Every idea

Ideas 2251–2400 of 7806.

Name	Kind	Subject
Idempotent element	Concept	Associative rings and algebras
Classification of conics by the discriminant	Theorem	Geometry
Degree of a simple extension is the degree of the minimal polynomial	Corollary	Field theory and polynomials
Fermat primality test	Concept	Number theory
Vector field	Definition	Real functions
Simple extension	Concept	Field theory and polynomials
Eigenvector	Concept	Linear and multilinear algebra; matrix theory
Monoid	Concept	Group theory and generalizations
Classification of equilibria of planar linear systems	Concept	Ordinary differential equations
Kronecker product	Concept	Linear and multilinear algebra; matrix theory
Equilibrium point	Concept	Ordinary differential equations
Mean value theorem for integrals	Theorem	Real functions
Fermat prime	Definition	Number theory
Nilpotent element	Definition	Associative rings and algebras
Symmetric relation	Definition	Mathematical logic and foundations
Basis of a topology	Concept	General topology
Discrete metric	Example	General topology
Cauchy distribution	Definition	Probability theory and stochastic processes
Ore's theorem	Theorem	Combinatorics
Holomorphic function	Concept	Functions of a complex variable
Apollonius's theorem	Theorem	Geometry
Harmonic number	Concept	Number theory
Inner product	Concept	Linear and multilinear algebra; matrix theory
exp(1/z) has an essential singularity at 0	Example	Functions of a complex variable
Partial sum	Definition	Sequences, series, summability
Asymptotic stability	Concept	Ordinary differential equations
Composition series	Definition	Group theory and generalizations
Divergent series	Definition	Sequences, series, summability
The integral of a continuous function is an antiderivative	Corollary	Real functions
Planar graph	Concept	Combinatorics
Rational numbers	Object	Number theory
Graph colouring	Concept	Combinatorics
Principal part	Definition	Functions of a complex variable
Linear recurrence with constant coefficients	Concept	Difference and functional equations
Right coset	Concept	Group theory and generalizations
Conditional convergence	Concept	Sequences, series, summability
Implicit function theorem for a surjective derivative	Corollary	Real functions
Self-adjoint operator	Concept	Operator theory
Restriction of a function	Concept	Mathematical logic and foundations
Curl	Concept	Real functions
Double negation law	Theorem	Mathematical logic and foundations
The minimal polynomial is irreducible	Proposition	Field theory and polynomials
Probability space	Concept	Probability theory and stochastic processes
Fundamental theorem of calculus	Theorem	Real functions
Perfect matching	Concept	Combinatorics
Sample variance	Concept	Statistics
von Mangoldt function	Concept	Number theory
Double integral	Definition	Real functions
Series	Concept	Sequences, series, summability
Bayes' theorem	Theorem	Statistics
Variance as the mean of the square minus the square of the mean	Proposition	Probability theory and stochastic processes
Implication	Concept	Mathematical logic and foundations
Epsilon-net characterisation of total boundedness	Proposition	General topology
Transvection	Definition	Linear and multilinear algebra; matrix theory
Birthday problem	Example	Probability theory and stochastic processes
Trace is the sum of the eigenvalues	Theorem	Linear and multilinear algebra; matrix theory
0.999... equals 1	Example	Number theory
Closed formula for Catalan numbers	Theorem	Combinatorics
Associativity	Definition	General algebraic systems
Schwarz's theorem for C^2 functions	Theorem	Real functions
Reduced row echelon form	Definition	Linear and multilinear algebra; matrix theory
Zero divisor	Concept	Associative rings and algebras
Moment-generating function	Definition	Probability theory and stochastic processes
Eulerian trail	Definition	Combinatorics
Cantor pairing function	Example	Mathematical logic and foundations
Euclidean distance	Concept	Geometry
Algebraic element	Definition	Field theory and polynomials
Quotient topology	Concept	General topology
Student's t-distribution	Definition	Probability theory and stochastic processes
Transcendental element	Concept	Field theory and polynomials
Winding number	Concept	Algebraic topology
Triangle inequality for integrals	Theorem	Real functions
Petersen graph	Example	Combinatorics
Quaternion group	Object	Group theory and generalizations
Composition of continuous functions is continuous	Proposition	Real functions
