Every idea

Ideas 1801–1950 of 7806.

Name	Kind	Subject
Pseudometric space	Definition	General topology
Semidirect product	Concept	Group theory and generalizations
Euclidean group	Object	Group theory and generalizations
Inner automorphism	Definition	Group theory and generalizations
Fundamental system of solutions	Definition	Ordinary differential equations
Limit inferior	Definition	Sequences, series, summability
Disjunction	Definition	Mathematical logic and foundations
Upper bound	Definition	Order, lattices, ordered algebraic structures
Line integral of a vector field	Concept	Real functions
Gamma function	Concept	Special functions
The order of a finite field is a prime power	Theorem	Field theory and polynomials
Taylor's theorem with the Lagrange remainder	Theorem	Approximations and expansions
Changing the order of integration	Proposition	Real functions
Algebraic element	Concept	Field theory and polynomials
Galton–Watson process	Definition	Probability theory and stochastic processes
Del operator	Concept	Real functions
Product of power series	Theorem	Commutative algebra
Scalar potential	Concept	Real functions
Cumulative distribution function	Concept	Probability theory and stochastic processes
Every finite tree with at least two vertices has a leaf	Lemma	Combinatorics
Rule of Sarrus	Proposition	Linear and multilinear algebra; matrix theory
Plane	Definition	Geometry
Abelianisation	Definition	Group theory and generalizations
Rectifiable curve	Concept	Real functions
Interior is the largest open subset	Proposition	General topology
Binomial series	Example	Functions of a complex variable
Markov property	Definition	Probability theory and stochastic processes
Limit point	Definition	General topology
Intersection	Definition	Mathematical logic and foundations
Induction on the integers	Theorem	Number theory
Riemann sum	Definition	Real functions
Zermelo–Fraenkel set theory	Concept	Mathematical logic and foundations
Union of open sets is open	Proposition	General topology
Russell's paradox	Theorem	Mathematical logic and foundations
Hamiltonian cycle	Concept	Combinatorics
Rotation	Concept	Geometry
Taylor polynomial	Definition	Approximations and expansions
First-countable space	Definition	General topology
Pigeonhole principle	Theorem	Combinatorics
Sum of a series	Concept	Sequences, series, summability
Generating function	Definition	Combinatorics
Differentiable function of several variables	Concept	Real functions
Solutions for distinct real roots	Theorem	Ordinary differential equations
Thomae's function	Example	Real functions
Second isomorphism theorem for rings	Theorem	Associative rings and algebras
Discrete logarithm	Concept	Number theory
Hamiltonian cycle	Definition	Combinatorics
Random experiment	Concept	Probability theory and stochastic processes
Distributive lattice	Concept	Order, lattices, ordered algebraic structures
RSA cryptosystem	Example	Information and communication theory, circuits
A sequence converges iff its liminf and limsup agree	Proposition	Sequences, series, summability
Order on the natural numbers	Concept	Mathematical logic and foundations
Centre of mass	Concept	Real functions
Eigenvectors with distinct eigenvalues are linearly independent	Theorem	Linear and multilinear algebra; matrix theory
Generalised Stokes theorem	Theorem	Global analysis, analysis on manifolds
Archimedean ordered field	Definition	Field theory and polynomials
Coefficient matrix	Concept	Linear and multilinear algebra; matrix theory
Green's theorem	Theorem	Real functions
Linear span	Definition	Linear and multilinear algebra; matrix theory
Rearrangement of a series	Definition	Sequences, series, summability
Solutions for repeated roots	Theorem	Ordinary differential equations
Axiom of choice	Axiom	Mathematical logic and foundations
Reduced residue system	Concept	Number theory
Rouché–Capelli theorem	Theorem	Linear and multilinear algebra; matrix theory
Group homomorphism	Definition	Group theory and generalizations
Eccentricity	Concept	Geometry
Limit comparison test	Theorem	Sequences, series, summability
Gram matrix	Definition	Linear and multilinear algebra; matrix theory
One-sided derivative	Definition	Real functions
Finitely generated group	Definition	Group theory and generalizations
Totient of a prime	Proposition	Number theory
Eigenvalues of a positive definite matrix are positive	Theorem	Linear and multilinear algebra; matrix theory
Injective iff it has a left inverse	Proposition	Mathematical logic and foundations
Polar form of a quadratic form	Concept	Linear and multilinear algebra; matrix theory
