Every idea

Ideas 1–150 of 14183.

Name	Kind	Subject
Vector space	Concept	Linear and multilinear algebra; matrix theory
The integers are a Euclidean domain	Theorem	Number theory
Sequential characterization of limits	Theorem	Real functions
Singular value decomposition	Theorem	Linear and multilinear algebra; matrix theory
Quotient set	Concept	Mathematical logic and foundations
Mutual independence of events	Concept	Probability theory and stochastic processes
Partition function	Definition	Number theory
Block diagonal matrix	Concept	Linear and multilinear algebra; matrix theory
Power series are differentiable inside the radius of convergence	Theorem	Functions of a complex variable
A function with zero derivative is constant	Corollary	Real functions
Closure is the set of limits of sequences	Proposition	General topology
Differential equation	Concept	Ordinary differential equations
Natural logarithm	Definition	Special functions
Jump discontinuity	Concept	Real functions
Exterior derivative	Definition	Global analysis, analysis on manifolds
Power set Boolean algebra	Example	Order, lattices, ordered algebraic structures
Square-free integer	Definition	Number theory
Sylow p-subgroup	Concept	Group theory and generalizations
A differentiable function is convex iff its derivative is increasing	Theorem	Real functions
Taylor's theorem with the Cauchy remainder	Theorem	Approximations and expansions
Row equivalence	Concept	Linear and multilinear algebra; matrix theory
The characteristic of an integral domain is zero or prime	Theorem	Commutative algebra
Quotient ring	Concept	Associative rings and algebras
Least common multiple	Concept	Number theory
Variance	Definition	Probability theory and stochastic processes
Dimension of the dual space	Proposition	Linear and multilinear algebra; matrix theory
Composite number	Concept	Number theory
Zero ring	Example	Associative rings and algebras
Linear map of a matrix	Definition	Linear and multilinear algebra; matrix theory
Local maximum	Definition	Real functions
Scaling a row scales the determinant	Proposition	Linear and multilinear algebra; matrix theory
Sum of divisors	Definition	Number theory
Stars and bars	Theorem	Combinatorics
Normed vector space	Definition	Functional analysis
Principal ideal	Definition	Commutative algebra
One-sided limit	Concept	Real functions
Platonic solid	Definition	Geometry
Composition of linear maps	Concept	Linear and multilinear algebra; matrix theory
Picard–Lindelöf theorem in integral form	Theorem	Ordinary differential equations
Finite intersection property	Proposition	General topology
Graph	Concept	Combinatorics
Polyhedron	Definition	Convex and discrete geometry
Euler–Mascheroni constant	Object	Number theory
Addition formula for Fibonacci numbers	Theorem	Number theory
Countably infinite set	Concept	Mathematical logic and foundations
Graph isomorphism	Definition	Combinatorics
The logarithm grows slower than any power	Theorem	Real functions
Laws of exponents in a group	Proposition	Group theory and generalizations
−1 is a square modulo p if and only if p is not 3 modulo 4	Corollary	Number theory
Power set	Concept	Mathematical logic and foundations
Euclidean vector	Definition	Geometry
Root of a polynomial	Definition	Commutative algebra
Hasse diagram	Concept	Order, lattices, ordered algebraic structures
Orbit	Definition	Group theory and generalizations
Closed map	Concept	General topology
Congruence is compatible with addition	Proposition	Number theory
Contour integral	Definition	Functions of a complex variable
Zero of a holomorphic function	Concept	Functions of a complex variable
Modular multiplicative inverse	Definition	Number theory
Direct product of groups	Concept	Group theory and generalizations
Conic section	Concept	Geometry
Norm of a Gaussian integer	Definition	Number theory
Trisecting the angle	Problem	Geometry
Lower triangular matrix	Concept	Linear and multilinear algebra; matrix theory
Divisibility rule	Concept	Number theory
Multinomial coefficient	Definition	Combinatorics
Nullity	Definition	Linear and multilinear algebra; matrix theory
Non-uniqueness for a non-Lipschitz equation	Counterexample	Ordinary differential equations
Intermediate value theorem	Theorem	Real functions
Determinant	Concept	Linear and multilinear algebra; matrix theory
Modulus of the conjugate	Proposition	Functions of a complex variable
Prime ideal	Concept	Commutative algebra
Independent and identically distributed random variables	Concept	Probability theory and stochastic processes
Every vector space has a basis	Theorem	Linear and multilinear algebra; matrix theory
