6,052 articles
Boltzmann sampler
A Boltzmann sampler is a randomized algorithm that draws objects from a combinatorial class with probability proportional to a power of their size, introduced in 2004.
Bolzano–Weierstrass theorem
The Bolzano–Weierstrass theorem is a result of real analysis stating that every bounded sequence of real numbers has a convergent subsequence, proved in original form by Bernard Bolzano in 1817.
Bombieri–Vinogradov theorem
A 1965 theorem of Enrico Bombieri and A. I. Vinogradov showing primes are well distributed in arithmetic progressions on average over moduli up to about the square root.
Bonferroni correction
The Bonferroni correction, also called the Bonferroni adjustment, is a statistical method for multiple testing that sets each test's significance level to alpha divided by the number of tests.
Book embedding
Book embedding (of a graph) positions all vertices on a spine. Book thickness is defined as the minimum number of pages required for drawing edges without crossing.
Book graph
The book graph B_p is a graph of p triangles all sharing one common edge, like an open book with triangular pages, standard in extremal graph theory.
Boole's inequality
Boole's inequality, also called the union bound, is a probability theorem stating that the probability of a union of events is at most the sum of their probabilities.
Boolean algebra
Boolean algebra, also known as Boolean logic or switching algebra, is the algebra of two-valued logic and of sets under union and complementation, introduced by George Boole in 1847.
Boolean function
A Boolean function, also called a switching function, is a function whose inputs and output are 0 or 1, basic to propositional logic, digital circuit design, and cryptography.
Boolean lattice
A Boolean lattice is a distributive lattice in which every element has a unique complement, exemplified by the power set of a set ordered by inclusion, where meet is intersection and join is union.
Boolean Pythagorean triples problem
A Ramsey theory problem posed by Ronald Graham asking whether the positive integers can be two-colored with no monochromatic Pythagorean triple, answered no in 2016 by Heule, Kullmann, and Marek.
Boolean ring
A Boolean ring is a ring in which every element satisfies x² = x; such rings are automatically commutative of characteristic 2 and are definitionally equivalent to Boolean algebras.
Boolean satisfiability problem
The Boolean satisfiability problem (SAT) asks whether a Boolean formula has an assignment of true and false values that makes it true, and was the first problem proved NP-complete.
Boolean-valued model
A Boolean-valued model is a mathematical structure in which statements take truth values in a complete Boolean algebra, developed by Scott and Solovay as a presentation of forcing.
Booth's multiplication algorithm
Booth's multiplication algorithm, also known as Booth's algorithm, is a signed binary multiplication technique published by Andrew D. Booth in 1951 that handles two's complement numbers of either sign without separate correction.
Bootstrap confidence interval
A bootstrap confidence interval is an interval constructed by resampling the data to approximate the sampling distribution of a statistic, a method introduced by Bradley Efron in 1979.
Bootstrap inference
Bootstrap inference is a statistical method that estimates the sampling distribution of an estimator by resampling the observed data with replacement, introduced by Bradley Efron in 1979.
Bootstrapping (statistics)
Bootstrapping is a statistical method for estimating the distribution of a statistic by repeatedly resampling the observed data with replacement, introduced by Bradley Efron at Stanford University in 1979.
Borel determinacy theorem
The Borel determinacy theorem, or Borel determinacy, states that every infinite two-player game whose Borel payoff set gives one player a winning strategy, proved by Donald A. Martin in 1975.
Borel measure
A Borel measure is a measure defined on the Borel σ-algebra of a topological space, the smallest σ-algebra containing every open set; it underlies probability and integration.
Borel set
A Borel set, or Borel subset, is a subset of a topological space belonging to the Borel σ-algebra, the smallest σ-algebra containing every open set.
Borel subalgebra
A Borel subalgebra of a Lie algebra is a maximal solvable subalgebra, named for Armand Borel. It organizes the structure and representation theory of semisimple Lie algebras.
Borel summation
Borel summation is a summation method introduced by Émile Borel in 1899 that assigns finite values to divergent series, notably factorially divergent asymptotic series in perturbative physics.
Borel–Cantelli lemma
The Borel–Cantelli lemma is a result in probability theory, introduced by Émile Borel in 1909, that determines whether infinitely many events in a sequence occur.
Borromean rings
The Borromean rings are three loops linked so that no two are linked, and cutting any one frees the other two; named for the Borromeo family emblem.
Borsuk's conjecture
Borsuk's conjecture, also known as the Borsuk problem, is a 1933 claim by Karol Borsuk that every bounded set in d-dimensional space splits into d + 1 smaller-diameter parts.
Bose–Einstein statistics
Bose–Einstein statistics, also called the Bose–Einstein distribution, describes identical particles with integer spin (bosons), any number of which may occupy the same quantum state; Bose introduced it in 1924.
Bose–Mesner algebra
The Bose–Mesner algebra is the commutative matrix algebra generated by the adjacency matrices of an association scheme, named for Bose and Mesner, who introduced it in 1959.
Bott periodicity theorem
The Bott periodicity theorem, proved by Raoul Bott in 1959, states that the stable homotopy groups of the classical groups repeat with period 2 or 8.
Boundary integral method
The boundary integral method is a numerical technique that reformulates a partial differential equation as an integral equation on the domain's boundary; discretizing it yields the boundary element method.