Mathematics and statistics

Melnikov method

The Melnikov method is an analytical technique in dynamical systems theory that predicts chaos by measuring the splitting of stable and unstable manifolds under small perturbations.

Mendelian randomization, or MR, is a method in genetic epidemiology that uses inherited genetic variants as instrumental variables to test causal effects, reducing confounding in observational studies.

Menger sponge

The Menger sponge, also called the Sierpiński sponge, is a three-dimensional fractal made by repeatedly drilling holes in a cube, described by Karl Menger in 1926.

Menger's theorem

Menger's theorem is a graph theory result proved by Karl Menger in 1927 equating the maximum number of disjoint paths between two vertices with the minimum separating set.

Mental calculation

Mental calculation, also known as mental arithmetic or mental math, is the solving of arithmetic problems entirely in the head without aids such as a calculator or pen and paper.

Mercer's theorem

Mercer's theorem, proved by James Mercer in 1909, states that a continuous symmetric positive semidefinite kernel expands as a uniformly convergent series of eigenfunctions with nonnegative coefficients.

Meromorphic function

A meromorphic function is a function of a complex variable that is holomorphic on a domain except at isolated poles, exemplified by rational functions, tan z, and the gamma function.

Mersenne prime

A Mersenne prime is a prime number of the form 2^p − 1, named after Marin Mersenne. The largest known prime, found in 2024, is one.

Mersenne primes

Mersenne primes are prime numbers of the form 2^p − 1 with p prime, named for Marin Mersenne; 52 are known, and they correspond to even perfect numbers.

Mertens function

The Mertens function, M(x) = Σ μ(n), sums the Möbius function up to x. Mertens conjectured |M(x)| < √x in 1897; Odlyzko and te Riele disproved it in 1985.

Meshfree method

A meshfree method is a numerical technique that approximates solutions of partial differential equations using scattered points, with no explicit connectivity between nodes, useful for large deformations and fracture.

Meshless method

A meshless method is a numerical technique that solves partial differential equations using scattered points or particles, useful where mesh distortion breaks finite element analysis.

Meta-analysis

A meta-analysis is a statistical method that combines the results of several independent studies into a single estimate of an effect, with a measure of uncertainty.

Meta-regression

Meta-regression is a statistical technique in meta-analysis that regresses the effect sizes of multiple studies on study-level covariates, called moderators, to explain why studies differ.

Metabolic network modelling

Metabolic network modeling, also known as metabolic network reconstruction and simulation, is the mathematical representation of biochemical reactions in a cell, used to predict metabolite and flux behavior.

metafor

metafor is a free, open-source package for the R statistical environment that provides functions for conducting meta-analyses, written and maintained by Wolfgang Viechtbauer and distributed on CRAN.

Metaheuristic

A metaheuristic, also known as a meta-algorithm, is a problem-independent framework for building heuristic optimization algorithms, used when problems like scheduling and vehicle routing are too complex for exact methods.

Method of analytic tableaux

The method of analytic tableaux, also called semantic tableaux, is a tree-shaped proof procedure for logic introduced by Evert Beth and Jaakko Hintikka in 1955, testing satisfiability by searching for counterexamples.

Method of averaging

The method of averaging, or Krylov–Bogoliubov–Mitropolski method, is a perturbation technique for differential equations with a small parameter and rapidly oscillating terms, replacing the exact equation by an averaged one.

Method of characteristics

The method of characteristics, also known as the Charpit method, solves first-order partial differential equations by reducing them to ordinary differential equations along characteristic curves.

Method of fundamental solutions

The method of fundamental solutions (MFS), also known as the charge simulation method, is a meshfree boundary-type numerical method for PDEs, introduced by Kupradze and Aleksidze in 1964.

Method of lines

The method of lines is a numerical technique for solving time-dependent partial differential equations: space is discretized, time is left continuous, yielding a system of ODEs.

Method of moments (statistics)

The method of moments is a statistical estimation technique introduced by Karl Pearson in 1894 that equates sample moments to population moments to estimate distribution parameters.

Method of moments quantile regression

Method of moments quantile regression (MM-QR) is a statistical method that fits quantile regression models by matching sample moments, introduced by Machado and Santos Silva in 2019.

Method of steepest descent (asymptotics)

The method of steepest descent, also called the saddle-point method, estimates contour integrals of analytic functions with a large parameter by deforming the contour through a saddle point.

Method of undetermined coefficients

The method of undetermined coefficients is a technique for solving nonhomogeneous linear ODEs with constant coefficients: guess a trial particular solution matching the forcing, then solve for its coefficients by substitution.

Metric dimension (graph theory)

The metric dimension of a graph, also called the locating number, is the smallest set of vertices whose distances uniquely identify every vertex, introduced in 1975.

Metric Diophantine approximation

Metric Diophantine approximation is the branch of number theory that classifies, by Lebesgue measure, which real numbers admit infinitely many rational approximations of a prescribed quality.

Metric interval temporal logic

Metric interval temporal logic (MITL) is a real-time temporal logic, introduced by Alur, Feder, and Henzinger in 1996, whose temporal operators carry non-singular time intervals, making satisfiability decidable in EXPSPACE.