Every idea

Ideas 3301–3450 of 7806.

Name	Kind	Subject
x^n converges pointwise but not uniformly on [0, 1]	Counterexample	Sequences, series, summability
Cyclic subgroup generated by an element	Definition	Group theory and generalizations
Critical point	Concept	Real functions
Dyck word	Concept	Computer science
Root of unity	Concept	Number theory
Conditional probability distribution	Definition	Probability theory and stochastic processes
Metric topology	Concept	General topology
Skewness	Concept	Statistics
Floor function	Definition	Real functions
Homotopy invariance of line integrals of closed forms	Theorem	Real functions
Number of distinct prime factors	Definition	Number theory
Decomposition of a permutation into disjoint cycles	Theorem	Group theory and generalizations
Catalan numbers	Concept	Combinatorics
Tangent plane to a graph	Definition	Real functions
Choice function	Definition	Mathematical logic and foundations
Quadratic reciprocity for the Jacobi symbol	Theorem	Number theory
Moore–Penrose inverse	Concept	Linear and multilinear algebra; matrix theory
Matrix of a linear map	Definition	Linear and multilinear algebra; matrix theory
Conformal map	Concept	Functions of a complex variable
Quotient group	Definition	Group theory and generalizations
Determinant as a group homomorphism	Example	Linear and multilinear algebra; matrix theory
Mercator series	Theorem	Functions of a complex variable
Cycle	Concept	Combinatorics
Pell's equation	Concept	Number theory
Power series of complex cosine	Proposition	Special functions
Diffeomorphism	Definition	Global analysis, analysis on manifolds
Stirling numbers of the first kind	Definition	Number theory
Separable space	Concept	General topology
Minimum spanning tree	Definition	Combinatorics
Diagonalisation of a quadratic form	Theorem	Number theory
Decomposition into generalised eigenspaces	Theorem	Linear and multilinear algebra; matrix theory
Linear first-order equation	Definition	Ordinary differential equations
Intermediate field	Concept	Field theory and polynomials
A function with nonnegative second derivative is convex	Corollary	Real functions
Kernel of a homomorphism	Definition	Group theory and generalizations
Burnside's lemma	Theorem	Group theory and generalizations
Symmetric difference	Definition	Mathematical logic and foundations
Taylor series	Concept	Approximations and expansions
Determinant of the identity matrix	Proposition	Linear and multilinear algebra; matrix theory
Proper metric space	Definition	General topology
Product topology	Definition	General topology
Alternating group	Concept	Group theory and generalizations
Interval of convergence	Definition	Functions of a complex variable
Greatest element	Definition	Order, lattices, ordered algebraic structures
Computing the inverse by row reduction	Concept	Linear and multilinear algebra; matrix theory
Matching	Definition	Combinatorics
The complex conjugate is not holomorphic	Counterexample	Functions of a complex variable
Local homeomorphism from the inverse function theorem	Corollary	Real functions
Countable union of countable sets is countable	Theorem	Mathematical logic and foundations
Probability-generating function	Definition	Probability theory and stochastic processes
Trial division	Concept	Number theory
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
Greatest common divisor in an integral domain	Concept	Commutative algebra
Memorylessness	Concept	Probability theory and stochastic processes
Nilpotent element	Concept	Associative rings and algebras
Pairwise independence	Concept	Probability theory and stochastic processes
A complex number times its conjugate	Proposition	Functions of a complex variable
Bernoulli equation	Definition	Ordinary differential equations
Gradient points in the direction of steepest ascent	Proposition	Real functions
Orbits partition the set	Proposition	Group theory and generalizations
Rank of a matrix	Concept	Linear and multilinear algebra; matrix theory
Ascending chain condition	Definition	Order, lattices, ordered algebraic structures
Closed set	Concept	General topology
Jacobian determinant	Concept	Real functions
Companion matrix	Concept	Linear and multilinear algebra; matrix theory
Neighbourhood	Concept	Combinatorics
Tangent vector of a curve	Concept	Differential geometry
Dual basis	Concept	Linear and multilinear algebra; matrix theory
Angle at a point	Definition	Geometry
Exponent of a group	Concept	Group theory and generalizations
Angle between two vectors	Concept	Geometry
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
