Mathematics and statistics

Cotangent complex

The cotangent complex is a homological invariant of a ring map or scheme morphism that replaces Kähler differentials for nonsmooth maps and controls first-order deformation theory.

Count regression

Count regression is a family of statistical regression models for non-negative integer outcomes like insurance claims or hospital visits, chiefly Poisson and negative binomial regression.

Countable set

A countable set is a set whose elements can be matched one-to-one with some or all of the natural numbers, a concept introduced by Georg Cantor.

Counterfactual analysis (statistics)

Counterfactual analysis is a statistical approach to causal inference that estimates a treatment's effect by comparing each unit's observed outcome with the outcome under the treatment it did not receive.

Counterfactual inference

Counterfactual inference is a statistical method for estimating a treatment's effect by comparing observed outcomes with potential outcomes under other treatments, forming the Rubin Causal Model.

Counterpart theory

Counterpart theory is David Lewis's 1968 semantic framework for modality: an individual exists in only one possible world, and its modal properties are evaluated through counterparts.

Counting

Counting, in mathematics, determines the number of elements of a finite set or of objects satisfying stated conditions; as a research field it is called enumerative combinatorics.

Coupon collector's problem

The coupon collector's problem, also called the stamp collecting problem, asks how many draws are needed to collect all n coupon types, on average n log n.

Courcelle's theorem

Courcelle's theorem is a 1990 result of Bruno Courcelle stating that every graph property definable in monadic second-order logic is decidable in linear time on graphs of bounded treewidth.

Cours d'analyse infinitésimale

Cours d'analyze infinitésimale is a two-volume French treatise on analysis by the Belgian mathematician Charles-Jean de La Vallée Poussin, first published at Louvain and Paris in 1903 and 1906.

Covariance

Covariance is a measure of the joint variability of two random variables, positive when they tend to rise together, and the basis of the correlation coefficient.

Covariance and contravariance (computer science)

Covariance and contravariance are properties of type constructors such as generic interfaces and arrays that describe how subtyping of their type arguments translates into subtyping of the constructed types.

Covariance and contravariance of vectors

Covariance and contravariance, including contravariant vectors, describe the two ways vector components transform under a change of coordinates; the metric tensor converts between the two types.

Covariance and correlation

Covariance and correlation measure how two random variables vary together: covariance is unbounded and carries units, while Pearson's correlation is a scale-free value between −1 and 1.

Covariance matrix

The covariance matrix, also called the variance-covariance matrix, is a square, symmetric matrix whose diagonal holds variances and whose off-diagonal entries hold pairwise covariances of random variables.

Covariance matrix estimation

Covariance matrix estimation is the statistical problem of estimating the matrix of variances and pairwise covariances among variables, using shrinkage and other regularized methods when variables outnumber observations.

Covariant derivative

The covariant derivative, written ∇, is the differential operator in geometry that extends differentiation to tensor fields on a manifold, correcting the partial derivative so the result transforms as a tensor.

Coverage probability

Coverage probability is the probability, under repeated sampling from a statistical model, that a confidence interval contains the true parameter; it is the formal content behind "95% confidence."

Covering array

A covering array is an N × k matrix of symbols in which every selection of t columns contains each possible t-tuple at least once, the basis of combinatorial testing.

Covering lemma

A covering lemma is a theorem of set theory stating that, absent large cardinals, every uncountable set of ordinals can be covered by a same-sized set in L.

Covering relation

The covering relation is the binary relation on a partially ordered set where y covers x when x < y and no element lies strictly between them.

Covering space

A covering space is a space mapped onto a topological space so that each point has a neighborhood evenly covered in disjoint sheets, a central tool of algebraic topology.

Cox process

The Cox process, or doubly stochastic Poisson process, is a point process whose random intensity makes its points cluster, introduced by David Cox in 1955.

Cox proportional hazards model

The Cox proportional hazards model is a semiparametric regression method for censored time-to-event data, proposed by David Cox in 1972 and widely used in medical research.

Coxeter group

A Coxeter group, or Coxeter system, is a group generated by involutions satisfying relations (r_i r_j)^{n_ij} = 1, introduced by H. S. M. Coxeter in 1934 through reflection groups.

Craig interpolation

Craig interpolation is a theorem of mathematical logic, proved by William Craig in 1957, stating that whenever one formula implies another, an intermediate formula in their shared vocabulary connects the two.

Cramér–Rao bound

The Cramér–Rao bound, or Cramér–Rao lower bound (CRLB), is a lower bound on the variance of any unbiased estimator of a parameter, proved by Rao and Cramér in the 1940s.

Cramér's conjecture

Cramér's conjecture, proposed by Swedish probabilist Harald Cramér in 1936, states that prime gaps near large numbers grow no faster than a constant times the square of the logarithm.

Cramer's rule

Cramer's rule, also known as Cramer's law or Cramer's method, solves a square system of linear equations by writing each unknown as a ratio of determinants.