Mathematics and statistics

Computational group theory

Computational group theory (CGT) is the study of algorithms for groups, ranging from provably unsolvable decision problems to practical systems such as GAP and Magma.

Computational science, also called scientific computing or technical computing, is a multidisciplinary field using advanced computing to solve complex problems in science, engineering, and other domains.

Computer algebra

Computer algebra, also called symbolic computation, is the branch of computer science that develops software for the exact, symbolic solution of equations, unlike approximate numerical computing.

Computer experiment

A computer experiment is an experiment in which observations come from running a computer model, or simulator, at chosen inputs instead of measuring a physical process.

Computer-assisted proof

A computer-assisted proof is a mathematical proof in which a computer performs calculations or exhaustive case checks impractical to verify by hand, as in the 1976 four-color theorem proof.

Concatenation

Concatenation is the operation of joining two strings end to end into one of the combined length, the fundamental operation of formal language theory and a basic primitive in programming, written + in Python.

Concave function

A concave function, also called concave downwards, is a function defined on a convex set whose graph lies on or above every chord joining two of its points.

Concentration compactness

Concentration compactness is a principle in the calculus of variations and partial differential equations, introduced by Pierre-Louis Lions in 1984, describing how bounded sequences fail to be compact.

Concentration inequality

A concentration inequality is a mathematical bound on how likely a function of many random variables, like a sum, is to deviate far from its expected value.

Concentration of measure

Concentration of measure is a phenomenon of high-dimensional probability in which a function of many random variables takes values in a narrow range with overwhelming probability.

Concordance correlation coefficient

The concordance correlation coefficient (CCC) is a statistic measuring agreement between two methods or raters measuring the same continuous quantity, proposed by Lawrence Lin in 1989.

Condensation algorithm

The Condensation algorithm, or Conditional Density Propagation, is a particle-filtering method for visual tracking in clutter, introduced by Michael Isard and Andrew Blake at Oxford in 1996.

Condition number

The condition number measures how sensitive a problem's solution is to small changes in its input; for an invertible matrix A it is κ(A) = ‖A‖‖A⁻¹‖.

Conditional convergence

Conditional convergence is a property of an infinite series that converges to a finite sum while its absolute values diverge, as in the alternating harmonic series summing to ln 2.

Conditional density estimation

Conditional density estimation (CDE) is the statistical task of estimating the full conditional density p(y|x) from data, supplying modes, prediction intervals, and samples that ordinary regression cannot.

Conditional entropy

Conditional entropy, written H(Y|X), measures in information theory the average uncertainty remaining in a random variable Y once another variable X is known; Claude Shannon introduced it in 1948.

Conditional expectation

Conditional expectation, also known as conditional mean, is the expected value of a random variable once part of the outcome is known, defined via sub-σ-algebras by Kolmogorov in 1933.

Conditional independence

Conditional independence is the property that two quantities carry no information about each other once a third quantity is known; it underlies graphical models and sufficiency theory.

Conditional inference (statistics)

Conditional inference is a statistical approach to testing and estimation that conditions on ancillary statistics or sufficient statistics for nuisance parameters, eliminating them and allowing exact conditional tests and confidence intervals.

Conditional logistic regression

Conditional logistic regression is a regression method for binary outcomes in matched or finely stratified data, the predominant analysis for matched case-control studies, known in economics as the fixed-effects logit.

Conditional probability

Conditional probability is the probability of an event given that another has occurred, defined as P(A∩B)/P(B) for P(B) > 0; it underlies Bayes' rule and conditioning in statistics.

Conditional probability distribution

A conditional probability distribution is the distribution of a random variable given other information, such as Y = y, computed as a joint distribution divided by a marginal.

Conditional proof

Conditional proof is a proof technique for deriving a conditional statement: one temporarily assumes A, derives B, and concludes A → B with the assumption discharged.

Conditional variance

Conditional variance, also called the scedastic or skedastic function, is the variance of a random variable once another variable is known, and it obeys the law of total variance.

Conductance (Markov chain)

Conductance, in Markov chain theory, is a measure of how hard it is for a chain to leave any large minority region of its state space, and it controls mixing time through Cheeger's inequality.

Conductor (class field theory)

In class field theory, the conductor of a finite abelian extension, also called the conductor ideal, is the smallest modulus whose ray class field contains the extension.

Cone

A cone, also called a conic solid, is a solid geometric figure with a flat circular base and a single apex, with volume one third of a cylinder.

Confidence interval

A confidence interval, also known as confidence limits, is a range computed from sample data likely to contain a population parameter, usually reported at a 95% confidence level.

Confidential Information Protection and Statistical Efficiency Act

The Confidential Information Protection and Statistical Efficiency Act (CIPSEA) is a United States federal law, enacted in 2002, protecting data collected for statistical purposes from disclosure in identifiable form.