6,052 articles
Fan Chung
Fan Chung, also known as Fan Chung Graham, is a Taiwanese-born American mathematician, born in 1949, known for spectral graph theory, quasirandom graphs, and random graph models of networks.
Fano plane
The Fano plane, or Fano configuration, is the smallest finite projective plane: 7 points and 7 lines, with 3 points on each line, constructed by Gino Fano in 1892.
Fano variety
A Fano variety is a smooth projective algebraic variety whose anticanonical divisor is ample, placing it at the positive-curvature end of the classification of algebraic varieties.
Fano's inequality
Fano's inequality is an information theory result lower-bounding the error probability of estimating a random variable X from an observation Y in terms of the conditional entropy.
Farey sequence
The Farey sequence, or Farey series, is the ordered list of all reduced fractions between 0 and 1 with denominator at most n, a basic object of number theory.
Fast Fourier transform
The fast Fourier transform (FFT) is a family of algorithms computing the discrete Fourier transform in about N log N operations instead of N squared.
Fast inverse square root
Fast inverse square root, also called Fast InvSqrt, is an algorithm that estimates 1/√x by treating a float's bits as an integer, famous from the 1999 game Quake III Arena.
Fast multipole method
The fast multipole method (FMM) is a numerical algorithm, introduced by Leslie Greengard and Vladimir Rokhlin in 1987, that evaluates pairwise particle interactions in O(N) operations instead of O(N²).
Fault tree analysis
Fault tree analysis, also called failure tree analysis, is a deductive risk analysis method that links an undesired top event to combinations of component failures using Boolean logic gates.
Feasible generalized least squares
Feasible generalized least squares (FGLS) is a two-step regression estimator that first estimates the error covariance matrix from least squares residuals, then applies generalized least squares.
Federal Competitiveness and Statistics Centre
The Federal Competitiveness and Statistics Centre (FCSC) is the UAE federal agency that produces official national statistics and monitors the country's performance in global competitiveness reports.
Feedback arc set
A feedback arc set of a directed graph is a set of arcs whose removal makes the graph acyclic; finding a smallest one is NP-hard.
Feedback vertex set
A feedback vertex set, also known as a cycle cutset, is a set of vertices whose removal leaves a graph acyclic; finding the smallest one is an NP-complete problem.
Feigenbaum constants
The Feigenbaum constants are two universal numbers, δ ≈ 4.6692 and α ≈ −2.5029, governing how many nonlinear systems approach chaos through period doubling, discovered by Mitchell Feigenbaum in 1975.
Feit–Thompson theorem
The Feit–Thompson theorem, also called the odd order theorem, states that every finite group of odd order is solvable, proved by Walter Feit and John Thompson in 1963.
Felipe Cucker
Felipe Cucker, also known as Juan Felipe Cucker Farkas, is a Spanish mathematician at City University of Hong Kong who co-founded the Society for the Foundations of Computational Mathematics.
Felix Hausdorff
Felix Hausdorff, who also wrote philosophy and literature as Paul Mongré, was a German mathematician who founded set-theoretic topology with his 1914 Grundzüge der Mengenlehre.
Feller process
A Feller process, also called a Feller-Dynkin process, is a continuous-time Markov process introduced by William Feller in the 1950s that includes Brownian motion and all Lévy processes.
Fermat number
A Fermat number is an integer of the form 2^(2^n) + 1, named after Pierre de Fermat. Only the first five, 3 through 65537, are known to be prime.
Fermat pseudoprime
A Fermat pseudoprime to a base is a composite number that satisfies Fermat's little theorem, so it passes the Fermat primality test; the smallest base-2 example is 341.
Fermat's Last Theorem
Fermat's Last Theorem, also called Wiles' theorem, states that xⁿ + yⁿ = zⁿ has no positive integer solutions for n > 2, proved by Andrew Wiles in 1995.
Fermat's little theorem
Fermat's little theorem is a number theory result stating that a^(p-1) ≡ 1 mod p for any prime p not dividing a. Fermat stated it in 1640.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares, also called Fermat's Christmas Theorem, states that an odd prime is a sum of two squares exactly when it is 1 modulo 4.
Feynman–Kac formula
The Feynman–Kac formula represents the solution of a parabolic partial differential equation as an expected value of a functional of a diffusion process, such as Brownian motion.
Fiber bundle
A fiber bundle is a map between topological spaces that locally looks like a product, describing how a fiber space attaches to a base space.
Fiber product of schemes
The fiber product of schemes X ×S Y is the categorical pullback of two morphisms to a common base S, underlying intersections, fibers, and base change.
Fibonacci
Fibonacci, also known as Leonardo Pisano or Leonardo of Pisa (c. 1170–c. 1250), was an Italian mathematician who introduced Hindu-Arabic numerals to Europe in his 1202 Liber Abaci.
Fibonacci coding
Fibonacci coding, also called the Gopala-Hemachandra code, is a universal, prefix-free code for positive integers that uses the Zeckendorf representation and ends each codeword with the pair 11.
Fibonacci cube
The Fibonacci cube is a graph whose vertices are binary strings with no two consecutive 1s, introduced by Wen-Ping Hsu in 1993 as an interconnection network topology.
Fibonacci sequence
The Fibonacci sequence, also known as the Fibonacci series, is the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, in which each term is the sum of the two before it.