Connected components are closed	Proposition	General topology
Linear map	Concept	Linear and multilinear algebra; matrix theory
Finite extension	Definition	Field theory and polynomials
Characteristic function of the normal distribution	Proposition	Probability theory and stochastic processes
Derivative of a map into R^n by components	Proposition	Real functions
Product of two subgroups	Definition	Group theory and generalizations
Gradient	Definition	Real functions
Construction of the integers from the natural numbers	Concept	Number theory
Local minimum	Definition	Real functions
Meromorphic function	Definition	Functions of a complex variable
Normal space	Concept	General topology
Ordinary differential equation	Concept	Ordinary differential equations
Direct proof	Concept	General and overarching topics
Discrete Grönwall inequality	Lemma	Real functions
Exterior angle theorem	Theorem	Geometry
Multiplicative function	Concept	Number theory
Z/pZ is a field for p prime	Theorem	Number theory
Open cover	Definition	General topology
Multiplicativity of the Legendre symbol	Theorem	Number theory
T1 space	Concept	General topology
Second Borel–Cantelli lemma	Lemma	Probability theory and stochastic processes
Weierstrass M-test	Theorem	Sequences, series, summability
Sum of independent normal random variables	Theorem	Probability theory and stochastic processes
Euclidean isometry	Definition	Geometry
Adjoining a root of a polynomial	Concept	Field theory and polynomials
Theorem on friends and strangers	Theorem	Combinatorics
Closed map	Definition	General topology
Module over a ring	Concept	Associative rings and algebras
Adjacency matrix	Definition	Combinatorics
Angle-angle similarity	Theorem	Geometry
Leading coefficient	Definition	Commutative algebra
Cesàro mean	Definition	Sequences, series, summability
Independence of two events	Definition	Probability theory and stochastic processes
Classification of isometries of the plane	Theorem	Geometry
Subgraph	Definition	Combinatorics
Hermitian matrix	Concept	Linear and multilinear algebra; matrix theory
Removable singularity	Definition	Functions of a complex variable
Equivalent matrices	Definition	Linear and multilinear algebra; matrix theory
Hyperbola	Definition	Geometry
Matrix of a bilinear form	Definition	Linear and multilinear algebra; matrix theory
Continuous function	Definition	Real functions
Second-order Taylor expansion	Corollary	Real functions
Negation of a universal statement	Theorem	Mathematical logic and foundations
Solvable group	Definition	Group theory and generalizations
Divergent sequence	Concept	Sequences, series, summability
Ordered field	Concept	Field theory and polynomials
Glide reflection	Definition	Geometry
Standard deviation	Concept	Probability theory and stochastic processes
Degree of a polynomial	Concept	Commutative algebra
Sine is 2π-periodic	Theorem	Special functions
Iterated integral	Definition	Real functions
Non-commutativity of matrix multiplication	Counterexample	Linear and multilinear algebra; matrix theory
A function with bounded derivative is Lipschitz	Corollary	Real functions
Picard–Lindelöf theorem	Theorem	Ordinary differential equations
Compactness via open covers	Proposition	General topology
Simple extension	Definition	Field theory and polynomials
Bilinear form	Definition	Linear and multilinear algebra; matrix theory
Coefficient matrix	Definition	Linear and multilinear algebra; matrix theory
Characteristic of a ring	Definition	Commutative algebra
Composition of an integer	Concept	Combinatorics
Faithful action	Concept	Group theory and generalizations
Linearity of expectation	Theorem	Probability theory and stochastic processes
Vandermonde determinant	Theorem	Linear and multilinear algebra; matrix theory
Limit superior	Definition	Sequences, series, summability
Action by conjugation	Example	Group theory and generalizations
Bounded set	Definition	General topology
Ordinary differential equation	Definition	Ordinary differential equations
The exponential function is positive	Proposition	Special functions
Metric spaces are Hausdorff	Proposition	General topology
Existence of a complementary subspace	Theorem	Linear and multilinear algebra; matrix theory
Continuity is equivalent to sequential continuity	Theorem	Real functions
Sup norm on bounded continuous functions	Example	Functional analysis
Law of sines	Theorem	Geometry
Linear differential equation of order n	Definition	Ordinary differential equations
Jordan block	Definition	Linear and multilinear algebra; matrix theory