Every idea

Ideas 2851–3000 of 7806.

Name	Kind	Subject
Prime subfield	Concept	Field theory and polynomials
Partial derivatives do not imply differentiability	Counterexample	Real functions
Circumcentre	Definition	Geometry
Congruence modulo n	Definition	Number theory
An algebraic extension of an algebraic extension is algebraic	Theorem	Field theory and polynomials
Strictly monotone function	Definition	Real functions
Euclidean algorithm	Concept	Number theory
Orthogonal vectors	Definition	Linear and multilinear algebra; matrix theory
Law of a random variable	Definition	Probability theory and stochastic processes
Convergence in mean	Definition	Probability theory and stochastic processes
Conditional expectation	Concept	Probability theory and stochastic processes
Estimator	Definition	Statistics
Real exponentiation	Definition	Real functions
Compact space	Concept	General topology
Incentre	Definition	Geometry
Equivalent metrics	Definition	General topology
Invertible matrix	Definition	Linear and multilinear algebra; matrix theory
Symmetric bilinear form associated with a quadratic form	Definition	Linear and multilinear algebra; matrix theory
Integration over a non-rectangular region	Concept	Real functions
Primitive polynomial	Concept	Commutative algebra
Limit of a function	Definition	Real functions
Product of a subgroup and a normal subgroup is a subgroup	Proposition	Group theory and generalizations
Isolated singularity	Definition	Functions of a complex variable
Characteristic polynomial does not depend on the basis	Proposition	Linear and multilinear algebra; matrix theory
Surjective iff it has a right inverse	Proposition	Mathematical logic and foundations
Principal part	Concept	Functions of a complex variable
Row rank equals column rank	Theorem	Linear and multilinear algebra; matrix theory
Maximal element	Definition	Order, lattices, ordered algebraic structures
The sequence r^n tends to infinity for r > 1	Example	Sequences, series, summability
Connected space	Concept	General topology
Induced subgraph	Definition	Combinatorics
Variance of a sum of independent random variables	Theorem	Probability theory and stochastic processes
Sign of a cycle	Proposition	Group theory and generalizations
Complete bipartite graph	Example	Combinatorics
Frobenius coin problem	Theorem	Number theory
Derivative	Concept	Real functions
Derivative of cosine	Theorem	Special functions
Aleph-null	Object	Mathematical logic and foundations
Norm	Concept	Functional analysis
Smooth function	Concept	Real functions
Intersection of subspaces	Proposition	Linear and multilinear algebra; matrix theory
Semigroup	Definition	Group theory and generalizations
Gamma function	Definition	Special functions
Cauchy principal value	Definition	Real functions
Plane	Concept	Geometry
Laplace transform	Concept	Integral transforms, operational calculus
Continuous real function on a compact set attains its bounds	Theorem	General topology
Separable equation	Definition	Ordinary differential equations
Vacuous truth	Concept	Mathematical logic and foundations
Fibonacci numbers as sums of binomial coefficients	Theorem	Number theory
Mean squared error	Definition	Statistics
Subgroups of index two are normal	Proposition	Group theory and generalizations
Minimal polynomial	Definition	Linear and multilinear algebra; matrix theory
Characteristic function	Concept	Probability theory and stochastic processes
Leading coefficient	Concept	Commutative algebra
Regular polygon	Definition	Geometry
Biconditional	Definition	Mathematical logic and foundations
Regular curve	Concept	Differential geometry
Square root function	Definition	Real functions
Covariance matrix	Concept	Statistics
Standard basis	Object	Linear and multilinear algebra; matrix theory
Quotient topology	Definition	General topology
Linear combination	Concept	Linear and multilinear algebra; matrix theory
Logarithm of a power	Corollary	Special functions
Determinant of a family of vectors in a basis	Definition	Linear and multilinear algebra; matrix theory
First Sylow theorem	Theorem	Group theory and generalizations
Product rule	Theorem	Real functions
Dirichlet's test	Theorem	Sequences, series, summability
Special linear group	Object	Linear and multilinear algebra; matrix theory
Preorder	Concept	Order, lattices, ordered algebraic structures
Power series in the complex plane	Definition	Functions of a complex variable
Square root	Definition	Real functions
Multiplicativity of the Möbius function	Proposition	Number theory
Kummer's theorem	Theorem	Number theory
Internal direct product	Concept	Group theory and generalizations
