Mathematics and statistics

Magic square

A magic square is a square array of numbers in which every row, column, and main diagonal sums to the same value; the oldest known example is China's 3×3 Lo Shu square.

Magic square of squares

A magic square of squares is a 3 × 3 magic square whose nine entries are all perfect squares; whether one exists with distinct entries is an open problem.

Magma (computer algebra system)

Magma is a computer algebra system for computation in algebra, number theory, and algebraic geometry, developed by the Computational Algebra Group at the University of Sydney.

Magnitude (mathematics)

Magnitude in mathematics is the property that determines whether an object is larger or smaller than others of the same kind, from Euclid's geometry to vector norms.

Mahalanobis distance

The Mahalanobis distance is a statistical measure of distance between a point and a distribution that accounts for correlations among variables, introduced by P. C. Mahalanobis in 1936.

Mahlo cardinal

A Mahlo cardinal, also called a strongly Mahlo cardinal, is a large cardinal that is inaccessible and a stationary limit of regular cardinals, introduced by Paul Mahlo in 1911.

Mahonian statistic

A Mahonian statistic is a statistic on permutations whose distribution equals that of the inversion number; the major index is the other prototype, both named for Percy MacMahon.

Major adverse cardiovascular events

Major adverse cardiovascular events, also expanded as major adverse cardiac events (MACE), is a composite clinical trial endpoint combining cardiovascular death, nonfatal myocardial infarction, and stroke.

Malliavin calculus

Malliavin calculus is a stochastic calculus of variations introduced by Paul Malliavin in the 1970s, differentiating random variables with respect to Brownian noise to prove smoothness of densities.

Malmquist index

The Malmquist index is a total factor productivity index measuring productivity change between two periods through ratios of distance functions, with no price data needed.

Mandelbrot set

The Mandelbrot set, also known as the Mandelbrot fractal, is a set of complex numbers whose iterated quadratic map stays bounded, the most recognizable image of fractal geometry.

Manhattan distance

Manhattan distance, also known as the taxicab metric or city block distance, is the sum of absolute coordinate differences between two points, measuring travel along a rectangular grid rather than a straight line.

Manifold

A manifold is a topological space in which every point has a neighborhood homeomorphic to Euclidean space, so curved shapes like spheres and spacetimes can be studied with ordinary calculus.

Manifold optimization

Manifold optimization is a family of numerical methods for minimizing functions on smooth manifolds, such as orthogonal or fixed-rank matrices, with applications in machine learning and signal processing.

Mann–Kendall test

The Mann–Kendall test is a nonparametric statistical test that detects a monotonic upward or downward trend in a time series, widely used in atmospheric and hydrologic research.

Mann–Whitney U test

The Mann–Whitney U test, also called the Wilcoxon rank-sum test, is a nonparametric statistical test comparing two independent samples, and the standard nonparametric alternative to the t-test.

Mantel test

The Mantel test is a permutation-based statistical test that assesses the association between two distance matrices for the same objects, such as geographic and genetic distances.

Mantel–Haenszel method

The Mantel–Haenszel method is a statistical technique for combining stratified two-by-two tables into a single adjusted estimate of an effect, introduced by Nathan Mantel and William Haenszel in 1959.

Many-one reduction

Many-one reduction, also called mapping reduction, is a way of comparing decision problems in computability theory: A reduces to B when a computable function preserves membership.

Many-sorted logic

Many-sorted logic is a version of first-order logic in which quantification ranges over several distinct domains, called sorts; it underlies the SMT-LIB standard used by SMT solvers.

Many-valued logic

Many-valued logic, also called multivalued logic, is a family of logical systems generalizing classical two-valued logic to three or more truth values, originating with Jan Łukasiewicz in 1920 and including fuzzy logic.

Map (mathematics)

In mathematics, a map, or mapping, is a rule assigning each element of a domain to exactly one element of a codomain, usually synonymous with function.

Maple (software)

Maple, also known as the Maple computer algebra system, is a general-purpose mathematics software developed by Maplesoft, conceived at the University of Waterloo in November 1980.

Mapping class group

The mapping class group of a surface is the group of isotopy classes of orientation-preserving homeomorphisms, first studied by Max Dehn in 1922 and central to low-dimensional topology.

Mapping cone (homological algebra)

The mapping cone of a chain map f is a chain complex Cone(f) whose homology measures exactly the failure of f to be a quasi-isomorphism.

Marching cubes

Marching cubes is an algorithm that extracts an isosurface as a triangle mesh from a 3D scalar field, presented by Lorensen and Cline at SIGGRAPH 1987.

Margin of error

The margin of error is the half-width of a confidence interval, reported in polls as a plus-or-minus range; it covers only sampling error and shrinks as sample size grows.

Marginal distribution

A marginal distribution, also called a marginal probability distribution, is the distribution of a subset of random variables, obtained by summing or integrating a joint distribution over the other variables.

Marginal model

A marginal model is a semiparametric regression model for clustered or longitudinal data that describes the population-averaged mean of a response, typically fitted by generalized estimating equations introduced by Liang and Zeger in 1986.