. ... Financial mathematics is the branch of applied mathematics concerned with the financial markets. ... In mathematics, and in particular number theory, the fundamental theorem of arithmetic or unique factorization theorem is the statement that every positive integer greater than 1 is either a prime number or can be written as a product of prime numbers. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... In abstract algebra, for a number of algebraic structures, the fundamental theorem on homomorphisms relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ...

G

• Gauss theorem (vector calculus)
• Gauss's Theorema Egregium (differential geometry)
• Gauss-Bonnet theorem (differential geometry)
• Gauss-Markov theorem (statistics)
• Gauss-Wantzel theorem (geometry)
• Gelfand-Naimark theorem (functional analysis)
• Gelfond-Schneider theorem (transcendence theory)
• Gibbard-Satterthwaite theorem (voting methods)
• Girsanov's theorem (stochastic processes)
• Goddard-Thorn theorem (vertex algebras)
• Gödel's completeness theorem (mathematical logic)
• Gödel's incompleteness theorem (mathematical logic)
• Going-up and going-down theorems (commutative algebra)
• Goodstein's theorem (mathematical logic)
• Green's theorem (vector calculus)
• Gromov's compactness theorem (Riemannian geometry)
• Gromov's theorem (group theory)
• Gromov-Ruh theorem (differential geometry)

In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky-Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... The Theorema Egregium (Remarkable Theorem) is an important theorem of Carl Friedrich Gauss concerning the curvature of surfaces. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... The Gauss-Bonnet theorem in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... This article is not about Gauss-Markov processes. ... Jump to: navigation, search Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, the Gelfand-Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, the Gelfond-Schneider theorem is the following statement, originally proved by Aleksandr Gelfond: If is an algebraic number (with and ), and is an irrational algebraic number, then is a transcendental number. ... In mathematics, transcendence theory investigates transcendental numbers, in a qualitative and quantitative way. ... The Gibbard-Satterthwaite theorem is a result about voting systems designed to choose a single winner from the preferences of certain individuals, where each individual ranks all candidates in order of preference. ... Voters at the voting booths in the US in 1945 Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. ... In probability theory, Girsanovs theorem tells how stochastic processes change under changes in measure. ... In the mathematics of probability, a stochastic process can be thought of as a random function. ... In mathematics, and in particular, in the mathematical background of string theory, the Goddard-Thorn theorem (also called the no-ghost theorem) is a theorem about certain vector spaces. ... In mathematics, a vertex operator algebra (abbreviated: VOA) is a certain kind of algebra that plays a key part in conformal field theory and other fields of study in physics, and has also proven useful in purely mathematical contexts such as moonshine theory. ... Gödels completeness theorem is a fundamental theorem in mathematical logic proved by Kurt Gödel in 1929. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... In mathematical logic, Goodsteins theorem is a statement about the natural numbers that is undecidable in Peano arithmetic but can be proven to be true using the stronger axiom system of set theory, in particular using the axiom of infinity. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In physics and mathematics, Greens theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. Greens theorem was named after British scientist George Green and is a special case of the more... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... In Riemannian geometry is Gromovs compactness theorem states that the set of Riemannian manifolds with Ricci curvature ≥ c and diameter ≤ D is pre-compact in the Gromov-Hausdorff metric. ... Jump to: navigation, search In mathematics, Riemannian geometry has at least two meanings, one of which is described in this article and another also called elliptic geometry. ... Gromovs theorem may mean one of a number of results of Mikhail Gromov: Gromovs compactness theorem Gromovs Betti number theorem Gromovs theorem on almost flat manifolds Gromovs theorem on groups of polynomial growth See also Bishop-Gromov inequality Gromov-Thurston 2pi theorem This is a... Group theory is that branch of mathematics concerned with the study of groups. ... In mathematics, a smooth compact manifold M is called almost flat if for any there is a Riemannian metric on M such that and is -flat, i. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...

H

• H-theorem (thermodynamics)
• Haag's theorem (quantum field theory)
• Haboush's theorem (algebraic groups, representation theory, invariant theory)
• Hadwiger's theorem (geometry, measure theory)
• Hahn embedding theorem (ordered groups)
• Hairy ball theorem (algebraic topology)
• Hahn-Banach theorem (functional analysis)
• Hales-Jewett theorem (combinatorics)
• Ham sandwich theorem (topology)
• Heine-Borel theorem (real analysis)
• Hellinger-Toeplitz theorem (functional analysis)
• Helly's theorem (convex sets)
• Herbrand-Ribet theorem (cyclotomic fields)
• Hilbert's basis theorem (commutative algebra,invariant theory)
• Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry)
• Hilbert-Speiser theorem (cyclotomic fields)
• Hinge theorem (geometry)
• Hopf-Rinow theorem (differential geometry)
• Hurewicz theorem (algebraic topology)
• Hurwitz's automorphisms theorem (algebraic curves)

