6,052 articles
Szemerédi's theorem
Szemerédi's theorem states that every set of integers with positive upper density contains arithmetic progressions of every finite length. Endre Szemerédi proved it in 1975.
T-norm
A t-norm, also called a triangular norm, is a commutative, associative binary operation on [0, 1] with 1 as its neutral element, modeling conjunction in fuzzy logic.
T-statistic
The t-statistic, or Student's t-statistic, is a test statistic that measures how far an estimated quantity departs from a hypothesized value, divided by its estimated standard error.
t-structure
A t-structure, introduced by Beilinson, Bernstein, and Deligne in 1982, is a pair of subcategories of a triangulated category whose heart is automatically an abelian category.
T1 space
A T1 space, also called an accessible space, is a topological space in which every singleton set is closed, so distinct points are mutually separable.
Table of prime factors
A table of prime factors, or factor table, is a reference listing the least prime divisor of each number in a range, a major computational project from the 1600s to 1909.
Tag system
A tag system is a string-rewriting model of computation that repeatedly deletes symbols from the front and appends words; it is computationally universal, with an undecidable halting problem.
Tagged union
A tagged union, also called a variant record or sum type, is a data structure holding a value of several fixed types with a tag recording which type is stored.
Taguchi design
A Taguchi design, or Taguchi experimental design, is a design of experiments method using orthogonal arrays to study many factors in few runs and make processes robust to noise.
Taguchi methods
Taguchi methods are statistical experimental-design methods developed by Genichi Taguchi for robust design, using orthogonal arrays and signal-to-noise ratios to make product performance insensitive to noise.
Tai's model
Tai's model, also known as Tai's method or Tai's formula, is a 1994 method by Mary M. Tai for computing the area under a metabolic curve, mathematically identical to the trapezoidal rule.
Tail dependence
Tail dependence is a property of a multivariate probability distribution measuring the limiting probability that one variable is extreme given another is, central to risk management in finance and insurance.
Takens's theorem
Takens's theorem, also known as the delay embedding theorem, is a dynamical systems result proved by Floris Takens in 1981, underlying state space reconstruction from time series.
Takeuti's conjecture
Takeuti's conjecture, also called Takeuti's fundamental conjecture, is the claim that Gentzen's cut-elimination theorem extends from first-order logic to simple type theory, formulated by Gaisi Takeuti in 1953.
Tally marks
Tally marks, also called the five-bar gate, are a counting notation in which one stroke is drawn per item and a fifth stroke crosses each group of four.
Tamari lattice
The Tamari lattice is a partially ordered set whose elements are binary bracketings of a fixed number of symbols, ordered by applying the associativity rule; Dov Tamari introduced it in his 1951 thesis.
Tangent
A tangent is a straight line or plane touching a curve or surface at a point and matching its direction, an idea dating back to Greek geometry.
Tangent bundle
The tangent bundle TM of a differentiable manifold M is the vector bundle whose total space is the union of the tangent spaces at each point, with fibers of dimension equal to that of M.
Tangent space
A tangent space is the vector space of all tangent vectors to a manifold at a single point; for a surface it is the familiar tangent plane.
Taniyama's problems
Taniyama's problems are 36 mathematical problems distributed at the 1955 Tokyo–Nikko symposium; problems 12 and 13, by Yutaka Taniyama, became the origin of the Taniyama–Shimura conjecture.
Tannakian category
A Tannakian category is a rigid abelian tensor category admitting a fiber functor, a formalism developed by Grothendieck and Deligne that reconstructs affine group schemes from their categories of representations.
Targeted learning (statistics)
Targeted learning is a statistical estimation framework that refines an initial machine-learning estimate of a target parameter, such as the average treatment effect, so inference stays valid.
Targeted maximum likelihood estimation
Targeted maximum likelihood estimation (TMLE) is a double-robust semiparametric method for estimating causal parameters, introduced by Mark van der Laan and Daniel Rubin in 2006.
Tarjan's strongly connected components algorithm
Tarjan's strongly connected components algorithm, or Tarjan's SCC algorithm, is a depth-first-search algorithm by Robert Tarjan that finds all strongly connected components of a directed graph.
Tarski–Grothendieck set theory
Tarski–Grothendieck set theory is an axiomatic set theory extending Zermelo–Frænkel set theory with Tarski's axiom, introduced by Alfred Tarski in 1938, and serves as the foundation of the Mizar system for formalizing mathematics.
Tarski's undefinability theorem
Tarski's undefinability theorem is a result in mathematical logic, proved by Alfred Tarski in 1933, showing that no sufficiently rich formal language can define its own truth predicate.
Tate conjecture
The Tate conjecture is an open conjecture in arithmetic algebraic geometry, formulated by John Tate in the 1960s, that every Galois-invariant cohomology class comes from an algebraic cycle.
Tate–Shafarevich group
The Tate–Shafarevich group of an elliptic curve or abelian variety measures failure of the Hasse principle; its finiteness is conjectured but not known in general.
Tau (mathematics)
Tau, also called the tau constant, is the number theory function that counts the positive divisors of a positive integer, also written d(n) or sigma-zero; tau(12) equals 6.
Tauberian theorem
A Tauberian theorem gives conditions under which a summability method's result can be converted back into an ordinary limit, first proved by Alfred Tauber in 1897.