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Factor analysis
Factor analysis is a statistical method that explains correlations among observed variables through fewer unobserved factors; invented by Charles Spearman in 1904, it is a core psychometrics tool.
Factor theorem
The factor theorem is an algebra theorem stating that a number a is a zero of a polynomial f(x) if and only if x − a is a factor.
Factorization
Factorization is the decomposition of an element of a ring into a product of simpler elements, generalizing prime factorization of integers; unique factorization domains are where this decomposition is unique.
Factorization of polynomials
Factorization of polynomials is the computation expressing a polynomial as a product of irreducible factors over a given coefficient ring, a central problem in computational algebra.
Factorization of polynomials over finite fields
Factorization of polynomials over finite fields is the task of writing a polynomial over Fq as a product of irreducible polynomials, computed by efficient algorithms.
Faithfully flat descent
Faithfully flat descent is a technique in algebra and algebraic geometry, developed by Grothendieck, for transferring properties from a faithfully flat extension back to the base.
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.
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 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.
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.
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.
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 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.
Field (mathematics)
In mathematics, a field is a set equipped with addition and multiplication satisfying the usual laws of arithmetic; the rational, real, and complex numbers are the familiar examples.
Field extension
A field extension is a pair of fields L/K where K is a subfield of L, the central object of Galois theory and its measure of size, the degree.
Field of fractions
The field of fractions of an integral domain is the smallest field containing it, built as the rationals are built from the integers; also called the quotient field.
Field of sets
A field of sets, also called an algebra of sets, is a collection of subsets of a set closed under finite union, intersection, and complementation.
Fields Medal
The Fields Medal (Fields Prize) is a mathematics prize awarded every four years at the International Congress of Mathematicians, first awarded in 1936 and limited to mathematicians under 40.
Finite field
A finite field, also called a Galois field, is a field with a finite number of elements. Its order is always a prime power, and one such field exists for each.
Finite field arithmetic
Finite field arithmetic, also called Galois field arithmetic, is arithmetic in a field with a finite number of elements rather than in infinite fields like the rationals.
Finite group
A finite group is a group containing only finitely many elements, the count being its order. Finite groups model symmetries of finite objects and arise throughout mathematics and physics.
Finitely generated group
A finitely generated group is a group whose every element is a product of powers of elements from some finite generating set, a basic finiteness condition in group theory.
Finitely generated module
A finitely generated module is a module expressible as combinations of finitely many elements, the analog of a spanning set in linear algebra over general rings.