In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Rudolf Haag showed in 1955 that the interaction picture cannot be rigorously defined in quantum field theory, a result now commonly cited as Haags Theorem. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In mathematics, the Mumford conjecture states that for any semisimple algebraic group G, over a field K, and for any linear representation ρ of G on a K-vector space V, given v in V that is fixed by the action of G, there is a G-invariant F on... In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. ... In integral geometry (otherwise called geometric probability theory), Hadwigers theorem states that the space of translation-invariant, finitely additive, not-necessarily-nonnegative set functions defined on finite unions of compact convex sets in Rn consists (up to scalar multiples) of one measure that is homogeneous of degree k for... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, a measure is a function that assigns a number, e. ... In mathematics, the Hahn embedding theorem states that every totally ordered abelian group can be embedded as a subgroup of the additive group of a real closed field. ... In abstract algebra, an ordered group is a group G equipped with a partial order ≤ which is translation-invariant; in other words, ≤ has the property that, for all a, b, and g in G, if a ≤ b then ag ≤ bg and ga ≤ gb. ... The hairy ball theorem of algebraic topology states that, in laymans terms, one cannot comb the hair on a ball in a smooth manner. This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem: there is no nonvanishing... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, the Hahn-Banach theorem is a central tool in functional analysis. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, the Hales-Jewett theorem [2] is a fundamental combinatorial result of Ramsey theory, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial structure; it is impossible for such objects to be completely random. An informal geometric statement of the theorem is that for any... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... The Ham sandwich theorem, also known as the Stone-Tukey theorem in topology in mathematics, states that given n objects in n-dimensional space, it is possible to divide each one in half with a single (n − 1)-dimensional hyperplane. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematical analysis, the Heine-Borel theorem, named after Eduard Heine and Émile Borel, states: A subset of the real numbers R is compact iff it is closed and bounded. ... Real analysis is that branch of mathematical analysis dealing with the set of real numbers and functions of real numbers. ... In functional analysis, a branch of mathematics, the Hellinger-Toeplitz theorem states that an everywhere defined symmetric operator on a Hilbert space is bounded. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In geometry, Hellys theorem is a basic combinatorial result on convex sets. ... In mathematics, an object is convex if for any pair of points within the object, any point on the straight line segment that joins them is also within the object. ... The Herbrand-Ribet theorem is a strengthening of Kummers theorem to the effect that the prime p divides the class number of the cyclotomic field of pth roots of unity if and only if p divides the denominator of the nth Bernoulli number Bn for some n, 0 < n... In mathematics, the n-th roots of unity or de Moivre numbers, named after Abraham de Moivre (1667 - 1754), are complex numbers located on the unit circle. ... In mathematics, Hilberts basis theorem, first proved by David Hilbert in 1888, states that, if k is a field, then every ideal in the ring of multivariate polynomials k[x1, x2, ..., xn] is finitely generated. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. ... Hilberts Nullstellensatz (German: theorem of zeros) is a theorem in algebraic geometry that relates varieties and ideals in polynomial rings over algebraically closed fields. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In mathematics, the Hilbert-Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. ... In mathematics, the n-th roots of unity or de Moivre numbers, named after Abraham de Moivre (1667 - 1754), are complex numbers located on the unit circle. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... If two objects are at a distance one mile from each other, it should be possible to construct a road of length one mile between them. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, Hurwitzs automorphisms theorem bounds the group of automorphisms, via conformal mappings, of a compact Riemann surface of genus g > 1, telling us that the order of the group of such automorphisms is bounded by 84(g − 1). ... In algebraic geometry, an algebraic curve is an algebraic variety of dimension equal to 1. ...

I

• Intermediate value theorem (calculus)
• Implicit function theorem (vector calculus)
• Infinite monkey theorem (probability)
• Inverse function theorem (vector calculus)
• Isomorphism theorem (abstract algebra)
• Isoperimetric theorem (curves, calculus of variations)

In calculus, the intermediate value theorem is either of two theorems of which an account is given below. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... In mathematics, in the field of calculus of several variables, the implicit function theorem says that for a suitable set of equations, some of the variables are defined as functions of the others. ... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... According to the second Borel-Cantelli lemma, given enough time, a chimpanzee like this one typing at random will eventually type out a copy of one of Shakespeares plays. ... The word probability derives from the Latin probare (to prove, or to test). ... In mathematics, the inverse function theorem gives sufficient conditions for a vector-valued function to be invertible on an open region containing a point in its domain. ... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... In mathematics, the isomorphism theorems are three theorems, applied widely in the realm of universal algebra, stating the existence of certain natural isomorphisms. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... Isoperimetry literally means having an equal perimeter. In mathematics, isoperimetry is the general study of geometric figures having equal boundaries. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... Calculus of variations is a field of mathematics which deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. ...

J

• Jacobson density theorem (ring theory)
• Jordan curve theorem (topology)
• Jordan-Hölder theorem (group theory)
• Jordan-Schönflies theorem (geometric topology)

The Jacobson Density Theorem is an important generalization of the Artin Wedderburn Theorem. ... In mathematics, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. ... In topology, the Jordan curve theorem states that every non-self-intersecting loop in the plane divides the plane into an inside and an outside. The precise mathematical statement is as follows. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematics, a composition series of a group G is a normal series such that each Hi is a maximal normal subgroup of Hi+1. ... Group theory is that branch of mathematics concerned with the study of groups. ... In mathematics, the Jordan-Schönflies theorem in geometric topology is a sharpening of the Jordan curve theorem in two dimensions. ... In mathematics, geometric topology is the study of manifolds and their embeddings, with representative topics being knot theory and braid groups. ...

K

• Kirchhoff's theorem (graph theory)
• Kirszbraun theorem (Lipschitz continuity)
• Kleene's recursion theorem (recursion theory)
• Knaster-Tarski theorem (order theory)
• Kolmogorov-Arnold-Moser theorem (dynamical systems)
• König's theorem (mathematical logic)
• Kronecker's theorem (diophantine approximation)
• Kronecker-Weber theorem (number theory)
• Krull's principal ideal theorem (commutative algebra)
• Künneth theorem (algebraic topology)

