Mathematics and statistics

Compartment model (statistics)

A statistical compartment model estimates rates of movement between states, called compartments, by fitting differential equations to time-course data such as drug concentrations or epidemic counts.

Compass (drawing tool)

A compass, also called a pair of compasses, is a technical drawing instrument with two legs hinged at one end, used to inscribe circles and arcs.

Compass and straightedge construction

Compass and straightedge construction is a classical Euclidean geometry method drawing figures with only an unmarked straightedge and a compass; the three classical problems of antiquity were proven impossible in the 19th century.

Competing risk model

A competing risk model is a survival analysis model estimating the hazard or cumulative incidence of one event type when other event types preclude it, used in medicine and engineering.

Competing risks

Competing risks are a survival-analysis setting in which several mutually exclusive event types can occur, so experiencing one, such as death before cancer recurrence, precludes ever observing the others.

Complement (set theory)

In set theory, the complement of a set is the elements, drawn from a fixed universe, that do not belong to the set, such as A \ B.

Complete bipartite graph

A complete bipartite graph K_m,n joins every vertex of one set to every vertex of the other, with m + n vertices and mn edges.

Complete Boolean algebra

A complete Boolean algebra, also called a complete Boolean lattice, is a Boolean algebra in which every subset, even an infinite one, has a join and a meet.

Complete category

A complete category is a category in which every small diagram has a limit, so products, equalizers, pullbacks, and terminal objects all exist; examples include Set, Top, and Group.

Complete ensemble empirical mode decomposition

Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is a signal-processing method that decomposes a nonstationary signal into intrinsic mode functions, fixing EEMD's incomplete reconstruction and residual noise.

Complete graph

A complete graph, denoted Kn, is a simple graph in which every pair of distinct vertices is joined by an edge; Kn has n(n-1)/2 edges.

Complete lattice

A complete lattice is a partially ordered set in which every subset has a least upper bound (join) and a greatest lower bound (meet) within the set.

Complete measure space

A complete measure space is a measure space in which every subset of a measurable set of measure zero is itself measurable, as with the Lebesgue σ-algebra.

Complete metric space

A complete metric space is a metric space in which every Cauchy sequence converges to a point of the space; the real line is complete, the rationals are not.

Complete multipartite graph

A complete multipartite graph K(p,q,...,r) is a graph whose vertices split into k independent sets, with every pair of vertices in different sets joined by an edge.

Complete numbering

A complete numbering is a numbering in computability theory where any partial computation can be effectively totalized, mapping divergences to a special element, introduced by Mal'tsev in 1963.

Complete spatial randomness

Complete spatial randomness (CSR), the homogeneous Poisson point process, assumes points occur at a constant density with independent locations, serving as the null model for detecting clustering or regularity.

Complete theory

A complete theory is a first-order theory that decides every sentence of its language: either the sentence or its negation is provable from the theory.

Complete-linkage clustering

Complete-linkage clustering is an agglomerative hierarchical clustering method that defines the distance between two clusters as the maximum distance between any members, favoring compact clusters over single linkage's chain-like ones.

Completely bounded and completely positive maps

Completely bounded maps are linear maps between operator algebras whose norm stays uniformly bounded on matrices of every size; completely positive maps are positive at every matrix level.

Completely randomized design

A completely randomized design is an experimental design in which treatments are assigned entirely at random to units, with no blocking, analyzed by one-way ANOVA.

Completely regular space

A completely regular space is a topological space where points are separated from closed sets by continuous functions; with the T₁ property it is called a Tychonoff space.

Completeness (statistics)

Completeness is a property of a statistic meaning no nonzero function of it has expectation zero under every distribution in the family, introduced by Lehmann and Scheffé in 1950.

Completeness of the real numbers

Completeness of the real numbers, also called the completeness axiom, is the property that every nonempty set of reals bounded above has a least upper bound.

Completing the square

Completing the square is an algebraic technique that rewrites a quadratic expression as a squared term plus a constant, used to solve quadratic equations and find a parabola's vertex.

Complex analysis

Complex analysis, also called complex function theory, extends calculus to functions of a complex variable, centered on holomorphic functions and applications from integrals to fluid dynamics.

Complex conjugate

The complex conjugate, or complex conjugation, maps a complex number x + iy to x − iy, reflecting it across the real axis in the complex plane.

Complex logarithm

The complex logarithm is the inverse of the complex exponential: every nonzero complex number has infinitely many logarithms, so a single-valued version requires choosing a branch, usually the principal one.

Complex manifold

A complex manifold is a topological space locally like an open subset of complex n-space, with holomorphic coordinate changes between charts; dimension-one examples are Riemann surfaces.