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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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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.
Canonical basis (Lusztig)
The canonical basis, also called the global basis, is a distinguished basis of a quantum group introduced by George Lusztig in 1990 and built independently by Masaki Kashiwara.
Canonical form
A canonical form is a standard way of writing a mathematical expression to which every equivalent expression can be transformed, used in computer algebra and term rewriting.
Canonical module
In commutative algebra, the canonical module, also called the dualising module, is a distinguished finitely generated module of a local ring serving as a dualizing object.
Cantor's diagonal argument
Cantor's diagonal argument, or diagonalization, is an 1891 proof by Georg Cantor that no list can contain every real number in [0,1], showing the reals are uncountable.
Cardano's formula
Cardano's formula is the closed-form radical solution of the cubic equation, published in Cardano's 1545 Ars Magna and historically the route through which complex numbers entered mathematics.
Cardinal arithmetic
Cardinal arithmetic is the arithmetic of cardinal numbers, the sizes of sets. For infinite cardinals, addition and multiplication collapse to the maximum, so the deep part is exponentiation.
Cardinal characteristic of the continuum
A cardinal characteristic of the continuum, also called a cardinal invariant, is a cardinal number, usually the minimal size of a set of reals with a given property, describing the structure of the real line.
Cardinality of the continuum
The cardinality of the continuum, also called the power of the continuum, is the size of the set of real numbers, strictly larger than that of the natural numbers.
Carl Friedrich Gauss
Carl Friedrich Gauss (1777–1855) was a German mathematician and astronomer called the Prince of Mathematicians, whose 1801 Disquisitiones Arithmeticae made number theory a systematic subject.
Carmichael function
The Carmichael function λ(n), also called the reduced totient function, is the least positive exponent m such that a^m ≡ 1 (mod n) for every a coprime to n.
Carmichael number
A Carmichael number, also called an absolute pseudoprime, is a composite number that satisfies Fermat's little theorem for every base coprime to it, defeating the Fermat primality test.
Carry-lookahead adder
The carry-lookahead adder (CLA), also known as a fast adder, is a digital circuit that adds binary numbers by computing every carry in parallel instead of rippling, introduced in 1958.
Cartan decomposition
The Cartan decomposition is a structural decomposition of a real semisimple Lie algebra into the eigenspaces of the Cartan involution, underlying the theory of symmetric spaces.
Cartan matrix
A Cartan matrix is an integer square matrix encoding the angles and relative lengths of a root system's simple roots, determining its Lie algebra and Dynkin diagram.
Cartan subalgebra
A Cartan subalgebra is a maximal abelian subalgebra of a semisimple Lie algebra whose elements act diagonally; fixing one yields the root space decomposition underlying the classification of semisimple Lie algebras.
Casimir element
The Casimir element, also known as the Casimir operator or Casimir invariant, is a central element of a Lie algebra's universal enveloping algebra, named for Hendrik Casimir.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an integer invariant of a coherent sheaf on projective space, or of a graded module, measuring the twist at which higher cohomology vanishes; introduced by David Mumford in 1966.
Catalan number
The Catalan numbers, also called the Catalan sequence, form an integer sequence beginning 1, 1, 2, 5, 14, 42 that counts balanced parentheses and triangulations.