In the mathematical field of graph theory Kirchhoffs theorem or Kirchhoffs matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph. ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics, the Kirszbraun theorem in mathematical analysis states that if U is a subset of Euclidean space En and f : U → Em is a Lipschitz-continuous map, then there is a Lipschitz-continuous map F: En → Em that extends f, and has the same Lipschitz constant as f. ... In mathematics, a function f : M → N between metric spaces M and N is called Lipschitz continuous (or is said to satisfy a Lipschitz condition) if there exists a constant K > 0 such that d(f(x), f(y)) ≤ K d(x, y) for all x and y in M... Kleenes recursion theorem is a result in computability theory first proved by Stephen Kleene; it allows to construct programs, Turing machines and recursive functions that refer back to their own description. ... Computability theory is that part of the theory of computation dealing with which problems are solvable by algorithms (equivalently, by Turing machines), with various restrictions and extensions. ... In the mathematical areas of order and lattice theory, the Knaster-Tarski theorem, named after Bronislaw Knaster and Alfred Tarski, states the following: Let L be a complete lattice and let f : L → L be an order-preserving function. ... Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering. ... The Kolmogorov-Arnold-Moser theorem is a theorem in non-linear dynamics that solves the small-divisor problem in classical perturbation theory. ... In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... There is also a proposition in graph theory called Königs lemma. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematics, Kroneckers theorem is a result in diophantine approximation applying to several real numbers xi, for 1 ≤ i ≤ N, which generalises the fact that an infinite cyclic subgroup of the unit circle group is a dense subset. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... In algebraic number theory, the Kronecker-Weber theorem states that every finite abelian extension of the field of rational numbers , or in other words every algebraic number field whose Galois group over is abelian, is a subfield of a cyclotomic field, i. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In commutative algebra, Krulls principal ideal theorem, named after Wolfgang Krull (1899 - 1971), gives a bound on the height of a principal ideal in a Noetherian ring. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... In mathematics, the Künneth theorem of algebraic topology describes the singular homology of the cartesian product X × Y of two topological spaces, in terms of singular homology groups Hi(X, R) and Hj(X, R). ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ...

L

• Lagrange's theorem (group theory)
• Lagrange's four-square theorem (number theory)
• Lagrange inversion theorem (mathematical analysis, combinatorics)
• Lagrange reversion theorem (mathematical analysis, combinatorics)
• Lami's theorem (statics)
• Laurent expansion theorem (complex analysis)
• Lefschetz fixed point theorem (algebraic topology)
• Lehmann-Scheffé theorem (statistics)
• Lindemann-Weierstrass theorem (transcendence theory)
• Lie-Kolchin theorem (algebraic groups, representation theory)
• Linear congruence theorem (number theory, modular arithmetic)
• Linear speedup theorem (computational complexity theory)
• Linnik's theorem (number theory)
• Liouville's theorem (complex analysis) (entire functions)
• Liouville's theorem (Hamiltonian) (Hamiltonian mechanics)
• Löb's theorem (mathematical logic)
• Löwenheim-Skolem theorem (mathematical logic)
• Lyapunov's central limit theorem (probability theory)

In mathematics, most commonly, Lagranges theorem states that if G is a finite group and H is a subgroup of G, then the order (that is, the number of elements) of H divides the order of G. This can be shown using the concept of left cosets of H... Group theory is that branch of mathematics concerned with the study of groups. ... Lagranges four-square theorem, also known as Bachets conjecture, was proved in 1770 by Joseph Louis Lagrange. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange-Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... This page is about Lagrange reversion. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... Jump to: navigation, search Lamis theorem in statics states that if three coplanar forces are acting on a same point and keep it stationary, then it obeys the relation where A, B and C are the magnitude of forces acting at the point (say P), and the values of... Statics is the branch of physics that is concerned with physical systems that are in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at rest under the action of external forces of equilibrium. ... In mathematics, a Laurent series is an infinite series. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, the Lefschetz fixed-point theorem counts the number of fixed points of a mapping from a topological space X to itself (subject to some mild conditions on X), by means of traces of the induced mappings on the homology groups of X. The counting is subject to some... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In statistics, the Lehmann-Scheffé theorem states the any estimator that is complete, sufficient, and unbiased is the unique best unbiased estimator of its expectation. ... Jump to: navigation, search Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... In mathematics, the Lindemann-Weierstrass theorem states that if α1,...,αn are algebraic numbers which are linearly independent over the rational numbers, then are algebraically independent over the algebraic numbers; in other words the set has transcendence degree n over . ... In mathematics, transcendence theory investigates transcendental numbers, in a qualitative and quantitative way. ... In mathematics, the Lie-Kolchin theorem is a theorem in the representation theory of linear algebraic groups. ... In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... In modular arithmetic, the question of when a linear congruence can be solved is answered by the linear congruence theorem. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Modular arithmetic is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ... In computational complexity theory, the linear speedup theorem for Turing machines proves that given any c > 0 and any Turing machine solving a problem in time f(n), there is another machine that solves the same problem in time cf(n). ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... Linniks theorem in analytic number theory answers a natural question after Dirichlets theorem. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Liouvilles theorem in complex analysis states that every bounded (i. ... In complex analysis, an entire function is a function that is holomorphic everywhere on the whole complex plane. ... In mathematical physics, Liouvilles theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ... In mathematical logic, Löbs theorem states that in a theory with Peano arithmetic, for any formula P, if it is provable that if P is provable then P, then P is provable. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematical logic, the classic Löwenheim-Skolem theorem states that any infinite model M has a countably infinite submodel N that satisfies exactly the same set of first-order sentences that M satisfies. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In probability theory, Lyapunovs central limit theorem is one of the variants of the central limit theorems. ... Probability theory is the mathematical study of probability. ...

