Mathematics and statistics

Cahn–Hilliard equation

The Cahn–Hilliard equation is a fourth-order nonlinear partial differential equation describing phase separation and coarsening in binary mixtures, introduced by John W. Cahn and John E. Hilliard in 1958.

Calabi–Yau manifold

A Calabi–Yau manifold, also called a Calabi–Yau space, is a compact Kähler manifold with vanishing first Chern class, equivalent by Yau's theorem to admitting a Ricci-flat Kähler metric.

Calculus

Calculus, also called infinitesimal calculus, is the branch of mathematics studying continuous change through derivatives and integrals, formulated independently by Newton and Leibniz in the late 17th century.

Calculus of communicating systems

The calculus of communicating systems (CCS) is a process algebra introduced by Robin Milner in 1980, a formal language for describing concurrent processes that synchronize through binary handshakes.

Calculus of variations

The calculus of variations, also called variational calculus, is the branch of analysis that studies maxima and minima of functionals, with its central condition the Euler–Lagrange equation.

Camassa–Holm equation

The Camassa–Holm equation is a nonlinear partial differential equation for shallow water waves, derived by Camassa and Holm in 1993 and known for its peakon solutions.

Cameron–Martin theorem

The Cameron–Martin theorem, also called the Cameron–Martin formula, is a result in Gaussian measure theory identifying which shifts preserve absolute continuity, established by Cameron and Martin in 1944.

Campbell's theorem (probability)

Campbell's theorem, also called Campbell's formula, is a result of point process theory that converts the expectation of a random sum into an integral against the process's intensity measure.

Canadian Census

The Canadian Census, officially the Census of Population, is a mandatory five-yearly count of everyone in Canada conducted by Statistics Canada in years ending in 1 and 6.

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 bundle

In algebraic geometry, the canonical bundle, or canonical divisor, is the line bundle of top-degree differential forms on a smooth variety, whose sections organize birational classification.

Canonical correlation analysis

Canonical correlation analysis (CCA) is a multivariate statistical method introduced by Harold Hotelling in 1936 that finds linear combinations of two variable sets maximizing their correlation, used to test independence.

Canonical correspondence analysis

Canonical correspondence analysis (CCA) is a multivariate ordination method that relates species composition to environmental variables, introduced by ter Braak in Ecology in 1986 and widely used in community ecology.

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.

Canonical variate analysis

Canonical variate analysis is a multivariate statistical method that finds linear combinations of variables maximizing the separation of pre-defined groups, used for classification and introduced by Harold Hotelling in 1936.

Cantor set

The Cantor set, also called the Cantor ternary set or Cantor discontinuum, is formed by repeatedly removing middle thirds of [0, 1]; it is uncountable yet has measure zero.

Cantor space

Cantor space, written 2^N, is the space of infinite binary sequences with the product topology; it is compact, perfect, and totally disconnected, and homeomorphic to the middle-thirds Cantor set introduced by Georg Cantor in 1883.

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.

Cantor's theorem

Cantor's theorem is the set-theory result that every set is strictly smaller than the set of all its subsets, proved by Georg Cantor in 1891 using the diagonal argument.

Cap set

A cap set is a subset of the vector space over the field with three elements containing no three collinear points; how large it can be was bounded in 2016.

Capital account

The capital account is a balance of payments component recording capital transfers and nonproduced, nonfinancial assets like land and patents; it is usually very small.

Caputo fractional derivative

The Caputo fractional derivative is a fractional derivative introduced by Michele Caputo in 1967, defined by an integral of an ordinary integer-order derivative against a power-law memory kernel.

Carathéodory's extension theorem

Carathéodory's extension theorem, also known as the Hahn–Kolmogorov theorem, extends a premeasure on an algebra of sets to a measure on the generated σ-algebra, uniquely when σ-finite.

Carathéodory's theorem (convex hull)

Carathéodory's theorem is a result in convex geometry, proved in 1907 by Constantin Carathéodory: any point in the convex hull of a set in R^d uses at most d+1 points.

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.

Cardinal number

A cardinal number is a number that measures the size of a set by counting its elements; Georg Cantor developed the concept in the nineteenth century.