6,052 articles
Continuous-time random walk
A continuous-time random walk is a stochastic process in which a particle makes random jumps separated by random waiting times, introduced by Montroll and Weiss in 1965.
Continuum hypothesis
The continuum hypothesis, listed by Hilbert in 1900 as his first problem, states that no cardinality lies strictly between that of the natural numbers and the real numbers.
Continuum percolation
Continuum percolation is the branch of percolation theory in which objects are placed at random positions in continuous space and studied for unbounded connected clusters, initiated by Edgar Gilbert in 1961.
Contour integration
Contour integration, also known as residue calculus or complex integration, evaluates integrals of complex functions along curves in the complex plane, chiefly through the residue theorem.
Contour line
A contour line, also called an isoline or isarithm, is a curve on a map joining points of equal value of a variable, such as elevation on topographic maps.
Contraction mapping
A contraction mapping is a map on a metric space that shrinks distances by a fixed factor below 1, and it has a unique fixed point.
Contraposition
Contraposition is the logical equivalence between a conditional and its contrapositive, where the contrapositive of P → Q is ¬Q → ¬P; the two are equivalent in classical logic.
Contrast analysis
Contrast analysis is a statistical method in ANOVA and general linear models that tests predefined weighted comparisons among group means, answering specific hypotheses rather than only the omnibus F test.
Control chart
The control chart, also called the Shewhart chart, is a statistical process control graph that separates common-cause from special-cause variation, devised by Walter Shewhart in 1924.
Control function approach
The control function approach is an econometric estimation method for models with endogenous explanatory variables, adding first-stage residuals as regressors; the name is credited to Heckman and Robb in 1985.
Control of chaos
Control of chaos applies tiny perturbations to a chaotic system to stabilize unstable periodic orbits, introduced by Ott, Grebogi, and Yorke in 1990 and first demonstrated the same year.
Control variates
Control variates is a variance-reduction technique for Monte Carlo simulation in which an auxiliary variable with a known expectation corrects the sample mean, lowering variance without bias.
Convection–diffusion equation
The convection–diffusion equation, also called the drift–diffusion equation, is a partial differential equation describing a quantity carried by a moving medium while spreading by diffusion.
Convenience sampling
Convenience sampling, also called accidental sampling or opportunity sampling, is a non-probability sampling method in which units are chosen because they are easy for the researcher to access, causing selection and undercoverage bias.
Convergence in distribution
Convergence in distribution, also called weak convergence, is a mode of convergence in probability theory in which a sequence of random variables' distributions approach a limiting distribution.
Convergence in measure
Convergence in measure is a mode of convergence for sequences of measurable functions, introduced by F. Riesz in 1909; in probability it is called convergence in probability.
Convergence in probability
Convergence in probability is a mode of convergence for sequences of random variables, requiring that large deviations from the limit become rare as n grows.
Convergence of particle methods
Convergence of particle methods is the branch of asymptotic analysis studying when and how fast sequential Monte Carlo particle estimates converge to the Feynman–Kac flow, with mean square error typically of order 1/N.
Convergence of random variables
Convergence of random variables, also known as almost sure or stochastic convergence, is the set of mathematical definitions describing how a sequence of random variables approaches a limit.
Convergence tests
Convergence tests, also known as series convergence tests, are theorems that determine whether an infinite series has a finite sum, including the ratio, root, comparison, and integral tests.
Convergent series
A convergent series is an infinite series whose partial sums approach a finite limit; convergence is decided by tests such as the ratio, root, and comparison tests.
Conversion between quaternions and Euler angles
Conversion between quaternions and Euler angles is the mathematical transformation between unit quaternions and Euler angles, two equivalent representations of a 3D rotation, with gimbal lock making one direction ambiguous.
Convex function
A convex function is a real-valued function on a convex set whose graph lies below every chord, with Jensen's inequality as its key consequence in probability.
Convex hull
The convex hull, also called the convex envelope, is the smallest convex set containing a set of points, like the shape a rubber band forms around them.
Convex hull algorithms
Convex hull algorithms compute the convex hull of n input points; key methods include Graham's scan, Jarvis's march, quickhull, and Chan's worst-case optimal O(n log h) algorithm.
Convex polygon
A convex polygon is a planar polygon that contains every line segment joining any two of its points, so it has no inward dents; squares and triangles are convex, star shapes are not.
Convex polytope
A convex polytope, or polyhedral set, is a bounded set formed as the intersection of finitely many closed halfspaces, such as polygons, cubes, and tetrahedra.
Convex set
A convex set is a subset of a vector space containing the entire line segment between any two of its points, such as balls, halfspaces, and ellipsoids.
Convolution
Convolution is a mathematical operation that combines two functions to produce a third, expressing how the shape of one modifies the other, defined by an integral.
Convolution of probability distributions
The convolution of probability distributions is the operation that gives the distribution of the sum of independent random variables, central to probability theory and first applied by Laplace in 1781.