Mathematics and statistics

Boundary value problem

A boundary value problem is a differential equation with conditions imposed on the solution at two or more separate points of its domain, unlike an initial value problem.

Bounded arithmetic

Bounded arithmetic is a family of weak subsystems of Peano arithmetic, started by Rohit Parikh in 1971, whose provably total functions characterize complexity classes like polynomial time.

Bounded mean oscillation

Bounded mean oscillation (BMO), also called the John–Nirenberg space, is a function space introduced by Fritz John and Louis Nirenberg in 1961 that strictly contains all bounded functions.

Bounded operator

A bounded operator is a linear map between normed vector spaces satisfying an inequality ‖Tx‖ ≤ C‖x‖, equivalently a continuous one, and is central to operator theory.

Bounded variation

Bounded variation is a property of real-valued functions whose total oscillation over an interval is finite; Camille Jordan introduced the class BV in 1881 to study Fourier series.

The Boussinesq equation is a second-order-in-time partial differential equation derived by Joseph Boussinesq around 1872 that models weakly nonlinear, weakly dispersive waves moving in both directions in shallow water.

Box counting

Box counting is a numerical method for estimating the fractal dimension of a set, pattern, or image, by counting how the number of boxes covering it grows as box size shrinks.

Box plot

A box plot, or box-and-whisker plot, is a statistical graphic that summarizes a distribution using the median, quartiles, whiskers, and individually plotted outliers, with comparison of groups its main strength.

Box–Behnken design

The Box–Behnken design is a three-level experimental design for fitting quadratic response surface models, introduced by Box and Behnken in 1960, placing runs at edge midpoints to avoid extreme factor combinations.

Box–Cox transformation

The Box–Cox transformation is a family of power transformations of positive data, introduced by Box and Cox in 1964 to help data meet the assumptions of the normal linear model.

Box–Jenkins method

The Box–Jenkins method is an iterative procedure in time series analysis for building ARIMA models, described by George Box and Gwilym Jenkins in their 1970 book Time Series Analysis: Forecasting and Control.

Brachistochrone curve

The brachistochrone curve, or curve of fastest descent, is the frictionless path of quickest descent under gravity, an inverted cycloid posed by Johann Bernoulli in 1696.

Bracket (mathematics)

In mathematics, a bracket is a pair of symbols like ( ), [ ], or { } used to group expressions or carry specialized meanings.

Bradford Hill criteria

The Bradford Hill criteria, also called Hill's criteria, are nine considerations for judging whether an exposure causes disease, presented by Austin Bradford Hill in 1965.

Braess's paradox

The Braess Paradox, described by Dietrich Braess in 1968, is the counterintuitive finding that adding a link to a congested network can worsen travel times for all users.

Brahmagupta (ब्रह्मगुप्त)

Brahmagupta (ब्रह्मगुप्त), Indian astronomer-mathematician born 598 in Bhillamāla/Bhinmal, author of the Brāhmasphuṭasiddhānta (628) and Khaṇḍakhādyaka (665); first systematic rules for zero and negative numbers, cyclic quadrilateral area formula, and astronomy transmitted to the Arab world.

Braid group

The braid group on n strands, introduced by Emil Artin in 1925, consists of braids multiplied by stacking; it connects topology, knot theory, and quantum computing.

Braided monoidal category

A braided monoidal category, also called a braided tensor category, is a monoidal category with a braiding that switches tensor factors, introduced by André Joyal and Ross Street in 1986.

Branch and cut

Branch and cut is an exact optimization algorithm for mixed-integer linear programming that combines branch and bound with cutting planes, introduced by Padberg and Rinaldi in 1987.

Branch point

A branch point is a point in the complex plane where analytic continuation of a multi-valued function is obstructed, causing functions like the square root and logarithm to be multi-valued.

Branching process

A branching process is a stochastic model in which each individual independently produces a random number of offspring; the Galton–Watson process is its canonical form.

Branching random walk

A branching random walk is a stochastic particle system in which reproducing particles displace randomly from their parents, combining branching and random walk, central to modern probability.

Branching rule

A branching rule describes how an irreducible representation of a Lie group or algebra decomposes into irreducible representations of a subgroup, with multiplicities; it underlies symmetry breaking in physics.

Branko Grünbaum

Branko Grünbaum (ברנקו גרונבאום, 1929–2018) was a Croatian-born mathematician at the University of Washington who worked on convex polytopes, tilings, and configurations, and wrote the influential Convex Polytopes (1967).

Brauer group

The Brauer group of a field K, written Br(K), is the group of similarity classes of finite-dimensional central simple algebras over K under tensor product, classified by Galois cohomology.

Bravais lattice

A Bravais lattice, also called a space lattice, is an infinite array of points in which every point has an identical environment, with 14 types in three dimensions.

Brazilian Census

The Brazilian Census (Censo Demográfico) is a decennial population and housing count of Brazil conducted by IBGE, most recently in 2022, counting 203 million people.

Brazilian Institute of Geography and Statistics

The Brazilian Institute of Geography and Statistics (Instituto Brasileiro de Geografia e Estatística, IBGE) is Brazil's federal agency for official statistics, including the decennial census.

Breakdown point (statistics)

The breakdown point of an estimator is the smallest fraction of contaminated data that can drive it to arbitrarily bad values. The sample mean's is zero; the median's is 50%.