Mathematics and statistics

Finsler metric

A Finsler metric is a function assigning each tangent vector its length, generalizing Riemannian metrics by dropping the quadratic restriction; Paul Finsler introduced it in 1918.

First passage and overshoots of Lévy processes

First passage and overshoots of Lévy processes study when a Lévy process first exceeds a fixed level; the overshoot is its excess at that moment, analyzed via the quintuple law and Wiener–Hopf factorisation.

First-order logic

First-order logic, also called first-order predicate calculus, is a formal logical system whose quantifiers range over individual objects only; it is the standard language for formalizing mathematics.

First-order theory

A first-order theory is a set of sentences in a first-order language, typically given by a signature and axioms, and is the standard way to axiomatize parts of mathematics.

Fisher information

Fisher information is a statistical quantity that measures how much a set of data carries about an unknown parameter of a probability distribution, introduced by Ronald Fisher in 1922.

Fisher transformation

The Fisher transformation, also known as Fisher's Z-transform, converts a Pearson correlation coefficient into a statistic with an approximately normal distribution, introduced by Ronald Fisher in 1915.

Fisher–Tippett–Gnedenko theorem

The Fisher–Tippett–Gnedenko theorem is a probability theory result stating that normalized maxima of random variables can only converge to the Gumbel, Fréchet, or Weibull types.

Fisher's exact test

Fisher's exact test, also called the Fisher-Irwin test, is a statistical test for association in a 2 × 2 table, introduced by R. A. Fisher in 1935.

Five whys

Five whys, also called the 5 Whys, is a root cause analysis technique that repeats the question why, about five times, to trace a problem to its underlying cause.

Five-dimensional space

Five-dimensional space is a space with five independent dimensions, in which a point is specified by five coordinates; in physics it often means five-dimensional spacetime with one extra spatial dimension.

Fixed point (mathematics)

A fixed point in mathematics, also called an invariant point, is a point that a function maps to itself, so Λ(x) = x; fixed point theorems give conditions for their existence.

Fixed-point arithmetic

Fixed-point arithmetic is a method of computing with real numbers by representing each value as an integer scaled by a fixed factor, with the radix point implicit.

Fixed-point combinator

The fixed-point combinator, known as the Y combinator, is a lambda calculus term Y satisfying Y f = f(Y f), supplying recursion in a language without named definitions.

Fixed-point iteration

Fixed-point iteration, also called Picard iteration or successive substitution, is a numerical method that solves equations by repeatedly applying a function to an initial guess.

Fixed-point logic

Fixed-point logic is a family of extensions of first-order predicate logic with operators defining relations as fixed points; its best-known member, least fixed-point logic, captures polynomial time on finite ordered structures.

FKG inequality

The FKG inequality, or Fortuin–Kasteleyn–Ginibre inequality, is a correlation inequality of probability theory stating that two increasing events are positively correlated; proved in 1971, it is a standard tool in percolation and statistical mechanics.

Flag algebra

A flag algebra is a formal calculus in extremal combinatorics, introduced by Alexander Razborov in 2007, that derives bounds on graph and hypergraph density problems via computer-assisted semidefinite programs.

Flag manifold

A flag manifold is the space of all flags, nested sequences of linear subspaces with prescribed dimensions, in a vector space, generalizing Grassmannians and projective space.

Flat dimension

Flat dimension, also called weak dimension, is a homological invariant of a module over a ring, the length of the shortest resolution of the module by flat modules.

Flat module

A flat module is one whose tensoring preserves exactness of sequences; Serre introduced flatness in his 1956 GAGA paper, and Grothendieck recognized its geometric significance.

Flat morphism

A flat morphism is a morphism of schemes whose local ring maps make every local ring of the source a flat module over the target.

Fleiss' kappa

Fleiss' kappa is a chance-corrected statistic measuring agreement among three or more raters classifying the same items into nominal categories, introduced by Joseph L. Fleiss in 1971.

Floer homology

Floer homology is an infinite-dimensional analog of Morse homology introduced by Andreas Floer around 1986, giving invariants in symplectic topology and of 3-manifolds and knots.

Flood fill

Flood fill is an algorithm that repaints the connected region of same-colored cells around a seed cell in a grid or image, as in a paint bucket tool.

Floor and ceiling functions

The floor and ceiling functions, also called the greatest integer function, round a real number down or up to an integer, with notation introduced by Kenneth Iverson in 1962.

Floquet theory

Floquet theory is the mathematical framework for linear differential systems with periodically varying coefficients, reducing their analysis to an eigenvalue problem over one driving period; it underpins Floquet engineering in quantum mechanics.

Flow network

A flow network is a directed graph in which each edge has a capacity, with a source that generates flow and a sink that absorbs it; the central problem is finding a maximum flow.

Flower pollination algorithm

The flower pollination algorithm (FPA) is a nature-inspired optimization method introduced by Xin-She Yang in 2012 that mimics plant pollination to find global optima of objective functions.

Fluid queue

A fluid queue is a stochastic model of a buffer filling and draining fluid at rates set by a background Markov chain, developed for dams in the 1950s.