1,733 articles
Monomial order
A monomial order is a total order on the monomials of a polynomial ring, compatible with multiplication, that fixes the leading terms used in Gröbner basis computation.
Monster group
The Monster group, also called the friendly giant, is the largest of the 26 sporadic finite simple groups, with order about 8 × 10^53, predicted by Fischer and Griess in 1973.
Monstrous moonshine
Monstrous moonshine, or the Conway–Norton conjecture, is the unexpected connection between the monster group and modular functions that Richard Borcherds proved in 1992, earning a Fields Medal.
Montgomery modular multiplication
Montgomery modular multiplication, or Montgomery reduction, is an algorithm introduced by Peter L. Montgomery in 1985 that computes products modulo an integer without division, enabling fast modular arithmetic in public-key cryptography.
Moonshine module
The moonshine module is an infinite-dimensional vertex operator algebra constructed by Frenkel, Lepowsky, and Meurman, on which the Monster group acts as its full automorphism group.
Moore graph
A Moore graph is a regular graph of given degree and diameter containing the maximum possible number of vertices, attaining the Moore bound; examples include the Petersen graph.
Moore–Penrose inverse
The Moore–Penrose inverse, also called the Moore–Penrose pseudoinverse, is a generalized matrix inverse that exists uniquely for any matrix, and reduces to the ordinary inverse for nonsingular matrices.
Mordell–Weil theorem
The Mordell–Weil theorem states that the group of rational points of an abelian variety over a number field is finitely generated; Mordell proved the elliptic curve case in 1922.
Morita equivalence
Morita equivalence is an equivalence relation on rings, introduced by Kiiti Morita in 1958, holding when two rings have equivalent module categories, so module properties transfer; a ring and its matrix rings are equivalent.
Morphism
A morphism is an abstract arrow from one object of a category to another, with composition and identities, defined without reference to functions or sets.
Motive (algebraic geometry)
In algebraic geometry, a motive is a conjectural elementary building block of algebraic varieties, proposed by Alexander Grothendieck in 1964 so that all cohomology theories factor through the category of motives.
Motivic cohomology
Motivic cohomology is a cohomology theory for algebraic varieties, with bidegrees H^{p,q}, recovering Chow groups, the Picard group, and Milnor K-theory; Voevodsky realized it in the late 1990s.
mpmath
mpmath is a free, BSD-licensed Python library for arbitrary-precision real and complex floating-point arithmetic, created by Fredrik Johansson in 2007 and serving as the numerical evaluation engine for SymPy.
Multigrid method
The multigrid method is an iterative solver and preconditioner for linear systems, especially elliptic PDEs, that corrects fine-grid solutions on coarser grids to solve N unknowns in O(N) work.
Multilinear algebra
Multilinear algebra is the branch of algebra dealing with multilinear maps between vector spaces, whose central objects are tensors; it underlies tensor calculus, differential forms, and tensor decompositions used in data analysis.
Multinomial theorem
The multinomial theorem, also called the multinomial formula, expands a power of a sum of any number of terms, generalizing the binomial theorem from two terms to k terms.
Multiplication
Multiplication is one of the four basic arithmetic operations, producing a product that represents repeated addition of one number a number of times equal to another.
Multiplication algorithm
A multiplication algorithm is a procedure for computing the product of two numbers or polynomials, from schoolbook long multiplication up to Karatsuba's and FFT-based methods approaching O(n log n).
Multiplication sign
The multiplication sign (×), also called the times sign, is a mathematical symbol for multiplication shaped as a diagonal cross, introduced by William Oughtred in 1631 and standard in elementary arithmetic.
Multiplication table
A multiplication table, also known as a times table, is a table showing the products of pairs of numbers, typically up to 10 or 12.
Multiplicative function
A multiplicative function is an arithmetic function on the positive integers with f(ab) = f(a)f(b) whenever gcd(a, b) = 1; examples include Euler's totient and the Möbius function.
Multiplicative group of integers modulo n
The multiplicative group of integers modulo n, also written Z n, is the finite abelian group of residue classes coprime to n, with order given by Euler's totient function.
Multiplicative inverse
A multiplicative inverse of a, written a⁻¹, is an element that multiplies a to give 1; for ordinary nonzero numbers it is the reciprocal, 1/a, and zero has none.
Multiplicative order
The multiplicative order of an integer a modulo n is the smallest positive k with a^k ≡ 1 (mod n); it always divides Euler's totient φ(n).
Multivector
A multivector is an element of a geometric algebra formed as a linear combination of blades of different grades, mixing scalars, vectors, and bivectors in one object.
Murray–von Neumann classification of II₁ factors
The Murray–von Neumann classification of II₁ factors is the program begun by Murray and von Neumann in 1936 and 1943, which introduced the fundamental group invariant of a II₁ factor.
MV-algebra
An MV-algebra, short for many-valued algebra, is an algebraic structure introduced by C. C. Chang in 1958 as the algebraic semantics of Łukasiewicz infinite-valued logic.
Myriad
A myriad is, precisely, the number ten thousand, the largest number named by one word in ancient Greek; in modern English it loosely means an indefinitely great number.
NAG Library
The NAG Library is a commercial collection of more than 1,600 numerical and statistical algorithms developed by the Numerical Algorithms Group in Oxford, first released in 1971.
Names for the number 0 in English
English has several names for the number 0: zero, the general term; oh for reading digits; nought in British use; nil for sports scores; and love in tennis.