Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 5206
- Definitions 5027
- Statements 3081
- Conjectures 75
- Problems 147
- Examples 431
- Counterexamples 71
- Objects 132
- Proofs 11
- Computations 1
- Topics 1
Ideas 1051–1200 of 3081.
| Name | Kind | Subject |
|---|---|---|
| A function with nonnegative second derivative is convex | Corollary | Real functions |
| Burnside's lemma | Theorem | Group theory and generalizations |
| Determinant of the identity matrix | Proposition | Linear and multilinear algebra; matrix theory |
| Local homeomorphism from the inverse function theorem | Corollary | Real functions |
| Countable union of countable sets is countable | Theorem | Mathematical logic and foundations |
| Constant multiple rule | Corollary | Real functions |
| Dimension of the space of linear maps | Proposition | Linear and multilinear algebra; matrix theory |
| Cauchy criterion for sequences | Theorem | Sequences, series, summability |
| A complex number times its conjugate | Proposition | Functions of a complex variable |
| Gradient points in the direction of steepest ascent | Proposition | Real functions |
| Orbits partition the set | Proposition | Group theory and generalizations |
| g to the order of the group is the identity | Corollary | Group theory and generalizations |
| Universal property of the quotient space | Theorem | Linear and multilinear algebra; matrix theory |
| Transfinite induction | Theorem | Mathematical logic and foundations |
| Canonical isomorphism with the double dual | Theorem | Linear and multilinear algebra; matrix theory |
| Absorption law | Proposition | Order, lattices, ordered algebraic structures |
| Path-connected spaces are connected | Proposition | General topology |
| First isomorphism theorem for rings | Theorem | Associative rings and algebras |
| Determinant of a 2 by 2 matrix | Proposition | Linear and multilinear algebra; matrix theory |
| K(a) is isomorphic to K[x] modulo the minimal polynomial | Theorem | Field theory and polynomials |
| p-series test | Theorem | Sequences, series, summability |
| Matrix of the dual map is the transpose | Proposition | Linear and multilinear algebra; matrix theory |
| Tower law for indices | Proposition | Group theory and generalizations |
| The logarithm is strictly concave | Proposition | Real functions |
| Intersection of subgroups is a subgroup | Proposition | Group theory and generalizations |
| Uniqueness of limits | Proposition | Sequences, series, summability |
| Second supplement to quadratic reciprocity | Theorem | Number theory |
| Determinant of a transpose | Proposition | Linear and multilinear algebra; matrix theory |
| Doob's upcrossing inequality | Theorem | Probability theory and stochastic processes |
| Stationary phase approximation | Theorem | Approximations and expansions |
| Homotopy lifting for covering maps | Proposition | Manifolds and cell complexes |
| Willmore conjecture | Theorem | Differential geometry |
| Weierstrass factorization theorem | Theorem | Functions of a complex variable |
| Rokhlin's theorem | Theorem | Manifolds and cell complexes |
| Huisken's theorem on convex hypersurfaces | Theorem | Differential geometry |
| Hales–Jewett theorem | Theorem | Combinatorics |
| Ryll-Nardzewski theorem | Theorem | Mathematical logic and foundations |
| Beta function in terms of the gamma function | Theorem | Special functions |
| Nakayama's lemma | Lemma | Commutative algebra |
| Abel–Ruffini theorem | Theorem | Field theory and polynomials |
| Abelian theorems for integral transforms | Theorem | Integral transforms, operational calculus |
| Liénard's theorem | Theorem | Ordinary differential equations |
| Spectral theorem for unbounded self-adjoint operators | Theorem | Operator theory |
| Artin approximation theorem | Theorem | Commutative algebra |
| Wagner's theorem | Theorem | Combinatorics |
| Banach–Alaoglu theorem | Theorem | Functional analysis |
| Heaviside expansion theorem | Theorem | Integral transforms, operational calculus |
| Dirichlet's unit theorem | Theorem | Number theory |
| Krylov–Bogolyubov theorem | Theorem | Dynamical systems and ergodic theory |
| Bernstein–von Mises theorem | Theorem | Statistics |
| Gauss's hypergeometric theorem | Theorem | Special functions |
| Enriques–Kodaira classification | Theorem | Algebraic geometry |
| Regular local rings are UFDs | Theorem | Commutative algebra |
| Evans's theorem on word problems | Theorem | General algebraic systems |
| Giroux correspondence | Theorem | Manifolds and cell complexes |
| Fundamental strip of a Mellin transform | Proposition | Integral transforms, operational calculus |
| Cramér–Rao bound | Theorem | Statistics |
| Fourier transform on Schwartz space | Theorem | Harmonic analysis on Euclidean spaces |
| Base change theorems | Theorem | Algebraic geometry |
| Poincaré's theorem that the ball and polydisc are not biholomorphic | Theorem | Several complex variables and analytic spaces |
| Compactness theorem | Theorem | Mathematical logic and foundations |
| Stone–Weierstrass theorem | Theorem | Functional analysis |
| Pettis measurability theorem | Theorem | Measure and integration |
| Birkhoff–Grothendieck theorem | Theorem | Algebraic geometry |
| Krull intersection theorem | Theorem | Commutative algebra |
| Szegő recurrence and Verblunsky coefficients | Theorem | Harmonic analysis on Euclidean spaces |
| Arakelyan's theorem | Theorem | Functions of a complex variable |
| Robinson–Schensted correspondence | Theorem | Combinatorics |
| Cap set problem | Theorem | Combinatorics |
| Huygens principle | Theorem | Partial differential equations |
| Derivation of the conjugate gradient method | Proposition | Numerical analysis |