Modulus is multiplicative	Proposition	Functions of a complex variable
Student's t-test	Concept	Statistics
Mean value property	Theorem	Potential theory
Norm of a Gaussian integer	Concept	Number theory
Hamiltonian graph	Concept	Combinatorics
Quadratic form	Definition	Linear and multilinear algebra; matrix theory
Pivot	Concept	Linear and multilinear algebra; matrix theory
Exponential function	Concept	Special functions
Reduced residue system	Definition	Number theory
Quotient map	Definition	Linear and multilinear algebra; matrix theory
Proof by contradiction	Concept	General and overarching topics
Fixed field	Concept	Field theory and polynomials
Euclidean isometry	Concept	Geometry
Liouville number	Definition	Number theory
Solutions of Pell's equation are powers of the fundamental solution	Theorem	Number theory
Existence of nth roots by the intermediate value theorem	Example	Real functions
Polar decomposition	Theorem	Linear and multilinear algebra; matrix theory
Inverse function	Concept	Mathematical logic and foundations
Equivalent norms	Definition	Functional analysis
Cycle type	Concept	Group theory and generalizations
Conjugacy classes of the symmetric group correspond to cycle types	Theorem	Group theory and generalizations
The symmetric group on five or more letters is not solvable	Theorem	Group theory and generalizations
Characteristic polynomial of a linear map	Concept	Linear and multilinear algebra; matrix theory
Congruence is compatible with powers	Corollary	Number theory
Intersecting secants theorem	Theorem	Geometry
Lyapunov's stability theorem	Theorem	Ordinary differential equations
Associativity of composition	Proposition	Mathematical logic and foundations
Kuratowski's theorem	Theorem	Combinatorics
Hyperbolic functions	Definition	Special functions
Discrete random variable	Definition	Probability theory and stochastic processes
Nine-point circle	Definition	Geometry
Rearrangements of an absolutely convergent series have the same sum	Theorem	Sequences, series, summability
Riemann sphere	Concept	Functions of a complex variable
Endomorphism	Concept	Linear and multilinear algebra; matrix theory
Picard–Lindelöf hypotheses	Definition	Ordinary differential equations
Logarithm of a quotient	Corollary	Special functions
Primitive root of unity	Definition	Number theory
Sperner's theorem	Theorem	Combinatorics
Composition of an integer	Definition	Combinatorics
Taylor's theorem in several variables	Theorem	Real functions
Reachability	Definition	Combinatorics
Limit of a function of several variables	Concept	Real functions
Bernoulli distribution	Definition	Probability theory and stochastic processes
Determinant of a block triangular matrix	Proposition	Linear and multilinear algebra; matrix theory
Riemann sum	Concept	Real functions
Euler method	Concept	Numerical analysis
Image of a linear map	Definition	Linear and multilinear algebra; matrix theory
Linear combination	Definition	Linear and multilinear algebra; matrix theory
Graph of a function	Concept	Mathematical logic and foundations
Ratio formula for the radius of convergence	Proposition	Functions of a complex variable
Vector calculus identities	Theorem	Real functions
Stirling numbers of the second kind	Concept	Number theory
Converse relation	Definition	Mathematical logic and foundations
Graph	Definition	Combinatorics
Analytic function	Definition	Real functions
Convergence in distribution	Definition	Probability theory and stochastic processes
Triangle	Definition	Geometry
Path	Definition	Combinatorics
Continuity in R^n	Concept	Real functions
Sign is a homomorphism	Theorem	Group theory and generalizations
The cumulative distribution function determines the distribution	Theorem	Probability theory and stochastic processes
Affine map	Concept	Geometry
Parametrised curve	Definition	Differential geometry
Regular space	Definition	General topology
Residue	Definition	Functions of a complex variable
Turán's theorem	Theorem	Combinatorics
Connected component	Concept	Combinatorics
Rank of a linear map	Definition	Linear and multilinear algebra; matrix theory
Presentation of a group	Concept	Group theory and generalizations
Space of polynomials of bounded degree	Example	Linear and multilinear algebra; matrix theory
Series	Definition	Sequences, series, summability
Eigenspaces of a self-adjoint operator are orthogonal	Proposition	Operator theory
The ring of integers	Example	Commutative algebra
Exponential generating function	Concept	Combinatorics
Underdamped	Concept	Mechanics of particles and systems
Boundary	Definition	General topology