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Crystal base
A crystal base is a combinatorial structure attached to a representation of a quantum group, introduced in the early 1990s by Masaki Kashiwara and George Lusztig.
Cube (algebra)
The cube of a number, or cubic number, is the number multiplied by itself twice, written a3; cubing gives the volume of a cube with edge a.
Cube root
The cube root, also called the cubic root, of a number b is the number a with a³ = b; every real number has exactly one real cube root.
Cubic equation
A cubic equation, also known as a third-degree equation, is a polynomial equation of degree three whose general solution, found in sixteenth-century Italy, was the first advance beyond the quadratic formula.
Cubic function
A cubic function, also called a cubic polynomial, is a polynomial function of degree three, of the form f(x) = ax³ + bx² + cx + d.
Cubic reciprocity
Cubic reciprocity is a number theory theorem, the degree-three analog of quadratic reciprocity, set in the Eisenstein integers and first proved by Eisenstein in 1844.
Cusp form
A cusp form is a modular form that vanishes at all cusps, meaning its Fourier expansion has no constant term, so it tends to 0 as q does.
Cyclic group
A cyclic group, also called a monogenous group, is a group in which every element is a power of a single element called a generator.
Cyclic homology
Cyclic homology is a homological invariant of associative algebras, created by Connes and by Feigin and Tsygan in the 1980s, whose periodic variant recovers algebraic de Rham cohomology.
Cyclic number
A cyclic number is an integer whose multiples are cyclic permutations of its own digits; 142857, the repeating decimal block of 1/7, is the classic example.
Cyclic permutation
A cyclic permutation, also called a cycle, is a permutation of a finite set that moves its elements in a single closed loop; a cycle on all n elements is an n-cycle.
Cyclic vector
A cyclic vector for a linear operator A on a vector space V is a vector whose repeated images under A span the whole space.
Cyclotomic field
A cyclotomic field is a number field obtained by adjoining a primitive n-th root of unity to the rationals; it is the splitting field of xn − 1.
Cyclotomic polynomial
The cyclotomic polynomial Φn(x) is the unique monic polynomial with roots the primitive nth roots of unity, with integer coefficients and irreducible over the rationals.
Cylindric algebra
A cylindric algebra is a Boolean algebra equipped with cylindrifications and diagonal elements, introduced by Alfred Tarski in 1948–1952 as an algebraic counterpart of first-order predicate logic.
Cylindrical algebraic decomposition
Cylindrical algebraic decomposition (CAD) is a computer algebra algorithm, introduced by George E. Collins in 1975, that partitions real space into sign-invariant cells for quantifier elimination.
D. R. Kaprekar (दत्तात्रेय रामचंद्र कापरेकर)
D. R. Kaprekar, full name Dattatreya Ramachandra Kaprekar (1905–1986), was an Indian schoolteacher and self-taught mathematician in Devlali who discovered Kaprekar's constant, 6174, and named Kaprekar, self, harshad, and Demlo numbers.
Daniel Krashen
Daniel Krashen is an American mathematician known for field patching, a technique for studying equations in function fields, and for work on the Brauer group and Galois cohomology.
De Moivre's formula
De Moivre's formula, also called De Moivre's theorem, states that (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ) for any integer n.
De Morgan's laws
De Morgan's laws, also called De Morgan's theorem, are a pair of rules stating that the negation of AND is the OR of negations, and vice versa.
Decimal
The decimal, or base-10, numeral system is the everyday number system whose digits 0 through 9 take place values in powers of ten, separated by a decimal point.
Decomposition theorem
The decomposition theorem is a 1981 result in algebraic geometry, proved by Beilinson, Bernstein, Deligne, and Gabber, stating that derived direct images of intersection cohomology complexes split into direct sums.
Dedekind cut
A Dedekind cut, also called a Dedekind section, is a partition of the rational numbers into two sets marking a real number, devised by Richard Dedekind in 1858.
Dedekind domain
A Dedekind domain, also called a Dedekind ring, is a Noetherian, integrally closed ring, named for Richard Dedekind, in which every nonzero ideal factors uniquely into prime ideals.
Dedekind zeta function
The Dedekind zeta function ζK(s) of a number field K is the analytic function summed over its integral ideals, generalizing the Riemann zeta function, the case K = Q.
Definite matrix
A definite matrix is a Hermitian (in the real case, symmetric) matrix whose quadratic form takes values of only one sign, classified as positive, negative, semidefinite, or indefinite.
Deformation quantization
Deformation quantization is a mathematical technique for constructing quantum theories by deforming the algebra of functions on a classical phase space into a noncommutative star product.
Degree
In mathematics, degree is a numerical measure of size or complexity, most familiarly a polynomial's highest total exponent, also naming the angle unit of 1/360 of a rotation.
Degree of a polynomial
The degree of a polynomial, or polynomial degree, is the largest exponent with a nonzero coefficient among its terms, naming it linear, quadratic, cubic, and so on.
Deligne–Mumford stack
A Deligne–Mumford stack is an algebraic stack locally modeled on schemes by an étale surjective covering, introduced by Deligne and Mumford in 1969 for the moduli of algebraic curves.