M

• Mahler's compactness theorem (geometry of numbers)
• Mahler's theorem (p-adic analysis)
• Marcinkiewicz theorem (functional analysis)
• Marriage theorem (combinatorics)
• Master theorem (recurrence relations, asymptotic analysis)
• Maschke's theorem (group representations)
• Matiyasevich's theorem (mathematical logic)
• Max flow min cut theorem (graph theory)
• Maximum power theorem (electrical circuits)
• Maxwell's theorem (probability theory)
• Mean value theorem (calculus)
• Menger's theorem (graph theory)
• Mercer's theorem (functional analysis)
• Mertens' theorems (number theory)
• Metrization theorems (topological spaces)
• Min-max theorem (functional analysis)
• Minimax theorem
• Minkowski's theorem (geometry of numbers)
• Mitchell's embedding theorem (category theory)
• Mittag-Leffler's theorem (complex analysis)
• Modigliani-Miller theorem (finance theory)
• Mohr-Mascheroni theorem (geometry)
• Monotone convergence theorem (mathematical analysis)
• Mordell-Weil theorem (number theory)
• Morera's theorem (complex analysis)
• Morley's categoricity theorem (model theory)
• Morley's trisector theorem (geometry)
• Multinomial theorem (algebra, combinatorics)
• Myers theorem (differential geometry)
• Myhill-Nerode theorem (formal languages)

In mathematics, Mahlers compactness theorem is a foundational result on lattices in Euclidean space, characterising sets of lattices that are bounded in a certain definite sense. ... In number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between convex sets and lattices in n-dimensional space. ... In the notation of combinatorialists, which conflicts with that used in the theory of special functions, the Pochhammer symbol denotes the falling factorial: Denote by Δ the forward difference operator defined by Then we have so that the relationship between the operator Δ and this polynomial sequence is much like that between... P-adic analysis (p-adic analysis) is a branch of mathematics that deals with functions of p-adic numbers. ... In mathematics, the Marcinkiewicz theorem, discovered by Józef Marcinkiewicz, is a result about ``interpolation of operators acting on Lp spaces and related spaces. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, the marriage theorem (1935), usually credited to mathematician Philip Hall, is a combinatorial result that gives the condition allowing the selection of a distinct element from each of a collection of subsets. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... In the analysis of algorithms, the master theorem, which is a specific case of the Akra-Bazzi theorem, provides a cookbook solution in asymptotic terms for recurrence relations of types that occur in practice. ... Recurrent redirects here; for the meaning of recurrent in contemporary hit radio, see Recurrent rotation. ... In mathematics and applications, particularly the analysis of algorithms, asymptotic analysis is a method of classifying limiting behaviour, by concentrating on some trend. ... In mathematics, in particular group representation theory, Maschkes theorem is the basic result proving that linear representations of a finite group over the complex numbers break up into irreducible pieces. ... Representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. ... Matiyasevichs theorem, proven in 1970 by Yuri Matiyasevich, implies that Hilberts tenth problem is unsolvable. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... The max flow min cut theorem is a statement in optimization theory about optimal flows in networks. ... A diagram of a graph with 6 vertices and 7 edges. ... This article contains information that is not verifiable. ... An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... In probability theory, Maxwells theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X1, ..., Xn )T is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then... Probability theory is the mathematical study of probability. ... For any function that is continuous on [a, b] and differentiable on (a, b) there exists some c in the interval (a, b) such that the secant joining the endpoints of the interval [a, b] is parallel to the tangent at c. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... In the mathematical discipline of graph theory and related areas Mengers theorem is a basic result about connectivity in finite undirected graphs. ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics and functional analysis Mercers theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, Mertens theorems are three results in number theory related to the density of prime numbers, and proved by Franz Mertens. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... A metrizable space is a topological space that is homeomorphic to a metric space. ... Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. ... In mathematics, the min-max theorem is an important result in the theory of Hilbert spaces. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... Minimax is a method in decision theory for minimizing the expected maximum loss. ... In mathematics, Minkowskis theorem in the geometry of numbers applies to convex symmetric sets and lattices; it relates the number of contained lattice points to the volume of such a set. ... In number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between convex sets and lattices in n-dimensional space. ... In mathematics, Mitchells embedding theorem is an important result about abelian categories; it states that these categories, while rather abstractly defined, are all quite concrete categories of modules. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... In complex analysis, Mittag–Lefflers theorem concerns the existence of functions with prescribed zeros or poles. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... The Modigliani-Miller theorem (of Franco Modigliani and Merton Miller) forms the basis for modern thinking on capital structure. ... In mathematics, the Mohr-Mascheroni theorem states that any geometric construction that can be performed by a ruler and compass can be performed by a compass alone. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, there are several theorems dubbed monotone convergence; here we present some major examples. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... In mathematics, the Mordell-Weil theorem states that for an abelian variety A over a number field K, the group A(K) of K-rational points of A is a finitely-generated abelian group. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In complex analysis, Moreras theorem states that if the integral of a continuous complex-valued function f of a complex variable along every simple closed curve within an open set is zero, that is, if for C any simple closed curve, then f is differentiable at every point in... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In model theory, Morleys categoricity theorem is a theorem of Michael D. Morley which states that if a first-order theory is complete in a countable language, then if it is categorical in some uncountable cardinality, it is categorical in all uncountable cardinalities. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ... In plane geometry, Morleys trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, the multinomial formula is an expression of a power of a sum in terms of powers of the addends. ... Algebra is a branch of mathematics, which studies structure and quantity. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... Myers theorem is a classical theorem in Riemannian geometry. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In the theory of formal languages, the Myhill-Nerode theorem provides a necessary and sufficient condition for a language to be regular. ... In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ...

