Mathematics and statistics

Full shift

The full shift is the dynamical system of all infinite sequences over a fixed alphabet with the shift map, and the largest shift space on that alphabet.

Full-time equivalent

A full-time equivalent (FTE) is a unit for converting part-time and full-time work hours into the number of full-time workers they equal, widely used in official statistics.

Function (mathematics)

In mathematics, a function is a relation that assigns each input from a domain exactly one output in a range, written y = f(x); the concept was redefined by Dirichlet in 1829.

Function composition

Function composition, also known as composite function or composition of maps, is an operation on functions where (g∘f)(x) = g(f(x)); it is associative but not commutative.

Functional (mathematics)

In mathematics, a functional is a function whose input is a function and whose output is a number, central to the calculus of variations and functional analysis.

Functional analysis is the branch of mathematical analysis that studies functions and operators on infinite-dimensional spaces such as Banach and Hilbert spaces, often described as infinite-dimensional linear algebra.

Functional calculus (logic)

Functional calculus, or first-order predicate logic, is a formal system in which statements about individuals are proved from axioms, and the standard logical framework of mathematics.

Functional clustering

Functional clustering is a set of statistical and machine-learning methods that groups curves, trajectories, and time-varying observations into clusters by shape similarity, treating each observation as a function.

Functional completeness

Functional completeness, also called expressive adequacy, is the property of a set of logical connectives that can express every truth function; NAND and NOR are each complete alone.

Functional derivative

The functional derivative, also called the variational derivative, generalizes the ordinary derivative to functionals, mappings from functions to numbers, and underlies the calculus of variations and the Euler–Lagrange equation.

Functional differential equation

A functional differential equation is a differential equation involving the unknown function at past or future argument values, modeling after-effect systems in physics, biology, economics, and control theory.

Functional equation (L-function)

The functional equation of an L-function is a symmetry relating its values at s to those at 1-s, one of the defining analytic properties of L-functions.

Functional principal component analysis

Functional principal component analysis (FPCA) extends principal component analysis to curves, surfaces, and other functions, and is the most widely used technique in functional data analysis.

Functional regression

Functional regression, also known as functional linear regression, is a family of statistical regression methods where predictors or responses are curves, applied to data like imaging and accelerometry.

Functor

A functor is a structure-preserving map between categories that sends objects to objects and morphisms to morphisms, introduced by Eilenberg and Mac Lane in 1945.

Fundamenta Mathematicae

Fundamenta Mathematicae is a Polish mathematics journal published in Warsaw by the Polish Academy of Sciences, founded in 1920 as the world's first specialized mathematical journal, devoted to set theory.

Fundamental domain

A fundamental domain is a subset of a space that contains exactly one representative of each orbit of a group action, so its translates tile the space.

Fundamental group

The fundamental group, also called the first homotopy group, is the group formed by the loops of a topological space up to continuous deformation, recording how loops wind around holes.

Fundamental theorem of algebra

The fundamental theorem of algebra, also called D'Alembert's theorem, states that every nonconstant polynomial with complex coefficients has at least one complex root; a degree n polynomial has exactly n.

Fundamental theorem of arithmetic

The fundamental theorem of arithmetic, also called the unique factorization theorem, states that every integer greater than 1 factors into primes in only one way.

Fundamental theorem of calculus

The fundamental theorem of calculus links the two central operations of calculus, stating that differentiation and integration are inverse processes; its evaluation formula is the Newton–Leibniz formula.

Fundamental theorem of Galois theory

The fundamental theorem of Galois theory is a field theory theorem giving an inclusion-reversing correspondence between intermediate fields of a Galois extension and subgroups of its Galois group.

Funnel plot

A funnel plot is a scatter plot of effect estimates against study size or precision in a meta-analysis, used to display small-study effects and assess publication bias.

Fused multiply-add

A fused multiply-add (FMA) is a floating-point operation that computes a × b + c with a single rounding, added to IEEE 754 in 2008.

Fusion rules

Fusion rules are non-negative integers that record how two representations of a chiral algebra, such as a vertex operator algebra, combine, given by dimensions of intertwining operator spaces.

Future of Marine Animal Populations

Future of Marine Animal Populations, or FMAP, was a project of the Census of Marine Life (2000–2010) that statistically modeled ocean biodiversity and the effects of fishing and climate change.

Fuzzy arithmetic

Fuzzy arithmetic is the extension of arithmetic operations from real numbers to fuzzy numbers, used to calculate with non-probabilistic uncertainty such as expert judgment or linguistic scales.

Fuzzy c-means

Fuzzy c-means, also known as fuzzy c-means clustering, is a clustering algorithm that gives every data point a membership degree in each cluster rather than one hard label.

Fuzzy calculus

Fuzzy calculus is the branch of mathematical analysis extending differentiation and integration to fuzzy-number-valued functions, emerging from fuzzy set theory and applied mainly to fuzzy differential equations.