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Irreducible polynomial
An irreducible polynomial is a nonconstant polynomial that cannot be written as a product of two lower-degree polynomials, the polynomial analog of a prime number, with irreducibility depending on the coefficient field.
Irreducible representation
An irreducible representation, or irrep, is a representation of a group or algebra with no smaller nontrivial representation; irreps are the building blocks of representation theory.
Isabelle (proof assistant)
Isabelle is an interactive theorem prover, introduced by Lawrence C. Paulson at Cambridge in 1986 and developed with Tobias Nipkow in Munich; its main instance, Isabelle/HOL, uses classical higher-order logic.
Ishikawa diagram
The Ishikawa diagram, also called the fishbone diagram, is a cause-and-effect tool developed by Japanese quality specialist Kaoru Ishikawa to organize the possible root causes of a quality problem.
Isidore of Miletus
Isidore of Miletus was a Byzantine mathematician and architect who, with Anthemius of Tralles, designed the original Hagia Sophia in Constantinople for Justinian I, built 532 to 537.
Islamic geometric patterns
Islamic geometric patterns, also called Islamic geometric designs, are a decorative idiom of Islamic art of interlocking stars and polygons adorning mosques, palaces, and ceramics.
Isolated point
An isolated point is a point of a subset of a topological space that has a neighborhood containing no other point of the subset; a space of only isolated points is discrete.
Isolated singularity
An isolated singularity of a complex function is a point where the function fails to be analytic yet stays analytic on a punctured neighborhood around it.
Isometric projection
Isometric projection, also called isometric view or isometric drawing, is an axonometric method for showing a three-dimensional object in two dimensions, with axes equally foreshortened at 120 degrees.
Isometry
An isometry, also called an isometric transformation, is a map between metric spaces that preserves distances exactly, serving as the notion of sameness in Euclidean and Riemannian geometry and tracing to Klein's 1872 Erlangen program.
Isomorphism
Isomorphism is a correspondence pairing elements of two mathematical objects so every relation and operation is preserved, treating isomorphic objects as the same structure with different labels.
Isomorphism theorems
The isomorphism theorems, also known as Noether's isomorphism theorems, are three or four results in abstract algebra describing how quotients and images of algebraic structures relate.
Isoperimetric inequality
The isoperimetric inequality states that among all closed curves of a given length, the circle encloses the largest area, in the form L² ≥ 4πA.
Isosceles trapezoid
An isosceles trapezoid, also called an isosceles trapezium, is a trapezoid whose non-parallel sides are equal in length, giving it equal base angles, congruent diagonals, and one line of symmetry.
Isosceles triangle
An isosceles triangle is a triangle with two equal sides; its base angles are equal, the theorem proved as Euclid's Proposition I.5, known as the Pons Asinorum.
Isotonic regression
Isotonic regression is a nonparametric method that fits a nondecreasing function to ordered data by minimizing weighted squared error, used for probability calibration and dose-response estimation.
Istituto Nazionale di Statistica
The Istituto Nazionale di Statistica (Istat), Italy's National Institute of Statistics, is a public research institute founded in 1926 that produces the country's official statistics from Rome.
Iterated function system
An iterated function system is a finite collection of contractive maps whose iteration converges to a unique compact attractor, typically a fractal, used in image compression.
Iteration
Iteration is the repeated application of a function or procedure that turns each value into the next, used to solve equations and prove solutions exist.
Iterative deepening depth-first search
Iterative deepening depth-first search (IDDFS), also called iterative deepening search, is a tree-search algorithm that repeatedly runs depth-limited depth-first searches with increasing depth limits, finding shortest solutions.
Iterative method
An iterative method, also called an iteration scheme or method of successive approximation, computes successively better approximations to a solution by refining an initial guess at each step.
Iteratively reweighted least squares
Iteratively reweighted least squares (IRLS) is an iterative estimation method that solves a sequence of weighted least squares problems, updating the weights each iteration, to fit robust regression M-estimators.
Itô calculus
Itô calculus, also called Ito stochastic calculus, is the branch of mathematics defining integration with respect to random processes like Brownian motion, created by Kiyosi Itô in 1942.
Itô's lemma
Itô's lemma, also called Itô's formula, is the chain rule of stochastic calculus, proved by Kiyosi Itô and central to the Black–Scholes option pricing framework.
Ivan Fesenko
Ivan Fesenko is a Russian-born mathematician in number theory, known for class field theory and adelic analysis, a distinguished professor at Westlake University since 2023.
Iwasawa theory
Iwasawa theory is a branch of number theory, founded by Kenkichi Iwasawa in the late 1950s, that studies how class groups grow in infinite towers of number fields.
j-invariant
The j-invariant is a quantity attached to an elliptic curve, taking the same value on two curves exactly when they are isomorphic over an algebraically closed field.
Jaccard index
The Jaccard index, or Jaccard similarity coefficient, measures the overlap of two sets as the size of their intersection divided by the size of their union.
Jack function
The Jack function, also called the Jack polynomial, is a symmetric polynomial depending on a partition and a parameter, introduced by Henry Jack in 1970.
Jackknife resampling
Jackknife resampling, or the jackknife method, is a statistical resampling technique that estimates the bias and variance of an estimator by systematically recomputing it on leave-one-out subsamples.