N

• Nagell-Lutz theorem (elliptic curves)
• Nash embedding theorem (differential geometry)
• Nielsen-Schreier theorem (free groups)
• No cloning theorem (quantum computation)
• Noether's theorem (Lie groups, calculus of variations, differential invariants, physics)
• No-ghost theorem (vertex algebras)
• Norton's theorem (electrical networks)
• Nyquist-Shannon sampling theorem (information theory)

In mathematics, the Nagell-Lutz theorem is a result in the diophantine geometry of elliptic curves. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ... The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded in a Euclidean space Rn. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... The Cayley graph of the free group on two generators a and b In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many... The Cayley graph of the free group on two generators a and b In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many... The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. ... Molecule of alanine used in NMR implementation of error correction. ... Noethers theorem is a central result in theoretical physics that expresses the one-to-one correspondence between the symmetries and the conservation laws. ... In mathematics, a Lie group (IPA ) is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... Calculus of variations is a field of mathematics which deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. ... Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ... In mathematics, and in particular, in the mathematical background of string theory, the Goddard-Thorn theorem (also called the no-ghost theorem) is a theorem about certain vector spaces. ... In mathematics, a vertex operator algebra (abbreviated: VOA) is a certain kind of algebra that plays a key part in conformal field theory and other fields of study in physics, and has also proven useful in purely mathematical contexts such as moonshine theory. ... Nortons theorem for electrical networks states that any collection of voltage sources and resistors with two terminals is electrically equivalent to an ideal current source I in parallel with a single resistor R. The theorem can also be applied to general impedances, not just resistors. ... An electrical network or electrical circuit is an interconnection of electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... The Nyquist-Shannon sampling theorem is the fundamental theorem in the field of information theory, in particular telecommunications. ... Information theory is the mathematical theory of data communication and storage founded in 1948 by Claude E. Shannon. ...

O

• Open mapping theorem (functional analysis)

In mathematics, there are two theorems with the name open mapping theorem. Functional analysis In functional analysis, the open mapping theorem, also known as the Banach-Schauder theorem, is a fundamental result which states: if A : X → Y is a surjective continuous linear operator between Banach spaces X and Y... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ...

P

• Paley-Wiener theorem (Fourier transforms)
• Pappus's centroid theorem (geometry)
• Parseval's theorem (Fourier analysis)
• Pascal's theorem (conics)
• Pentagonal number theorem (number theory)
• Perfect graph theorem (graph theory)
• Peter-Weyl theorem (representation theory)
• Picard theorem (complex analysis)
• Picard-Lindelöf theorem (ordinary differential equations)
• Pick's theorem (geometry)
• Pitman-Koopman-Darmois theorem (statistics)
• Plancherel theorem (Fourier analysis)
• Poincaré-Bendixson theorem (dynamical systems)
• Poincaré-Birkhoff-Witt theorem (universal enveloping algebras)
• Poincaré duality theorem (algebraic topology of manifolds)
• Poncelet-Steiner theorem (geometry)
• Post's theorem (mathematical logic)
• Prime number theorem (number theory)
• Primitive element theorem (field theory)
• Ptolemaios' theorem (geometry)
• Pythagorean theorem (geometry)

In mathematics the Paley-Wiener theorem relates growth properties of entire functions on Cn and Fourier transformation of Schwartz distributions of compact support. ... The Fourier transform, named after Joseph Fourier, is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i. ... Pappuss centroid theorem consists of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, Parsevals theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ... Pascals theorem states that if an arbitrary hexagon is inscribed in any conic section, and opposite pairs of sides are extended until they meet, the three intersection points will lie on a straight line, the Pascal line of that configuration. ... In mathematics, a conic section (or just conic) is a curved locus of points, formed by intersecting a cone with a plane. ... In mathematics, the pentagonal number theorem, originally due to Euler, states that This theorem can be given a combinatorial interpretation in terms of partitions. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the clique number of that subgraph. ... A diagram of a graph with 6 vertices and 7 edges. ... The Peter-Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... In complex analysis, mathematician Charles Émile Picards name is given to two theorems regarding the range of an analytic function. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, the Picard-Lindelöf theorem on existence and uniqueness of solutions of differential equations (Picard 1890, Lindelöf 1894) states that an initial value problem has exactly one solution if f is Lipschitz continuous in , continuous in as long as stays bounded. ... In mathematics, a differential equation is an equation that describes a prescribed relationship between a set of unknowns which are to be regarded as an unknown function and its (ordinary or partial) derivatives. ... Given a simple polygon constructed on a grid of equal-distanced points (i. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In statistics, the exponential family of probability density functions or probability mass functions comprises those that have the following form: where: h(x) is the reference density, η is the natural parameter, a column vector, so that ηT, its transpose, is a row vector, T(x) is called the sufficient... Jump to: navigation, search Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... In mathematics, the Plancherel theorem is a result in harmonic analysis, first proved by Michel Plancherel. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ... The Poincaré-Bendixson theorem is a statement about the behaviour of trajectories in two-dimensional continuous dynamical systems. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ... In the theory of Lie algebras, the Poincaré-Birkhoff-Witt theorem is a fundamental result characterizing the universal enveloping algebra of a Lie algebra. ... In mathematics, for any Lie algebra L one can construct its universal enveloping algebra U(L). ... In mathematics, the Poincaré duality theorem is a basic result on the structure of the homology and cohomology groups of manifolds. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... Jump to: navigation, search This page is about a higher mathematics topic. ... In geometry, the Poncelet-Steiner theorem on ruler-and-compass constructions states that whatever can be constructed by straightedge with compass, can be constructed by straightedge alone, if you are given a single circle and the location of its centre. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... In computability theory Posts theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Jump to: navigation, search In number theory, the prime number theorem (PNT) describes the approximate, asymptotic distribution of the prime numbers. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematics, a primitive element for an extension of fields L/K is an element ζ of L such that L = K(ζ), or in other words such that L is generated by ζ over K. This means that every element of L can be written as a quotient of... Field theory is a branch of mathematics which studies the properties of fields. ... In mathematics, Ptolemaios theorem is a relation in Euclidean geometry between the four sides and two diagonals or chords of a quadrilateral inscribed in circle. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... The Pythagorean theorem: The sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ...