Saddle point	Definition	Real functions
Change of variables in multiple integrals	Theorem	Real functions
Prior probability	Concept	Statistics
Complex sine and cosine	Concept	Special functions
Power of a point	Definition	Geometry
Positive definite quadratic form	Definition	Linear and multilinear algebra; matrix theory
Primitive element of a finite field	Concept	Field theory and polynomials
Compact set	Definition	General topology
Arc length parametrisation	Definition	Differential geometry
Derivative of sine	Theorem	Special functions
Divergence of the sum of the reciprocals of the primes	Theorem	Number theory
Second-countable space	Definition	General topology
Absolute value	Definition	Real functions
Asymptotic equivalence	Definition	Approximations and expansions
Gram matrix	Concept	Linear and multilinear algebra; matrix theory
Event	Definition	Probability theory and stochastic processes
Exponential growth and decay	Example	Ordinary differential equations
Transcendental element	Definition	Field theory and polynomials
Little o notation	Concept	Approximations and expansions
Ramsey's theorem	Theorem	Combinatorics
Picard operator	Definition	Ordinary differential equations
Irreducible polynomial	Definition	Field theory and polynomials
Lotka–Volterra equations	Example	Biology and other natural sciences
A finite group is nilpotent iff it is the product of its Sylow subgroups	Theorem	Group theory and generalizations
Linear subspace	Concept	Linear and multilinear algebra; matrix theory
Volume of a ball in R^n	Theorem	Measure and integration
Arcsine	Concept	Special functions
Additivity of line integrals under concatenation	Proposition	Real functions
Topological embedding	Concept	General topology
Ordered field	Definition	Field theory and polynomials
Uniqueness of finite fields of a given order	Theorem	Field theory and polynomials
Hensel's lemma	Theorem	Number theory
Recurrence for Bell numbers	Theorem	Number theory
Image of a homomorphism	Definition	Group theory and generalizations
Partial order	Definition	Order, lattices, ordered algebraic structures
Strictly monotone function	Concept	Real functions
A convex function on an open interval is continuous	Theorem	Real functions
Jordan–Chevalley decomposition	Theorem	Linear and multilinear algebra; matrix theory
Evaluation homomorphism	Definition	Commutative algebra
1 + x is at most exp x	Proposition	Special functions
Hölder continuity	Concept	Real functions
Reduction formula	Concept	Real functions
Differentiable function of several variables	Definition	Real functions
exp z = 1 iff z is an integer multiple of 2πi	Proposition	Special functions
Existence of splitting fields	Theorem	Field theory and polynomials
Strict differentiability	Definition	Real functions
Semidirect product	Definition	Group theory and generalizations
Chernoff bound	Theorem	Probability theory and stochastic processes
Cayley's theorem	Theorem	Group theory and generalizations
Integral equation form of an initial value problem	Proposition	Ordinary differential equations
Glide reflection	Concept	Geometry
Leibniz formula for determinants	Theorem	Linear and multilinear algebra; matrix theory
Principal branch	Concept	Functions of a complex variable
Alternating series	Definition	Sequences, series, summability
Riemann's criterion for integrability	Theorem	Real functions
Platonic solid	Concept	Geometry
Dyck words are counted by Catalan numbers	Theorem	Combinatorics
Prime number	Concept	Number theory
Vector-valued function	Concept	Real functions
Finite-dimensional vector space	Definition	Linear and multilinear algebra; matrix theory
Rolle's theorem	Theorem	Real functions
Residue at a simple pole	Proposition	Functions of a complex variable
Derivative of the complex exponential	Proposition	Special functions
Root of a polynomial	Concept	Commutative algebra
Unit of a ring	Definition	Associative rings and algebras
Integral test	Theorem	Sequences, series, summability
Maximal solution	Definition	Ordinary differential equations
Weierstrass function	Counterexample	Real functions
First derivative test	Proposition	Real functions
cos pi = -1	Proposition	Special functions
Distance from a point to a line	Proposition	Geometry
Preimage of a set	Concept	Mathematical logic and foundations
Chapman–Kolmogorov equation	Theorem	Probability theory and stochastic processes
Block matrix	Definition	Linear and multilinear algebra; matrix theory
Bias of an estimator	Definition	Statistics
Well-ordering principle	Theorem	Mathematical logic and foundations