Mathematics and statistics

Cycle index

The cycle index of a permutation group is a polynomial recording how many group elements have each cycle structure; evaluating it counts colorings, graphs, and chemical structures up to symmetry.

Cyclic group

A cyclic group, also called a monogenous group, is a group in which every element is a power of a single element called a generator.

Cyclic homology

Cyclic homology is a homological invariant of associative algebras, created by Connes and by Feigin and Tsygan in the 1980s, whose periodic variant recovers algebraic de Rham cohomology.

Cyclic number

A cyclic number is an integer whose multiples are cyclic permutations of its own digits; 142857, the repeating decimal block of 1/7, is the classic example.

Cyclic permutation

A cyclic permutation, also called a cycle, is a permutation of a finite set that moves its elements in a single closed loop; a cycle on all n elements is an n-cycle.

A cyclic quadrilateral, also called an inscribed or concyclic quadrilateral, is a quadrilateral whose four vertices all lie on one circle, so opposite angles sum to 180° and its area follows Brahmagupta's formula.

Cyclic vector

A cyclic vector for a linear operator A on a vector space V is a vector whose repeated images under A span the whole space.

Cycloid

A cycloid is the curve traced by a point on the circumference of a circle rolling along a straight line, with cusps at each touch.

Cyclotomic field

A cyclotomic field is a number field obtained by adjoining a primitive n-th root of unity to the rationals; it is the splitting field of xn − 1.

Cyclotomic polynomial

The cyclotomic polynomial Φn(x) is the unique monic polynomial with roots the primitive nth roots of unity, with integer coefficients and irreducible over the rationals.

Cylinder

A cylinder is the solid bounded by a curved surface and two parallel planes; in everyday use the right circular cylinder, or can shape, has volume πr²h.

Cylinder set

A cylinder set is a subset of a Cartesian product whose members are constrained at only finitely many coordinates, leaving the rest free; cylinder sets generate the product σ-algebra.

Cylindric algebra

A cylindric algebra is a Boolean algebra equipped with cylindrifications and diagonal elements, introduced by Alfred Tarski in 1948–1952 as an algebraic counterpart of first-order predicate logic.

Cylindrical algebraic decomposition

Cylindrical algebraic decomposition (CAD) is a computer algebra algorithm, introduced by George E. Collins in 1975, that partitions real space into sign-invariant cells for quantifier elimination.

Cylindrical coordinate system

The cylindrical coordinate system, also called cylindrical polar coordinates, is a 3D coordinate system that locates a point by its distance from a fixed axis, angle about that axis, and height, extending polar coordinates.

Cytel

Cytel is a statistical software and contract research company founded in 1987 by Cyrus Mehta and Nitin Patel, known for its East trial design software used by the FDA.

d-separation

d-separation is a graphical criterion that decides from a directed acyclic graph whether two variable sets are independent given a third, treating colliders differently and underpinning Bayesian networks.

D. R. Kaprekar (दत्तात्रेय रामचंद्र कापरेकर)

D. R. Kaprekar, full name Dattatreya Ramachandra Kaprekar (1905–1986), was an Indian schoolteacher and self-taught mathematician in Devlali who discovered Kaprekar's constant, 6174, and named Kaprekar, self, harshad, and Demlo numbers.

Daniel Krashen

Daniel Krashen is an American mathematician known for field patching, a technique for studying equations in function fields, and for work on the Brauer group and Galois cohomology.

Darboux integral

The Darboux integral is a definition of the definite integral using upper and lower sums, equivalent to the Riemann integral, introduced by Jean-Gaston Darboux in 1875.

Darboux transformation

The Darboux transformation, named for Gaston Darboux's 1882 result and named by V. B. Matveev in 1979, generates new solutions of integrable partial differential equations from known ones.

Data

Data are recorded observations or measurements that can be used as evidence in inquiry, from instrument readings in metrology laboratories to administrative records collected for running government programs.

Data analysis

Data analysis is the process of examining, transforming, and interpreting data to answer questions and extract usable information, using statistical and logical techniques to describe, summarize, and compare data.

Data and safety monitoring board

A data and safety monitoring board (DSMB), or data monitoring committee, is an independent committee that reviews clinical trial data and recommends continuing, modifying, or stopping the trial.

Data augmentation algorithm

The data augmentation algorithm is a Markov chain Monte Carlo method for Bayesian computation introduced by Martin A. Tanner and Wing Hung Wong in 1987.

Data collection

Data collection, also known as information collection or data gathering, is the systematic gathering of information from sources such as people, documents, and instruments to answer a research question.

Data Documentation Initiative

The Data Documentation Initiative (DDI) is an international metadata standard for describing social, behavioral, and other scientific data, maintained by the DDI Alliance and begun in 1995 as an effort to standardize codebook documentation.

Data envelopment analysis

Data envelopment analysis (DEA) is a nonparametric linear-programming method measuring the relative efficiency of units such as firms, schools, or bank branches with multiple inputs and outputs.

Data transformation (statistics)

Data transformation in statistics is a function applied to data or a random variable, most often to stabilize variance, linearize relationships, or make skewed data more normal.