6,052 articles
Free object
A free object is an algebraic structure built from a set of generators with no relations beyond those the structure type forces, so maps of the generators extend uniquely.
Free probability
Free probability is a branch of probability theory in which random variables are noncommuting operators and independence is modeled on free products, introduced by Dan-Virgil Voiculescu in the 1980s.
Free product
The free product of groups is a group built from them by identifying only their identity elements, so elements of different factors do not commute; it is the coproduct in the category of groups.
Free variables and bound variables
In formal logic, a free variable is not bound by a quantifier and a bound variable is; the distinction applies to occurrences, and formulas without free variables are sentences.
Frege system
A Frege system, also called a Frege proof system, is a standard axiomatic proof system for propositional logic, named after Gottlob Frege and central to proof complexity.
Frege's propositional calculus
Frege's propositional calculus is the axiomatic system for propositional logic in Gottlob Frege's 1879 Begriffsschrift, using only negation and the conditional, with six key axioms and modus ponens.
Freiman's theorem
Freiman's theorem is a result of additive combinatorics, proved by Gregory Freiman, stating that sets of integers with a small sumset lie in generalized arithmetic progressions.
Frenet–Serret formulas
The Frenet–Serret formulas, or Frenet formulas, are differential geometry equations describing how the tangent, normal, and binormal frame of a space curve changes along the curve.
Frequency domain
The frequency domain, also known as the Fourier domain or frequency space, is the domain in which a signal is expressed by its frequency content rather than its time content.
Frequency domain decomposition
Frequency domain decomposition (FDD) is an operational modal analysis method that extracts natural frequencies, mode shapes, and damping ratios from a structure's ambient vibration without knowing the exciting forces.
Frequentist probability
Frequentist probability, also called frequentism, interprets probability as the long-run relative frequency of an event in repeated trials, underpinning the statistical methods of Fisher, Neyman, and Pearson.
Friedberg–Muchnik theorem
The Friedberg–Muchnik theorem, proved independently by Richard Friedberg and Andrei Muchnik in 1956–1957, is a computability theory result stating that there exist two computably enumerable sets whose Turing degrees are incomparable.
Friedman test
The Friedman test is a non-parametric statistical test for detecting differences among three or more treatments measured on the same blocks, introduced by Milton Friedman in 1937.
Friendship graph
A friendship graph, also called a windmill graph, is a graph in which every two vertices have exactly one common neighbor, always triangles sharing one center.
Frobenius algebra
A Frobenius algebra is a finite-dimensional algebra over a field carrying a nondegenerate bilinear form compatible with multiplication, with examples including group algebras and matrix rings.
Frobenius coin problem
The Frobenius coin problem, also called the coin problem or money-changing problem, asks for the largest integer not expressible as a nonnegative combination of given coprime integers.
Frobenius group
A Frobenius group is a transitive permutation group in which no non-identity element fixes more than one point, studied by Georg Frobenius in 1900 and 1901 using his new theory of group characters.
Frobenius method
The Frobenius method, reported by Georg Frobenius in 1873, solves linear ordinary differential equations by power series and produces classical special functions such as Bessel and Legendre functions.
Frobenius norm
The Frobenius norm, also called the Hilbert-Schmidt norm, is a matrix norm defined as the square root of the sum of squared absolute entries, named for Ferdinand Georg Frobenius.
Frobenius reciprocity
Frobenius reciprocity is a theorem of representation theory stating that induction and restriction between a group and a subgroup are adjoint, introduced by Frobenius in 1898.
Frobenius theorem (real division algebras)
The Frobenius theorem is a result in abstract algebra stating that the only finite-dimensional associative division algebras over the real numbers are R, C, and the quaternions, proved by Ferdinand Georg Frobenius in 1877.
Frontier analysis
Frontier analysis is a family of statistical and econometric methods that estimate a best-practice production frontier from data and measure how far each firm falls short of it.
Frustum
A frustum (plural frusta, frustums) is the portion of a solid lying between two parallel planes, most commonly a cone or pyramid cut by a plane parallel to its base.
FTSE4Good Index Series
The FTSE4Good Index Series is a family of equity indexes launched by FTSE in 2001 that selects companies using transparent environmental, social, and governance (ESG) criteria rather than market size alone.
Fubini–Study metric
The Fubini–Study metric is the Hermitian metric on complex projective space introduced by Guido Fubini and Eduard Study, and in quantum mechanics it measures how distinguishable neighboring pure quantum states are.
Fubini's theorem
Fubini's theorem, also called Fubini's theorem for the Lebesgue integral, is a measure theory result proven by Guido Fubini in 1907, stating that the order of integration can be interchanged.
Fuchsian group
A Fuchsian group is a discrete subgroup of PSL2(R) acting as hyperbolic isometries of the upper half-plane; quotients are hyperbolic orbifolds, named by Poincaré for Lazarus Fuchs.
Fukaya category
The Fukaya category is an A-infinity category whose objects are Lagrangian submanifolds of a symplectic manifold, with composition defined by counting pseudoholomorphic curves; Kenji Fukaya introduced it in 1993.
Fulkerson Prize
The Fulkerson Prize, formally the Delbert Ray Fulkerson Prize, is an award for outstanding papers in discrete mathematics, sponsored by the Mathematical Optimization Society and the American Mathematical Society.
Full information maximum likelihood
Full information maximum likelihood (FIML) is an estimation method in econometrics and structural equation modeling that estimates all parameters of a model jointly by maximizing the joint likelihood.