6,052 articles
Bring radical
The Bring radical, also called the ultraradical, is a function solving z^5 + z + t = 0, which lets the general quintic be solved once admitted as a new operation.
British Birth Cohort Studies
The British birth cohort studies are national longitudinal studies following people born in single weeks, starting with the 1946 NSHD and continuing through the 2000–2001 Millennium Cohort Study.
Brook Taylor
Brook Taylor (1685–1731) was an English mathematician best known for Taylor's theorem and the Taylor series, and also credited with creating the calculus of finite differences and founding Britain's mathematical theory of linear perspective.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem, or Brouwer's theorem, states that every continuous function from a compact convex set into itself has a fixed point, proved by Brouwer in 1911.
Brownian bridge
A Brownian bridge is a stochastic process: standard Brownian motion on [0, 1] conditioned to return to 0 at time 1, used in statistics and finance.
Brownian excursion
A Brownian excursion is a stochastic process on [0, 1] that behaves like Brownian motion conditioned to stay nonnegative and to return to 0 at both endpoints.
Brownian meander
The Brownian meander is a stochastic process, the weak limit of Brownian motion conditioned to stay positive, identified by Durrett, Iglehart, and Miller in 1977.
Brownian motion in higher dimensions
Brownian motion in higher dimensions is the vector-valued generalization of the Wiener process to n dimensions, where planar paths return infinitely often but paths in three or more dimensions escape to infinity.
Brownian motion on manifolds
Brownian motion on manifolds is the diffusion generated by half the Laplace–Beltrami operator, whose transition density is the heat kernel, the intrinsic analog of Euclidean Brownian motion.
Bruhat order
The Bruhat order, also called the strong Bruhat order, is a partial order on elements of a Coxeter group defined by subwords of reduced expressions.
Buchberger's algorithm
Buchberger's algorithm is an algorithm for computing a Gröbner basis of a polynomial ideal, introduced by Bruno Buchberger in his 1965 PhD thesis and built into all major computer algebra systems.
Büchi automaton
A Büchi automaton is a finite automaton that reads infinite words, accepting a run that visits an accepting state infinitely often; nondeterministic ones recognize exactly the ω-regular languages.
Budapest school of mathematics
The Budapest school of mathematics grew from Lipót Fejér's circle at the University of Budapest in the early 1900s, producing leading mathematicians including von Neumann, Pólya, and Erdős.
Buffon's needle problem
Buffon's needle problem, posed by Georges-Louis Leclerc, Comte de Buffon in 1733, asks the probability that a needle dropped at random crosses one of a set of parallel lines.
BUGS project
The BUGS project, whose language is Bayesian inference Using Gibbs Sampling, provides software that performs Bayesian inference via MCMC; started in Cambridge in 1989, it inspired JAGS and Stan.
Building (mathematics)
A building, also called a Tits building or Bruhat-Tits building, is a combinatorial and geometric structure introduced by Jacques Tits about 1965, encoding simple groups of Lie type as simplicial complexes assembled from apartments.
Bulk sampling
Bulk sampling is a statistical method for estimating properties of bulk materials like ore, coal, and grain by combining many small increments into composite samples.
Bulk synchronous parallel
Bulk synchronous parallel (BSP) is a parallel computation model, introduced by Leslie Valiant in 1990, where programs run in supersteps ending at a global synchronization barrier.
Bulletin of Symbolic Logic
The Bulletin of Symbolic Logic is a quarterly peer-reviewed journal founded in 1995 by the Association for Symbolic Logic, publishing accessible accounts of developments in logic.
Bump function
A bump function is a smooth function that is nonzero only on a compact set, equalling 1 on an inner region and falling smoothly to 0 outside.
Bureau of Labor Statistics
The Bureau of Labor Statistics (BLS) is a United States federal statistical agency within the Department of Labor that publishes the monthly jobs report and the Consumer Price Index.
Burgers' equation
Burgers' equation is a nonlinear partial differential equation combining advection and diffusion, introduced by J.M. Burgers in the late 1930s as a simple model of fluid turbulence.
Burling's conjecture
Burling's conjecture, proved by J. P. Burling in his 1965 doctoral thesis at the University of Colorado, Boulder, states that triangle-free intersection graphs of axis-aligned boxes in three dimensions have unbounded chromatic number.
Burnside's lemma
Burnside's lemma, also called the Cauchy–Frobenius lemma, states that the number of orbits of a finite group action equals the average number of fixed points.
Business rules engine
A business rules engine, also known as a rule engine, is software that executes business rules like IF/THEN policies separately from application code, so policy changes need no reprogramming.
Busy beaver
The busy beaver function, defined by Tibor Radó in 1962, maps a Turing machine's states to the most steps a halting machine of that size can run.
Butterfly effect
The butterfly effect, or sensitive dependence on initial conditions, is a property of chaotic systems in which an arbitrarily small change in starting state grows into large differences in later behavior.
C*-algebra
A C-algebra is a complex Banach algebra with an involution satisfying ‖a*a‖ = ‖a‖², introduced in 1943; the Gelfand–Naimark–Segal theorem represents every one as bounded operators on a Hilbert space.
Càdlàg function
A càdlàg function, also written cadlag or corlol, is right-continuous at every point with a left limit at every point, the two possibly differing at jumps.
Caesar cipher
The Caesar cipher, also called the shift cipher, is a substitution cipher that replaces each letter with one a fixed number of positions further along the alphabet.