6,052 articles
Artin–Hasse exponential
The Artin–Hasse exponential is a formal power series associated to a prime p whose coefficients are all p-adic integers, unlike the ordinary exponential, and is a tool in p-adic analysis.
Artinian ring
An Artinian ring is a ring satisfying the descending chain condition on ideals, named after Emil Artin, who studied such rings around 1928. Examples include every finite ring.
Aryabhata (आर्यभट)
Aryabhata (आर्यभट, also Aryabhata I) was an Indian mathematician and astronomer, 476–550 CE, whose 499 CE Sanskrit treatise the Āryabhaṭīya became the founding text of classical Indian mathematics.
Aspect ratio
An aspect ratio is the ratio of width to height of an image, written as 16:9 or 1.78:1, common ratios running from 1.375:1 to 2.76:1 in film.
Assignment algorithm
An assignment algorithm solves the linear assignment problem: given an n by n cost matrix of agents and tasks, it finds the minimum-cost one-to-one pairing, classically via Kuhn's 1955 Hungarian method.
Associahedron
The associahedron, also called the Stasheff polytope, is a convex polytope whose vertices encode the ways of associating a product, equivalently triangulations of a convex polygon, counted by Catalan numbers.
Associated graded ring
The associated graded ring, or associated graded algebra, is a graded ring built from a filtered ring's successive quotients, often turning a complicated ring into a polynomial ring.
Association for Symbolic Logic
The Association for Symbolic Logic (ASL) is an international organization founded in 1936 that supports research in logic and publishes three journals with Cambridge University Press.
Association scheme
An association scheme is a finite set whose ordered pairs are partitioned into regular associate classes, whose adjacency matrices span an algebra, central to algebraic combinatorics.
Associative property
The associative property, also called the associative law, says regrouping operands does not change a binary operation's result; addition and multiplication have it, while subtraction and division do not.
Assurance (statistics)
Assurance, also known as average power, is a Bayesian alternative to statistical power for clinical trial sample size, averaging power over a prior for the unknown treatment effect.
Asymmetric Laplace distribution
The asymmetric Laplace distribution (ALD) is a skewed continuous probability distribution, introduced by Kozubowski and Podgórski, whose maximum likelihood reproduces quantile regression, making it standard in Bayesian quantile regression.
Asymmetric simple exclusion process
The asymmetric simple exclusion process (ASEP) is a stochastic interacting-particle model in which particles hop with directional bias on a one-dimensional lattice, one particle per site.
Asymptote
An asymptote is a straight line whose distance from a point on a curve tends to zero as the point moves to infinity; a term dating to Apollonius of Perga.
Asymptotic analysis
Asymptotic analysis, also known as asymptotics, is the branch of mathematics that studies the limiting behavior of functions and derives approximations, associated with Henri Poincaré's 1886 work.
Asymptotic expansion
An asymptotic expansion, or Poincaré expansion, is a series approximation of a function whose truncation error matches the first omitted term, even when the series diverges.
Asymptotic theory (statistics)
Asymptotic theory, also called large sample theory, is the branch of mathematical statistics describing how estimators and tests behave as sample size grows without bound.
Asymptotic theory of M-estimators
The asymptotic theory of M-estimators studies estimators defined by maximizing a criterion, such as maximum likelihood and sample quantiles, giving conditions for consistency, root-n rates, and asymptotic normality.
Asymptotic theory of the bootstrap
The asymptotic theory of the bootstrap studies when and why resampling approximations to sampling distributions converge to correct limits as sample size grows, and at what rate.
Atan2
Atan2, also called Arctan2, is the two-argument arctangent function returning the angle to a point (x, y) in [−π, +π], fixing the quadrant from both signs.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer in 1963, equates the analytical index of an elliptic operator with a topological index.
Atomic domain
An atomic domain is an integral domain in which every nonzero nonunit can be written as a finite product of irreducible elements, though the factorization need not be unique.
Atomic model (model theory)
In model theory, an atomic model is a model of a first-order theory whose every realized type is isolated by a single formula, making it a small model.
Attractor
An attractor, or dynamical attractor, is an invariant set of states in a dynamical system's phase space toward which nearby trajectories evolve; famous examples include the chaotic Lorenz attractor.
Augmented inverse probability weighting
Augmented inverse probability weighting (AIPW) is a doubly robust estimator in causal inference that stays consistent if either its treatment or outcome model is correct.
Augmenting path
An augmenting path is a path along which a maximum flow or matching can be improved, in algorithms such as Ford-Fulkerson, Edmonds-Karp, and Hopcroft-Karp; finding none certifies optimality.
Augustin-Louis Cauchy
Augustin-Louis Cauchy (1789–1857) was a French mathematician, professor at the École Polytechnique and the Sorbonne, who gave the calculus rigorous foundations, founded complex analysis, and developed elasticity theory.
Australian and New Zealand Standard Industrial Classification
The Australian and New Zealand Standard Industrial Classification (ANZSIC) is the standard industry classification used in Australia and New Zealand, jointly developed by the Australian Bureau of Statistics and Statistics New Zealand in 1993.
Australian Bureau of Statistics
The Australian Bureau of Statistics (ABS), formerly the Commonwealth Bureau of Census and Statistics, is Australia's official statistical agency, an independent statutory authority that conducts the five-yearly Census of Population and Housing.
Autocorrelation
Autocorrelation, also called serial correlation, is the correlation of a variable with itself at different points in time, a defining feature of time-series data that makes standard statistical tests invalid.