R

• Radon's theorem (convex sets)
• Radon-Nikodym theorem (measure theory)
• Ramsey's theorem (graph theory,combinatorics)
• Rank-nullity theorem (linear algebra)
• Rao-Blackwell theorem (statistics)
• Rational root theorem (algebra,polynomials)
• Reeh-Schlieder theorem (local quantum field theory)
• Residue theorem (complex analysis)
• Rice's theorem (recursion theory, computer science)
• Riemann mapping theorem (complex analysis)
• Riemann-Roch theorem (Riemann surfaces, algebraic curves)
• Riesz representation theorem (functional analysis,Hilbert space)
• Riesz-Thorin theorem (functional analysis)
• Robertson-Seymour theorem (graph theory)
• Rolle's theorem (calculus)
• Roth's theorem (diophantine approximation)
• Rouché's theorem (complex analysis)

In geometry, Radons theorem on convex sets states that any set of points in Rd can be partitioned into two (disjoint) sets whose convex hulls intersect. ... In mathematics, an object is convex if for any pair of points within the object, any point on the straight line segment that joins them is also within the object. ... In mathematics, the Radon-Nikodym theorem is a result in functional analysis that states that if a measure Q is absolutely continuous with respect to another sigma-finite measure P then there is a measurable function f, taking values in [0,∞], on the underlying space such that for any measurable... In mathematics, a measure is a function that assigns a number, e. ... In combinatorics, Ramseys theorem states that in colouring a large complete graph (that is a simple graph, where an edge connects every pair of vertices), one will find complete subgraphs all of the same colour. ... A diagram of a graph with 6 vertices and 7 edges. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... In mathematics, the rank-nullity theorem of linear algebra, in its simplest form, relates the rank and the nullity of a matrix together with the number of columns of the matrix. ... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ... In statistics, the Rao-Blackwell theorem describes a technique that can transform an absurdly crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. ... Jump to: navigation, search Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... In algebra, the rational root theorem states a constraint on solutions (also called roots) to the polynomial equation an xn + an-1 xn -1 + ... + a1 x + a0 = 0 with integer coefficients. ... Algebra is a branch of mathematics, which studies structure and quantity. ... In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. ... The Reeh-Schlieder theorem is a result of relativistic local quantum field theory, stating that the vacuum is a cyclic vector for the field algebra of any open set in Minkowski space. ... The Haag-Kastler axiomatic framework for quantum field theory is an application to local quantum physics of C-star algebra theory. ... The residue theorem in complex analysis is a powerful tool to evaluate path integrals of meromorphic functions over closed curves and can often be used to compute real integrals as well. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... Rices theorem (also known as The Rice-Myhill-Shapiro theorem) is an important result in the theory of recursive functions. ... Computability theory is that part of the theory of computation dealing with which problems are solvable by algorithms (equivalently, by Turing machines), with various restrictions and extensions. ... Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Downloadable Science and Computer Science books Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science ... The Riemann mapping theorem in complex analysis states the following: if U is a simply connected open subset of the complex number plane C which is not all of C, then there exists a bijective holomorphic conformal map f : U -> D, where D = { z in C : |z| < 1 } denotes the... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, specifically in complex analysis and algebraic geometry, the Riemann-Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. ... In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold. ... In algebraic geometry, an algebraic curve is an algebraic variety of dimension equal to 1. ... There are several well-known theorems in functional analysis known as the Riesz representation theorem. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. ... In mathematics, the Riesz-Thorin theorem, often referred to as the ``Riesz-Thorin Interpolation Theorem or the ``Riesz-Thorin Convexity Theorem is a result about ``interpolation of operators. This should not be confused with somewhat different mathematical procedure of interpolation of functions. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In graph theory, the Robertson-Seymour theorem states that every downwardly closed set of (isomorphism classes of) finite graphs is precisely the set of all (isomorphism classes of) graphs that lack a certain set of finitely many forbidden minors. ... A diagram of a graph with 6 vertices and 7 edges. ... In calculus, Rolles theorem states that if a function f is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), and f(a) = f(b) then there is some number c in the open interval (a,b) such that f (c) = 0. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... There are two major results of Klaus Roth in mathematics which go by the name of Roths theorem: The Thue-Siegel-Roth theorem in Diophantine approximation, which concerns the rarity to which an irrational algebraic number can be approximated by a rational number; and Roths theorem in arithmetic... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... In complex analysis, Rouchés theorem tells us that if the complex-valued functions f and g are holomorphic inside and on some closed contour C, with |g(z)| < |f(z)| on C, then f and f + g have the same number of zeros inside C, where each zero is... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ...

S

• Sahlqvist correspondence theorem (modal logic)
• Sarkovskii's theorem (dynamical systems)
• Savitch's theorem (computational complexity theory)
• Schauder fixed point theorem (functional analysis)
• Schreier refinement theorem (group theory)
• Schur's lemma (representation theory)
• Schur's theorem (Ramsey theory)
• Seifert-van Kampen theorem (algebraic topology)
• Shannon's theorem (information theory)
• Simplicial approximation theorem (algebraic topology)
• Skolem-Noether theorem (simple algebras)
• Soundness theorem (mathematical logic)
• Space hierarchy theorem (computational complexity theory)
• Spectral theorem (functional analysis)
• Speedup theorem (computational complexity theory)
• Sperner's theorem (combinatorics)
• Spin-statistics theorem (physics)
• Sprague-Grundy theorem (combinatorial game theory)
• Squeeze theorem (mathematical analysis)
• Stanley's reciprocity theorem (combinatorics)
• Stark-Heegner theorem (number theory)
• Stokes' theorem (vector calculus, differential topology)
• Stolper-Samuelson theorem (economics)
• Stone's representation theorem for Boolean algebras (mathematical logic)
• Stone's theorem on one-parameter unitary groups (functional analysis)
• Stone-Tukey theorem (topology)
• Stone-von Neumann theorem (functional analysis, representation theory of the Heisenberg group, quantum mechanics)
• Stone-Weierstrass theorem (functional analysis)
• Sturm's theorem (theory of equations)
• Swan's theorem (module theory)
• Sylow theorem (group theory)
• Sylvester's theorem (number theory)
• Sylvester-Gallai theorem (plane geometry)
• Szemerédi's theorem (combinatorics)
• Szemerédi-Trotter theorem (combinatorics)