Euler's theorem	Theorem	Number theory
Improper integral	Definition	Real functions
Matrix	Concept	Linear and multilinear algebra; matrix theory
Morera's theorem	Theorem	Functions of a complex variable
Poisson distribution	Definition	Probability theory and stochastic processes
Volume of a box	Proposition	Measure and integration
Field of fractions	Definition	Commutative algebra
Quotient ring	Definition	Associative rings and algebras
Every polynomial has a root in some extension field	Theorem	Field theory and polynomials
Abundant number	Concept	Number theory
Continuous map	Concept	General topology
Improper integral of x^p on an unbounded interval	Example	Sequences, series, summability
Probability measure	Definition	Probability theory and stochastic processes
Product of continuous functions is continuous	Proposition	Real functions
Continuity is equivalent to sequential continuity in metric spaces	Theorem	General topology
Conditional variance	Concept	Probability theory and stochastic processes
Inner product	Definition	Linear and multilinear algebra; matrix theory
Abel's identity	Theorem	Ordinary differential equations
Companion matrix	Definition	Linear and multilinear algebra; matrix theory
Subsequences of a convergent sequence converge to the same limit	Proposition	Sequences, series, summability
Chromatic number	Concept	Combinatorics
Conformal map	Definition	Functions of a complex variable
Symmetric polynomial	Concept	Combinatorics
Finite-dimensional spaces are isomorphic iff they have equal dimension	Theorem	Linear and multilinear algebra; matrix theory
Homogeneous linear system with constant coefficients	Definition	Ordinary differential equations
Walk	Definition	Combinatorics
De Morgan's laws for sets	Theorem	Mathematical logic and foundations
Size of a conjugacy class is the index of the centraliser	Proposition	Group theory and generalizations
Banach fixed point theorem	Theorem	Operator theory
Ellipse	Concept	Geometry
Metric space	Concept	General topology
Lagrange multipliers	Theorem	Operations research, mathematical programming
Decimal expansion	Concept	Number theory
Limit of a function of several variables	Definition	Real functions
Cartan–Dieudonné theorem	Theorem	Geometry
Smallest prime factor	Concept	Number theory
If 2^n + 1 is prime then n is a power of 2	Proposition	Number theory
Polynomials of degree two or three are irreducible iff they have no roots	Proposition	Field theory and polynomials
Pythagorean theorem	Theorem	Geometry
Frobenius automorphism of a finite field	Definition	Field theory and polynomials
Power series	Definition	Functions of a complex variable
Space of linear maps	Definition	Linear and multilinear algebra; matrix theory
Prime subfield	Definition	Field theory and polynomials
Rule of product	Theorem	Combinatorics
Sequence tending to infinity	Concept	Sequences, series, summability
Combinations with repetition	Concept	Combinatorics
Nowhere dense set	Concept	General topology
Symmetric matrix	Concept	Linear and multilinear algebra; matrix theory
Isometric isomorphism	Definition	General topology
Binomial distribution	Definition	Probability theory and stochastic processes
Abundant number	Definition	Number theory
Indicator function	Definition	Mathematical logic and foundations
A tree on n vertices has n − 1 edges	Theorem	Combinatorics
Cancellation laws	Proposition	Group theory and generalizations
Characteristic polynomial	Concept	Linear and multilinear algebra; matrix theory
Riccati equation	Concept	Ordinary differential equations
Gram–Schmidt process	Concept	Linear and multilinear algebra; matrix theory
Minimal polynomial divides every annihilating polynomial	Proposition	Linear and multilinear algebra; matrix theory
Sup metric on R^n	Example	General topology
Turán graph	Example	Combinatorics
Ring homomorphism	Concept	Associative rings and algebras
Standard deviation	Definition	Probability theory and stochastic processes
Basis	Definition	Linear and multilinear algebra; matrix theory
Transcendental number	Concept	Number theory
Euler's totient function	Definition	Number theory
Convex function	Definition	Real functions
Number of divisors	Concept	Number theory
Discriminant of a polynomial	Concept	Field theory and polynomials
Order of a power	Proposition	Group theory and generalizations
Term test	Proposition	Sequences, series, summability
Continuously differentiable function	Concept	Real functions
Likelihood function	Concept	Statistics
Euler line	Theorem	Geometry
Minimal polynomial (field theory)	Concept	Field theory and polynomials
Standard score	Concept	Statistics