6,052 articles
Einstein notation
Einstein notation, also called the Einstein summation convention, is a notational convention in which an index appearing twice in a term is implicitly summed, omitting the summation sign.
Eisenstein series
Eisenstein series are modular forms defined as sums of inverse powers over the nonzero points of a lattice, the simplest explicit examples in the theory of modular forms.
Eisenstein's criterion
Eisenstein's criterion, also called the Schönemann–Eisenstein theorem, is a test in algebra that proves a polynomial with integer coefficients irreducible over the rationals, published by Eisenstein in 1850.
Eldon Hansen
Eldon Hansen, full name Eldon Robert Hansen, is an American mathematician born in 1927, coauthor of Global Optimization Using Interval Analysis and namesake of interval methods.
ELECTRE
ELECTRE (ELimination Et Choix Traduisant la REalité), also known as the ELECTRE method, is a family of outranking methods in multi-criteria decision analysis developed by Bernard Roy since the mid-1960s.
Electronic Journal of Combinatorics
The Electronic Journal of Combinatorics (E-JC) is a peer-reviewed open-access online journal for discrete mathematics, founded in 1994 by Herbert Wilf and Neil Calkin as one of the first journals delivered over the World Wide Web.
Element (category theory)
In category theory, a generalized element of an object X is a morphism x : A → X, whose domain A is called its shape or stage of definition.
Element of a set
An element of a set, also called a member, is an object that belongs to the set, written a ∈ A; membership is the basic relation of set theory.
Elementary algebra
Elementary algebra, also known as college algebra or high school algebra, is the branch of mathematics that uses letters as variables to write and solve equations, taught in school and introductory college courses.
Elementary equivalence
Elementary equivalence, or elementarily equivalent structures, is a relation between structures of the same first-order language that satisfy exactly the same first-order sentences, formulated by Alfred Tarski in 1930.
Elementary function
An elementary function is a function built by repeated composition from constants, addition, multiplication, division, root extraction, and algebraic, exponential, logarithmic, and trigonometric functions and their inverses.
Elementary matrix
An elementary matrix, or elementary matrices collectively, is a square matrix made from the identity by one row operation: a swap, a scaling, or a row addition.
Elementary symmetric polynomial
An elementary symmetric polynomial σₖ is the sum of all products of k distinct variables x₁, ..., xₙ; by the fundamental theorem, every symmetric polynomial is uniquely a polynomial in them, a fact underlying Vieta's formulas.
Éléments de mathématique
Éléments de mathématique is a treatise on mathematics by Nicolas Bourbaki, a largely French collective, rebuilding modern mathematics axiomatically in ten books across roughly forty volumes.
Elimination theory
Elimination theory is the branch of algebra that removes unknowns from systems of multivariate polynomial equations, using resultants and Gröbner bases, with applications in equation solving, geometric theorem proving, and computer-aided design.
Ellipse
An ellipse is a closed plane curve where the sum of the distances to two fixed points, the foci, is constant; it describes planetary orbits.
Ellipsoid
An ellipsoid is a closed quadric surface in three dimensions defined by three semi-axes, the three-dimensional analog of the ellipse, with the sphere as a special case.
Elliptic curve
An elliptic curve is a smooth curve of genus one with a group law, given by y² = x³ + ax + b, used in modern cryptography.
Elliptic function
An elliptic function is a meromorphic function of a complex variable that is doubly periodic, with two periods whose ratio is not real; it arose from inverting elliptic integrals.
Elliptic integral
Elliptic integral is a special function, first studied by John Wallis in 1655 regarding the arc length of an ellipse. It is an integral involving cubic or quartic polynomials.
Elliptic partial differential equation
An elliptic partial differential equation, or elliptic PDE, is a PDE whose highest-order terms have no real characteristic directions, exemplified by the Laplace and Poisson equations governing steady-state physics.
Elliptical copula
An elliptical copula is the copula of an elliptically contoured distribution, capturing its dependence structure separately from its marginals; examples include the Gaussian and Student t copulas.
Elliptical distribution
An elliptical distribution is a multivariate probability distribution whose density is constant on ellipsoids centered at a location vector, generalizing the multivariate normal distribution and widely applied in statistics, econometrics, and financial risk modeling.
Embedding
An embedding is a map that places one mathematical space inside another while preserving all of its structure, such as a graph drawn on a surface without edges crossing.
Embeddings and elementary maps between model-theoretic structures
In model theory, an elementary map between two structures preserves and reflects the truth of every first-order formula; every isomorphism is elementary, but elementary embeddings need not be surjective.
Emmy Noether
Emmy Noether, born Amalie Emmy Noether, was a German mathematician whose 1918 theorems linked symmetries to conservation laws, and whose 1921 ideal theory founded modern abstract algebra.
Empirical Bayes estimation
Empirical Bayes estimation is a statistical approach that estimates the prior distribution from observed data rather than fixing it in advance, introduced by Herbert Robbins in 1955.
Empirical Bayes method
The empirical Bayes method is a statistical technique that estimates a prior distribution's parameters from the data, then computes posterior distributions as if the prior were known.
Empirical Bayes methods
Empirical Bayes methods are statistical techniques that estimate the prior distribution of a model from the data itself, then apply Bayes' rule with that estimated prior; Herbert Robbins named the approach in 1956.
Empirical distribution function
The empirical distribution function (EDF), also called the empirical cumulative distribution function, is a statistical estimator that assigns each of n observations probability 1/n and underlies goodness-of-fit tests.