Mathematics and statistics

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.

A cubic surface is a smooth algebraic surface in projective 3-space defined by a homogeneous cubic equation, and every smooth one contains exactly 27 straight lines, the Cayley–Salmon theorem of 1849.

Cuboctahedron

The cuboctahedron, also called the vector equilibrium or dymaxion, is an Archimedean solid with 8 triangular and 6 square faces, 12 identical vertices, and 24 edges.

Cumulant

The cumulant, also called a semi-invariant, is a quantity describing a probability distribution; the first is the mean, the second the variance, and higher ones measure skewness and kurtosis.

Cumulant-generating function

The cumulant-generating function (CGF) of a random variable is the natural logarithm of its moment-generating function; its derivatives at zero are the cumulants, which add exactly for sums of independent variables.

Cumulative distribution function

The cumulative distribution function (CDF) is the function F(x) giving the probability that a random variable takes a value less than or equal to x.

Cuntz algebra

The Cuntz algebra is the universal C-algebra generated by n isometries with pairwise orthogonal ranges summing to the identity, introduced by Joachim Cuntz in 1977 and fundamental to classification theory.

Cure model

A cure model is a survival analysis model that estimates the fraction of subjects who will never experience the event, first implemented by Boag in 1949.

Curl (mathematics)

The curl of a vector field, written ∇×F, is a vector differential operator of vector calculus that measures the local rotation of the field at each point.

Current Population Survey

The Current Population Survey is a monthly U.S. Census Bureau survey of households for the Bureau of Labor Statistics, and the source of the national unemployment rate.

Curry–Howard correspondence

The Curry–Howard correspondence, also known as the propositions-as-types principle, identifies propositions with types and proofs with programs, so writing a program is constructing a proof.

Curry's paradox

Curry's paradox, or Löb's paradox, is a self-reference paradox from Haskell Curry's 1942 work that proves an arbitrary conclusion using only implication, without negation, unlike the liar paradox.

Currying

Currying, also called Schönfinkelisation or curryfication, is the transformation of a function taking multiple arguments into a chain of functions that each take one argument, enabling partial application.

Curse of dimensionality

The curse of dimensionality is the rapid, typically exponential growth in the cost or difficulty of a computational or statistical problem as dimensions increase, a term introduced by Richard Bellman.

Curvature

Curvature is the collection of mathematical quantities that measure how a curve, surface, or Riemannian manifold deviates from being flat, underlying differential geometry and Einstein's general relativity.

Curve

A curve is a one-dimensional continuous geometric object, intuitively the path traced by a moving point, and can be a straight line, a circle, or a conic section.

Curve fitting

Curve fitting, also called data fitting, is the construction of a mathematical curve that best fits data points, most often by least squares, first published by Legendre in 1805.

Curve shortening flow

Curve shortening flow is a geometric evolution equation that moves each point of a plane curve inward with speed equal to its local curvature, shrinking length.

Curvelet transform

The curvelet transform is a multiscale geometric transform that decomposes images into coefficients indexed by scale, orientation, and location, representing curved edges far more efficiently than wavelets.

Curvilinear coordinates

Curvilinear coordinates, also called a curvilinear coordinate system, locate points by coordinates whose constant-value surfaces are curved; cylindrical and spherical coordinates are the standard examples.

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.

CUSUM

CUSUM, also known as the cumulative sum control chart, is a change-detection method by E. S. Page in 1954 that accumulates deviations from a target value and signals when the sum crosses a decision limit.

Cut elimination

Cut elimination is a proof theory theorem, proved by Gerhard Gentzen in 1935, stating that any sequent-calculus derivation using the cut rule can be transformed into a cut-free derivation.

Cut vertex

A cut vertex, also called an articulation point, is a graph vertex whose removal increases the number of connected components; networks containing cut vertices are vulnerable to single-point failure.

Cutoff phenomenon (Markov chains)

The cutoff phenomenon is the abrupt transition of a Markov chain from far from equilibrium to close to it, discovered in 1981 in the context of card shuffling.

Cutting stock problem

The cutting stock problem, also known as the nesting problem, is a combinatorial optimization problem: cut required smaller pieces from larger stock at minimum cost.

Cutting-plane method

The cutting-plane method is an optimization algorithm that solves a relaxed problem and adds linear constraints, called cuts, to remove parts of the relaxation containing no optimal solution of the original problem.

CW complex

A CW complex is a topological space built by gluing cells of increasing dimension along their boundary spheres, introduced by J. H. C. Whitehead in 1949.

Cycle (graph theory)

A cycle in graph theory, also called a simple cycle, is a closed walk returning to its start without repeating vertices or edges; odd cycles determine bipartiteness.