| Minkowski bound | Theorem | Number theory |
| Clarkson's inequalities | Theorem | Functional analysis |
| Conformal invariance of harmonic functions | Proposition | Potential theory |
| Holmgren's uniqueness theorem | Theorem | Partial differential equations |
| Cuthill–McKee algorithm | Proposition | Numerical analysis |
| Cartan–Thullen theorem | Theorem | Several complex variables and analytic spaces |
| Saccheri–Legendre theorem | Theorem | Geometry |
| Lebesgue's theorem on differentiability of monotone functions | Theorem | Real functions |
| Loewner's torus inequality | Theorem | Differential geometry |
| Favard's theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Newton–Kantorovich theorem | Theorem | Numerical analysis |
| Local index theorem | Theorem | Global analysis, analysis on manifolds |
| Lickorish–Wallace theorem | Theorem | Manifolds and cell complexes |
| Continuous additive functions are linear | Theorem | Difference and functional equations |
| Radon–Nikodym theorem | Theorem | Measure and integration |
| Berger's classification of holonomy groups | Theorem | Differential geometry |
| Shell theorem | Theorem | Potential theory |
| Paley–Zygmund inequality | Theorem | Probability theory and stochastic processes |
| Zassenhaus lemma | Lemma | Group theory and generalizations |
| Ergodic decomposition | Theorem | Dynamical systems and ergodic theory |
| Jung's theorem | Theorem | Convex and discrete geometry |
| Weyl character formula for compact groups | Theorem | Topological groups, Lie groups |
| Nonexistence of infinite-dimensional Lebesgue measure | Theorem | Measure and integration |
| Fundamental theorem of Γ-convergence | Theorem | Calculus of variations and optimal control; optimization |
| Thom's classification of elementary catastrophes | Theorem | Global analysis, analysis on manifolds |
| Cohn's irreducibility criterion | Theorem | Number theory |
| Expansion of iterated differences in shifts | Proposition | Difference and functional equations |
| Conjugate residual method | Theorem | Numerical analysis |
| Schur test | Theorem | Integral equations |
| Ball's existence theorem in nonlinear elasticity | Theorem | Mechanics of deformable solids |
| Holomorphic inverse function theorem | Theorem | Several complex variables and analytic spaces |
| Minimal curvature property of natural cubic splines | Theorem | Approximations and expansions |
| Malgrange preparation theorem | Theorem | Global analysis, analysis on manifolds |
| Osgood uniqueness criterion | Theorem | Ordinary differential equations |
| Grätzer–Schmidt theorem | Theorem | General algebraic systems |
| Artin's induction theorem | Theorem | Group theory and generalizations |
| Grauert's Oka principle for vector bundles | Theorem | Several complex variables and analytic spaces |
| Koksma–Hlawka inequality | Theorem | Number theory |
| Martingale representation theorem | Theorem | Probability theory and stochastic processes |
| Darboux's theorem on additive functions bounded on an interval | Theorem | Difference and functional equations |
| Von Neumann's theorem on self-adjoint extensions | Theorem | Operator theory |
| Phragmén–Lindelöf principle for subharmonic functions | Theorem | Potential theory |
| Whitney embedding theorem | Theorem | Manifolds and cell complexes |
| Garden of Eden theorem | Theorem | Dynamical systems and ergodic theory |
| Itô's lemma | Theorem | Probability theory and stochastic processes |
| Hopf–Lax formula | Theorem | Partial differential equations |
| Weyl's law | Theorem | Partial differential equations |
| Inverse transform sampling | Theorem | Numerical analysis |
| Matrix Wiener–Hopf factorization | Theorem | Integral equations |
| Eberlein–Šmulian theorem | Theorem | Functional analysis |
| Poncelet–Steiner theorem | Theorem | Geometry |
| Lempert's theorem on convex domains | Theorem | Several complex variables and analytic spaces |
| Parallel postulate | Fact | Geometry |
| Uniqueness of adjoints | Proposition | Category theory; homological algebra |
| Bulirsch–Stoer algorithm | Theorem | Numerical analysis |
| Hahn decomposition theorem | Theorem | Measure and integration |
| Ziggurat algorithm | Theorem | Numerical analysis |
| Elliptic regularity | Theorem | Partial differential equations |
| Steinitz's theorem | Theorem | Convex and discrete geometry |
| Jordan–Brouwer separation theorem | Theorem | Algebraic topology |
| Classification of surfaces | Theorem | Manifolds and cell complexes |
| Holomorphic functions on compact complex manifolds are constant | Proposition | Several complex variables and analytic spaces |
| Ohsawa–Takegoshi extension theorem | Theorem | Several complex variables and analytic spaces |
| Monotone class theorem | Theorem | Measure and integration |
| Hankel contour integral for the gamma function | Theorem | Special functions |
| Beurling's theorem | Theorem | Operator theory |
| Matlis duality | Theorem | Commutative algebra |
| Namioka--Phelps | Theorem | Functional analysis |
| Mac Lane's coherence theorem | Theorem | Category theory; homological algebra |
| Z* theorem | Theorem | Group theory and generalizations |
| Benamou–Brenier formula | Theorem | Calculus of variations and optimal control; optimization |
| Cartan formula | Theorem | Algebraic topology |
| von Neumann stability analysis | Theorem | Numerical analysis |
| Wold's decomposition theorem | Theorem | Probability theory and stochastic processes |
| Schwartz kernel theorem | Theorem | Functional analysis |
| Kirszbraun theorem | Theorem | Real functions |
| Lyapunov's convexity theorem | Theorem | Measure and integration |
| Artin–Rees lemma | Lemma | Commutative algebra |
| Stein's unbiased risk estimate | Theorem | Statistics |