6,052 articles
Gromov–Witten invariants
Gromov–Witten invariants are numbers counting, in a loose sense, holomorphic maps from Riemann surfaces to a variety or symplectic manifold, defined via the virtual fundamental class of the moduli space of stable maps.
Gronwall's inequality
Gronwall's inequality, also called Grönwall's lemma or the Gronwall–Bellman inequality, is an integral inequality that converts implicit bounds into explicit exponential bounds for a function.
Gross value added
Gross value added (GVA) is a measure of economic output equal to what an industry, sector, or region produces minus the goods and services consumed in producing it.
Gross world product
Gross world product (GWP) is the combined gross domestic product of all economies in the world, measured by national statistics agencies under the System of National Accounts.
Grothendieck construction
The Grothendieck construction turns an indexed category, a functor assigning a category to each object of a base category, into a single total category over the base, giving an equivalence between indexed categories and Grothendieck fibrations.
Grothendieck spectral sequence
The Grothendieck spectral sequence is a tool in homological algebra that computes the derived functors of a composite of two functors; Grothendieck introduced it in 1957.
Grothendieck topology
A Grothendieck topology is a structure on a category specifying which families of morphisms count as coverings, generalizing open covers; a category with one is called a site.
Grothendieck topos
A Grothendieck topos is a category equivalent to sheaves of sets on a site, introduced by Alexander Grothendieck in SGA 4 (1963–1964) as the framework for étale cohomology.
Grothendieck's Galois theory
Grothendieck's Galois theory is Alexander Grothendieck's axiomatic reformulation of Galois theory, covering space theory, and the algebraic fundamental group, given in SGA 1 (1960/61); it characterizes Galois categories via a fiber functor.
Group (mathematics)
In mathematics, a group is a set with a single operation that is associative and has an identity element and inverses, with examples including integers under addition.
Group action
A group action, also called an action of a group, is a way for a group to operate on a set, defined as a homomorphism into its permutations.
Group algebra of a locally compact group
The group algebra of a locally compact group G is the Banach -algebra L¹(G), integrable functions under convolution, the basic object linking Banach algebra theory to harmonic analysis.
Group cohomology
Group cohomology is a branch of homological algebra that assigns abelian groups Hn(G, A) to a group G, measuring how G acts on a module.
Group divisible design
A group divisible design (GDD) is a combinatorial design whose point set is split into groups, with cross-group pairs of points appearing together in a constant number of blocks.
Group extension
A group extension is a group E containing a given group N as a normal subgroup with quotient group Q, usually written as a short exact sequence.
Group homomorphism
A group homomorphism, also called a group morphism or morphism of groups, is a function between two groups that preserves the group operation; its kernel and image underlie the first isomorphism theorem.
Group lasso
The group lasso is a regularization method for linear and generalized linear regression that keeps or removes whole predefined groups of coefficients, introduced by Yuan and Lin in 2005.
Group of Lie type
A group of Lie type is a finite group of rational points of a reductive algebraic group over a finite field, including the classical matrix groups.
Group presentation
A group presentation is a description of a group by a set of generators and relators, written ⟨S | R⟩, giving a compact way to define infinite groups.
Group representation
A group representation, the subject of group representation theory, realizes an abstract group as invertible linear transformations of a vector space, with applications in chemistry, physics, and quantum mechanics.
Group ring
A group ring R[G] is a ring of formal finite sums of group elements with coefficients in a ring R; when R is a field it is a group algebra.
Group scheme
A group scheme is a scheme with a group structure given by morphisms for multiplication, inverse, and identity, so its points form groups for every base scheme.
Group testing
Group testing is a statistical method that tests pooled samples instead of individual ones, introduced by Robert Dorfman in 1943 to screen US army conscripts for syphilis.
Group theory
Group theory is the branch of mathematics studying groups, algebraic structures that capture symmetry and operations like addition, founded in Galois's 1830s work on equations.
Groupoid
A groupoid is a small category in which every morphism is an isomorphism, equivalently a set with a partial multiplication, introduced by Heinrich Brandt in 1926.
Growth curve analysis
Growth curve analysis is a statistical method for modeling how an outcome changes over time, using repeated measures to estimate individual trajectories and their differences.
Growth mixture model
A growth mixture model is a latent-variable statistical method that identifies unobserved subgroups, called latent classes, each with its own developmental trajectory, in longitudinal data.
Growth mixture modeling
Growth mixture modeling is a statistical method for longitudinal data that divides a population into latent classes with different trajectories, introduced by Muthén and Shedden in 1999.
Growth rate (group theory)
In group theory, the growth rate of a finitely generated group measures how quickly the number of elements reachable by short words grows with word length.
Grundlagen der Arithmetik
Die Grundlagen der Arithmetik (The Foundations of Arithmetic) is an 1884 book by the German logician Gottlob Frege, arguing that arithmetic is a development of logic.