Mathematics and statistics

Innovative trend analysis

Innovative trend analysis is a graphical method that detects trends in hydrological or climatic time series without assumptions about serial correlation, proposed by Zekâi Şen in 2012.

Insertion sort

Insertion sort, or linear insertion sort, is a stable comparison sorting algorithm that inserts each element into place among the sorted part, fast on nearly sorted data.

Institut des Hautes Études Scientifiques

The Institut des Hautes Études Scientifiques (IHES) is an independent French research institute in Bures-sur-Yvette near Paris, founded in 1958 by Léon Motchane for mathematics and theoretical physics.

Institute of Combinatorics and its Applications

The Institute of Combinatorics and its Applications is an international scholarly society founded in 1990 by Ralph Stanton, publishing the Bulletin of the Institute since 1991.

Institute of Mathematics and its Applications

The Institute of Mathematics and its Applications (IMA), founded in 1964, is a UK professional society for mathematicians and the only awarder of the Chartered Mathematician designation.

Instrumental variables analysis

Instrumental variables analysis is a statistical method for estimating causal effects from observational data, using an instrument that shifts the exposure but has no other route to the outcome.

Integer

An integer, also called an integer number, is a whole number that may be positive, negative, or zero, and the set ℤ is closed under addition, subtraction, and multiplication.

Integer factorization

Integer factorization, also called prime factorization, is the problem of decomposing a composite integer into smaller factors, best known as the basis of RSA cryptography.

Integer overflow

Integer overflow, also called bit overflow, is the condition where an arithmetic operation on a fixed-width integer produces a result the type cannot represent, potentially causing memory-safety vulnerabilities.

Integer quadratic programming

Integer quadratic programming (IQP) is an optimization method that minimizes a quadratic objective over integer variables subject to constraints, and is NP-hard even in two variables.

Integral

An integral, also called integral calculus, is a fundamental object of calculus assigning a function over an interval a number, the net signed area under its graph.

Integral basis

An integral basis of a number field K of degree n is a set of n algebraic integers that spans the ring of integers as a free module over the integers.

Integral domain

An integral domain, also called an entire ring, is a commutative ring in which ab = 0 forces a = 0 or b = 0; the integers are the standard example.

Integral element

An integral element of a ring S over a base ring R satisfies a monic polynomial with coefficients in R, generalizing algebraic elements of field extensions.

Integral symbol

The integral symbol ∫, also called the integral sign, is the mathematical symbol for integration, introduced by Leibniz in 1675 as a long S for summa.

Integral transform

An integral transform converts a function of one variable into another by integrating against a fixed two-variable kernel, turning differential equations into algebraic ones that are easier to solve.

Integrally closed domain

An integrally closed domain is an integral domain containing every element of its fraction field integral over it, that is, satisfying a monic polynomial over the domain.

Integrated nested Laplace approximations

Integrated nested Laplace approximations (INLA) is a deterministic method for approximate Bayesian inference in latent Gaussian models, introduced by Håvard Rue, Sara Martino, and Nicolas Chopin in 2009.

Integrated Public Use Microdata Series

The Integrated Public Use Microdata Series (IPUMS) is a family of harmonized census and survey microdata collections, maintained at the University of Minnesota since 1985, free to registered researchers.

Integrating factor

An integrating factor is a function that, when multiplied into a first-order ordinary differential equation, turns it into an exact equation whose solution follows from a potential function.

Integration by parts

Integration by parts is an integral calculus technique that turns the integral of a product of functions into a boundary term minus an easier integral.

Integration by reduction formulae

Integration by reduction formulae is an integral calculus technique expressing an integral carrying a parameter n through a recurrence relation in terms of a similar integral with smaller n.

Integration by substitution

Integration by substitution, also called u-substitution, is a method for evaluating integrals by reversing the chain rule, rewriting them in terms of a new variable u.

Integro-differential equation

An integro-differential equation is an equation containing derivatives and integrals of the unknown function; its solution depends on accumulated history, not just local values, in models of memory, radiative transfer, and viscoelasticity.

Intelligence quotient

An intelligence quotient (IQ) is a standard measure of intelligence from psychological tests, introduced through Lewis Terman's Stanford revision and scaled so scores average 100.

Intension

Intension, also called intensionality, is the sense or internal content of a term, as opposed to its extension, the range of things the term applies to.

Intention-to-treat analysis

Intention-to-treat analysis is a method for analyzing randomized controlled trials in which every participant is analyzed in the group they were randomized to, regardless of treatment received.

Inter-universal Teichmüller theory

Inter-universal Teichmüller theory (IUT) is a mathematical framework developed by Shinichi Mochizuki at Kyoto University and released in 2012, claiming a proof of the abc conjecture that remains disputed.

Interaction (statistics)

In statistics, an interaction, also called an interaction effect, occurs when the effect of one variable on an outcome depends on the level of another.