Mathematics and statistics

Definite matrix

A definite matrix is a Hermitian (in the real case, symmetric) matrix whose quadratic form takes values of only one sign, classified as positive, negative, semidefinite, or indefinite.

Deformation quantization

Deformation quantization is a mathematical technique for constructing quantum theories by deforming the algebra of functions on a classical phase space into a noncommutative star product.

Degree

In mathematics, degree is a numerical measure of size or complexity, most familiarly a polynomial's highest total exponent, also naming the angle unit of 1/360 of a rotation.

Degree (graph theory)

Degree (also vertex degree) is a graph theory measure of how many edges meet at a vertex; it underlies the handshaking lemma and degree centrality in networks.

Degree of a polynomial

The degree of a polynomial, or polynomial degree, is the largest exponent with a nonzero coefficient among its terms, naming it linear, quadratic, cubic, and so on.

Degree spectrum

A degree spectrum is the set of Turing degrees that compute isomorphic copies of a mathematical structure, introduced by Linda Jean Richter in computable structure theory.

Degrees of freedom (statistics)

Degrees of freedom in statistics is the number of independent pieces of information available to estimate a quantity, typically the number of observations minus the number of estimated parameters.

Dehn surgery

Dehn surgery is a construction in 3-manifold topology that removes a solid torus and reglues it along a slope p/q, yielding every closed orientable 3-manifold.

Dehn–Sommerville equations

The Dehn–Sommerville equations are linear relations among the face numbers of simplicial or simple polytopes, found by Max Dehn in 1905 and Sommerville in 1927.

Del

Del, written ∇ and also called nabla, is the vector differential operator of vector calculus; combined with three kinds of multiplication it yields the gradient, divergence, and curl.

Delaunay triangulation

The Delaunay triangulation, also known as the Delone triangulation or Delaunay tessellation, is a triangulation of a point set whose triangle circumcircles contain no other points.

Delay differential equation

A delay differential equation is a differential equation whose rate of change depends on past states, not only the present one, so the system carries a memory.

Deligne–Mumford stack

A Deligne–Mumford stack is an algebraic stack locally modeled on schemes by an étale surjective covering, introduced by Deligne and Mumford in 1969 for the moduli of algebraic curves.

Delta method

The delta method is a statistical technique that uses a Taylor expansion to approximate the variance or limit distribution of a function of a random quantity.

Delta operator

A delta operator is a shift-invariant linear operator on polynomials that lowers degree by exactly one, central to Rota's finite operator calculus of binomial-type polynomial sequences.

A delta-matroid is a combinatorial structure that generalizes a matroid by replacing equicardinal bases with feasible sets of varying sizes, introduced independently in the mid-1980s by André Bouchet and others.

Demographic and Health Surveys

The Demographic and Health Surveys (DHS) are standardized, nationally representative household surveys collecting population, health, and nutrition data in over 90 low- and middle-income countries since 1984.

Dempster–Shafer theory

Dempster–Shafer theory is a mathematical framework for reasoning under uncertainty that assigns degrees of belief to sets of propositions and combines evidence from independent sources.

Denotational semantics

Denotational semantics, also known as the Scott-Strachey approach, is a formal method assigning each programming language phrase a mathematical meaning, built compositionally from its parts using domain theory.

Dense set

A dense set, sometimes called an everywhere-dense set, is a subset of a topological space that intersects every nonempty open set, such as the rationals in the reals.

Density estimation

Density estimation is the statistical task of recovering a probability density function from observed data, using parametric mixture models or nonparametric methods like kernel density estimation.

Density evolution

Density evolution is an analytical technique in coding theory that tracks the probability densities of messages exchanged by iterative decoders, predicting code ensemble performance and yielding the decoding threshold.

Deontic logic

Deontic logic, or deontic modal logic, is the branch of logic studying obligation, permission, and prohibition, with roots in ethics and law and modern uses in computer science.

Dependent (NIP) theories

Dependent (NIP) theories, meaning theories without the independence property, are first-order theories in which no formula encodes the random bipartite graph; introduced by Shelah, they include the real field and p-adic numbers.

Dependent and independent variables

The dependent variable is the outcome a study measures, and the independent variable, or predictor, is the factor that is manipulated or treated as the explanation for changes in that outcome.

Dependent Dirichlet process

The dependent Dirichlet process is a collection of random probability measures indexed by a covariate or time, each marginally Dirichlet-process distributed, introduced by MacEachern in 1999 to model how a distribution changes with inputs.

Dependent random choice

Dependent random choice is a probabilistic technique in combinatorics that extracts a large vertex subset with many common neighbors from a dense graph, enabling greedy embedding of sparse bipartite graphs.

Dependent type

Dependent typing is the defining feature of dependent type theories: a family of types indexed by a value, so each value may yield a distinct type.

Depth (ring theory)

Depth, also called the depth of a module or of a local ring, is an invariant of commutative algebra measuring the length of a maximal regular sequence on a module.