In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. ... Modal logic, or (less commonly) intensional logic is the branch of logic that deals with sentences that are qualified by modalities such as can, could, might, may, must, possibly, and necessarily, and others. ... In mathematics, Sarkovskiis theorem (or Sharkovskys theorem) is a result, named for Oleksandr Mikolaiovich Sharkovsky, about discrete dynamical systems on the real line. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ... Overview In computational complexity theory, Savitchs theorem, proved by Walter Savitch in 1970, states that for any function f(n) ≥ log(n) NSPACE(f(n)) ⊆ DSPACE(f²(n)). In other words, if a nondeterministic Turing machine can solve a problem using f(n) space, an ordinary deterministic Turing machine... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... In mathematics, a number of fixed point theorems in infinite-dimensional spaces generalise the Brouwer fixed point theorem. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, the Schreier refinement theorem of group theory states that any two normal towers of subgroups, ending with the trivial group, have equivalent refinements. ... Group theory is that branch of mathematics concerned with the study of groups. ... In mathematics, Schurs lemma is now a generic term applied to theorems on the commutant of a module M that is simple. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... In mathematics, Schurs theorem is either of two different theorems of the mathematician Issai Schur. ... Ramsey theory, named for Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. ... In mathematics, the Seifert-van Kampen theorem of algebraic topology explains the structure of the fundamental group of a topological space X, in terms of those of two overlapping subspaces U and V, under certain hypothesis about connectedness. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In information theory, the Shannon-Hartley theorem states the maximum amount of error-free digital data (that is, information) that can be transmitted over a communication link with a specified bandwidth in the presence of noise interference. ... Information theory is the mathematical theory of data communication and storage founded in 1948 by Claude E. Shannon. ... In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, the Skolem-Noether theorem is a result on automorphisms of simple rings. ... In mathematics, an algebra is simple if it contains no non-trivial ideals. ... Soundness theorems are among the most fundamental results in mathematical logic. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions. ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... In mathematics, particularly linear algebra and functional analysis, the spectral theorem is a collection of results about linear operators or about matrices. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In computational complexity theory, a speedup theorem is a theorem that considers some algorithm solving a problem and demonstrates the existence of a faster algorithm solving the same problem (or more generally, an algorithm using less of any resource, not just time). ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... In combinatorics, a Sperner family (or Sperner system), named in honor of Emanuel Sperner, is a set system (F, E) in which no element is contained in another. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ... Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ... In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game is equivalent to a nimber. ... Combinatorial game theory (CGT) is a mathematical theory that studies a certain kind of game. ... In calculus, the squeeze theorem, (also known as the pinching theorem or sandwich theorem) is a theorem regarding the limit of a function. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... In combinatorial mathematics, Stanleys reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone and the generating function of the cones interior. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... The Stark-Heegner theorem is a theorem in number theory that tells precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... The Stokes theorem in differential geometry is a statement about the integration of differential forms which generalizes several theorems from vector calculus. ... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... The Stolper-Samuelson theorem is a basic theorem in trade theory. ... U.S. Economic Calendar Economics at the Open Directory Project Economics textbooks on Wikibooks The Economists Economics A-Z Institutions and organizations Bureau of Labor Statistics - from the American Labor Department Center for Economic and Policy Research (USA) National Bureau of Economic Research (USA) - Economics material from the organization... In mathematics, Stones representation theorem for Boolean algebras, named in honor of Marshall H. Stone, is the duality between the category of Boolean algebras and the category of Stone spaces, i. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Stones theorem on one-parameter unitary groups is a basic theorem of functional analysis which establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space H and one-parameter families of unitary operators which are strongly continuous, that is and are homomorphisms: Such one-parameter... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... The Ham sandwich theorem, also known as the Stone-Tukey theorem in topology in mathematics, states that given n objects in n-dimensional space, it is possible to divide each one in half with a single (n − 1)-dimensional hyperplane. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematics and in theoretical physics, the Stone-von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... In mathematics, the Heisenberg group is a group of 3×3 upper triangular matrices of the form Elements a,b,c can be taken from some (arbitrary) commutative ring. ... DO HWA MECHANICS[chang rhinn`theorem] ... In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on an interval [a,b] can be uniformly approximated as closely as desired by a polynomial function. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, Sturms theorem is a symbolic procedure to determine the number of unique real roots of a polynomial. ... In mathematics, the theory of equations comprises a major part of traditional algebra. ... Swans theorem relates vector bundles to projective modules and gives rise to a common intuition throughout mathematics: projective modules over commutative rings are like vector bundles on compact spaces. Differential geometry Suppose M is a compact C∞-manifold, and a smooth vector bundle V is given on M. The... In abstract algebra, a module is a generalization of a vector space. ... The Sylow theorems of group theory, named after Ludwig Sylow, form a partial converse to Lagranges theorem, which states that if H is a subgroup of a finite group G, then the order of H divides the order of G. The Sylow theorems guarantee, for certain divisors of the... Group theory is that branch of mathematics concerned with the study of groups. ... Bertrands postulate states that if n>3 is an integer, then there always exists at least one prime number p with n < p < 2n-2. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... The Sylvester-Gallai theorem asserts that given a finite number of points in the plane, either All the points are collinear; or There is a line which contains exactly two of the points. ... In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ... In mathematics, Szemerédis theorem states that a set of natural numbers of density > 0 contains finite arithmetic progressions, of any length k we may ask for. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... In mathematics, the Szemerédi-Trotter theorem is a result in the fields of combinatorial geometry and irregularities of distribution. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ...