Median of a triangle	Definition	Geometry
Minimum degree	Concept	Combinatorics
Homothety	Concept	Geometry
Symmetry group	Concept	Group theory and generalizations
Countable set	Definition	Mathematical logic and foundations
Parametrised surface	Concept	Differential geometry
Proposition	Concept	Mathematical logic and foundations
Baire space	Concept	General topology
Transfinite induction	Theorem	Mathematical logic and foundations
Exterior derivative	Concept	Global analysis, analysis on manifolds
Finite-dimensional vector space	Concept	Linear and multilinear algebra; matrix theory
Conditional independence	Definition	Probability theory and stochastic processes
Canonical isomorphism with the double dual	Theorem	Linear and multilinear algebra; matrix theory
Cycle notation	Concept	Group theory and generalizations
Absorption law	Proposition	Order, lattices, ordered algebraic structures
Path-connected spaces are connected	Proposition	General topology
Elementary symmetric polynomials	Definition	Combinatorics
First isomorphism theorem for rings	Theorem	Associative rings and algebras
Stirling numbers of the second kind	Definition	Number theory
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
Conditional probability distribution	Concept	Probability theory and stochastic processes
Eigenvalue	Definition	Linear and multilinear algebra; matrix theory
Intersection	Concept	Mathematical logic and foundations
p-series test	Theorem	Sequences, series, summability
Implication	Definition	Mathematical logic and foundations
Power sum symmetric polynomial	Concept	Combinatorics
Inverse element	Concept	General algebraic systems
Matrix of the dual map is the transpose	Proposition	Linear and multilinear algebra; matrix theory
Grönwall bound	Concept	Ordinary differential equations
Recursively defined sequence	Concept	Number theory
Tower law for indices	Proposition	Group theory and generalizations
The logarithm is strictly concave	Proposition	Real functions
Central moment	Definition	Probability theory and stochastic processes
Operator norm	Definition	Operator theory
Intersection of subgroups is a subgroup	Proposition	Group theory and generalizations
Zero matrix	Object	Linear and multilinear algebra; matrix theory
Closed and exact forms	Concept	Global analysis, analysis on manifolds
Solution of a linear recurrence	Definition	Difference and functional equations
Complex power	Definition	Special functions
Law of large numbers	Concept	Probability theory and stochastic processes
Quotient set	Definition	Mathematical logic and foundations
Bipartite graph	Concept	Combinatorics
Uniqueness of limits	Proposition	Sequences, series, summability
Isometric isomorphism	Concept	General topology
Second supplement to quadratic reciprocity	Theorem	Number theory
Finite field	Concept	Field theory and polynomials
Probability density function	Concept	Probability theory and stochastic processes
Probability space	Definition	Probability theory and stochastic processes
Taylor polynomial	Concept	Approximations and expansions
Meromorphic function	Concept	Functions of a complex variable
Determinant of a transpose	Proposition	Linear and multilinear algebra; matrix theory
Subnormal series	Concept	Group theory and generalizations
Argument of a complex number	Definition	Functions of a complex variable
Rank of a linear map	Concept	Linear and multilinear algebra; matrix theory
Sendov's conjecture	Conjecture	Functions of a complex variable
Cotton tensor	Concept	Differential geometry
Power iteration	Definition	Numerical analysis
Doob's upcrossing inequality	Theorem	Probability theory and stochastic processes
Completely normal space	Definition	General topology
Homotopy lifting for covering maps	Proposition	Manifolds and cell complexes
Rigged Hilbert space	Definition	Functional analysis
Free probability	Concept	Functional analysis
Graph of groups	Definition	Group theory and generalizations
Willmore conjecture	Theorem	Differential geometry
Relative CW complex	Definition	Manifolds and cell complexes
Weierstrass factorization theorem	Theorem	Functions of a complex variable
Rokhlin's theorem	Theorem	Manifolds and cell complexes
Transcendental extension	Concept	Field theory and polynomials
Filtration	Definition	Probability theory and stochastic processes
Betti numbers of a module	Definition	Commutative algebra
Geodesic curvature	Definition	Differential geometry
Calabi flow	Definition	Differential geometry
Set-valued measure	Concept	Measure and integration
Proof complexity	Definition	Mathematical logic and foundations