T

• Takagi existence theorem (number theory)
• Taniyama-Shimura theorem (number theory)
• Tarski's indefinability theorem (mathematical logic)
• Taylor's theorem (calculus)
• Thales' theorem (geometry)
• Thevenin's theorem (electrical circuits)
• Thue-Siegel-Roth theorem (diophantine approximation)
• Tietze extension theorem (general topology)
• Tikhonov fixed point theorem (functional analysis)
• Time hierarchy theorem (computational complexity theory)
• Tutte theorem (graph theory)
• Turán's theorem (graph theory)
• Tychonoff's theorem (general topology)

In class field theory, the Takagi existence theorem states in part that if K is a number field with class group G, there exists a unique abelian extension L/K with Galois group G, such that every ideal in K becomes principal in L, and that L is characterized by... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... The Taniyama-Shimura theorem establishes an important connection between elliptic curves, which are objects from algebraic geometry, and modular forms, which are certain periodic holomorphic functions investigated in number theory. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematical logic, Tarskis Indefinability Theorem is a theorem due to Alfred Tarski concerning the foundations of mathematics. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In calculus, Taylors theorem, named after the mathematician Brook Taylor, who stated it in 1712, gives the approximation of a differentiable function near a point by a polynomial whose coefficients depend only on the derivatives of the function at that point. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... In geometry, Thales theorem (named after Thales of Miletus) states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. ... // Introduction Geometry (Greek Γεωμετρια, geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. ... Thevenins theorem for electrical networks states that any combination of voltage sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem can also be applied to general impedances, not just resistors. ... An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... In mathematics, the Thue-Siegel-Roth theorem, also known simply as Roths theorem, is a foundational result in diophantine approximation to algebraic numbers. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... The Tietze extension theorem in topology states that, if X is a normal topological space and f : A → R is a continuous map from a closed subset A of X into the real numbers carrying the standard topology, then there exists a continuous map F : X → R with F(a... In mathematics, general topology or point set topology is that branch of topology which studies elementary properties of topological spaces and structures defined on them. ... In mathematics, a number of fixed point theorems in infinite-dimensional spaces generalise the Brouwer fixed point theorem. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In computational complexity theory, the time hierarchy theorems are important statements that ensure the existence of certain hard problems which cannot be solved in a given amount of time. ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... In the mathematical discipline of graph theory the Tutte theorem, named after William Thomas Tutte, is a characterization of graphs with perfect matchings. ... A diagram of a graph with 6 vertices and 7 edges. ... In graph theory, Turáns theorem is a result on the number of edges in a Ks+1-free graph. ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics, Tychonoffs theorem states that the product of any collection of compact topological spaces is compact. ... In mathematics, general topology or point set topology is that branch of topology which studies elementary properties of topological spaces and structures defined on them. ...

U

• Uniformization theorem (complex analysis, differential geometry)
• Universal coefficient theorem (algebraic topology)

In mathematics, the uniformization theorem for surfaces says that any surface admits a Riemannian metric of constant Gauss curvature. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, the universal coefficient theorem in algebraic topology establishes the relationship in homology theory between the integral homology of a topological space X, and its homology with coefficients in any abelian group A. It shows that the integral homology groups Hi(X,Z) do in a certain, definite sense... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ...

V

• Van der Waerden's theorem (combinatorics)
• Virial theorem (classical mechanics)
• Vitali theorem (measure theory)
• Vitali-Hahn-Saks theorem (measure theory)
• Von Neumann bicommutant theorem (functional analysis)

Van der Waerdens theorem is a theorem of the branch of mathematics called Ramsey theory. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... The virial theorem states that the average kinetic energy of a system of particles whose motions are bounded is given by where ri and Fi are the position and force vectors on the i th particle respectively. ... In physics, Classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the motions of bodies, and the forces that cause them. ... In mathematics, the Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable. ... In mathematics, a measure is a function that assigns a number, e. ... In mathematics, the Vitali-Hahn-Saks theorem states that given μn for each integer n >0, a countably additive function defined on a fixed sigma-algebra Σ, with values in a given Banach space B, such that exists for every set X in Σ, then μ is also countably additive. ... In mathematics, a measure is a function that assigns a number, e. ... The von Neumann bicommutant theorem relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ...

W

• Weierstrass-Casorati theorem (complex analysis)
• Weierstrass preparation theorem (several complex variables,commutative algebra)
• Well-ordering theorem (mathematical logic)
• Whitehead theorem (homotopy theory)
• Whitney embedding theorem (differential manifolds)
• Wigner-Eckhart theorem (Clebsch-Gordan coefficients)
• Wilson's theorem (number theory)
• Wolstenholme's theorem (number theory)

The Weierstrass-Casorati theorem in complex analysis describes the remarkable behavior of holomorphic functions near essential singularities. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic... The theory of functions of several complex variables is the branch of mathematics dealing with functions f(z1, z2, ... , zn) on the space Cn of n-tuples of complex numbers. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... The well-ordering theorem (not to be confused with the well-ordering axiom) states that every set can be well-ordered. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematics, the Whitehead theorem in homotopy theory states that if a continuous mapping f between topological spaces X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence provided X and Y are connected CW complexes. ... An illustration of a homotopy between the two bold paths In topology, two continuous functions from one topological space to another are called homotopic (Greek homeos = identical and topos = place) if one can be continuously deformed into the other, such a deformation being called a homotopy between the two functions. ... In differential topology, the Whitney embedding theorem states that Any smooth second-countable -dimensional manifold can be embedded in Euclidean -space. ... In mathematics, a manifold M is a type of space, characterised in one of two equivalent ways: near every point of the space, we have a coordinate system; or near every point, the environment is like that in Euclidean space of a given dimension. ... This article may be too technical for most readers to understand. ... In mathematics, Wilsons Theorem states that for a prime number p > 1, (see factorial and modular arithmetic for the notation). ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematics, Wolstenholmes theorem states that for a prime number p > 3, the congruence holds, where the LHS is a binomial coefficient. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ...

Z

• Zeckendorf's theorem
• Zermelo's theorem[1] (game theory)