Mathematics and statistics

Quadratic regression

Quadratic regression is a statistical method that fits a second-degree polynomial curve to data, estimating U-shaped or inverted-U relationships between one predictor and an outcome.

Quadratic residue, also called quadratic residuosity, describes an integer a for which x² ≡ a (mod m) is solvable; the concept underlies quadratic reciprocity and cryptosystems like Goldwasser–Micali.

Quadratic sieve

The quadratic sieve is a general-purpose integer factorization algorithm invented by Carl Pomerance in 1981, fastest known until 1996 and still used below roughly 100 digits.

Quadratic variation

Quadratic variation, also called the bracket or quadratic-variation process, measures a stochastic process's accumulated squared fluctuations; for Brownian motion it equals t, which produces the second-order term in Itô's formula.

Quadrature rule

A quadrature rule is a numerical method that approximates a definite integral of a function by a weighted sum of its values at selected points, or nodes.

Quadric

A quadric, also known as a quadric surface or quadric hypersurface, is a geometric set defined by a degree-two polynomial equation; ellipsoids, hyperboloids, cones, cylinders, and paraboloids are familiar quadric surfaces.

Quadrilateral

A quadrilateral is a polygon with four sides and four vertices, such as a square, rectangle, parallelogram, or trapezoid, with interior angles summing to 360°.

Quadrivium

The quadrivium is the group of four mathematical arts of the classical seven liberal arts: arithmetic, geometry, music, and astronomy. It followed the trivium in medieval university education.

Quality control

Quality control (QC), also known as total quality control, is the set of operational techniques, such as inspection, testing, and statistical monitoring, used to fulfill quality requirements.

Quality function deployment

Quality function deployment, also known as customer-driven engineering, is a structured method translating customer needs into technical requirements, developed in Japan in the late 1960s.

Quality management

Quality management is the coordinated set of organizational activities used to plan, control, assure, and improve product quality, combining statistical process control, continual improvement, and standards like ISO 9001.

Quandle

A quandle is an algebraic structure, introduced into knot theory independently by David Joyce and Sergei Matveev in 1982, whose axioms capture conjugation in a group.

Quantale

A quantale is a complete lattice equipped with an associative binary operation distributing over arbitrary joins in each variable, introduced by C. J. Mulvey to extend locales non-commutatively for quantum logic.

Quantified modal logic

Quantified modal logic (QML) combines a propositional modal logic with first-order quantifiers; the Barcan Formula is valid under constant domains but fails under the varying domains Kripke introduced in 1963.

Quantifier (logic)

A quantifier, also called a logical quantifier, is an operator in predicate logic, such as "for all" or "there exists", expressing how many objects satisfy a formula.

Quantifier elimination

Quantifier elimination is a property of first-order theories in model theory: every formula is equivalent, over the theory, to one with no quantifiers, which can yield decidability.

Quantile

A quantile is a value below which a specified fraction of a probability distribution or data sample falls; the median is the 0.5 quantile, and quartiles, deciles, and percentiles are other named cases.

Quantile function

The quantile function of a random variable, also called the inverse cumulative distribution function, maps a probability p to the smallest value x where the CDF reaches p, the basis of inverse transform sampling.

Quantile mapping

Quantile mapping is a statistical bias correction method that adjusts model or sensor data so its quantiles match an observed reference distribution, widely used in hydrologic modeling.

Quantity

A quantity is an attribute of a phenomenon, body, or substance that can be determined quantitatively, such as length, mass, or electric charge, with values expressed as a number and a unit.

Quantized enveloping algebra

A quantized enveloping algebra is a one-parameter Hopf algebra deformation of the universal enveloping algebra of a semisimple Lie algebra, introduced by Drinfeld and Jimbo around 1985.

Quantum affine algebra

A quantum affine algebra, or affine quantum group, is a Hopf algebra that q-deforms the enveloping algebra of an affine Kac–Moody algebra, introduced by Drinfeld and Jimbo around 1985.

Quantum cohomology

Quantum cohomology is a deformation of the ordinary cohomology ring of a manifold in which the product counts holomorphic curves, introduced in the early 1990s from quantum string theory.

Quantum group

A quantum group is a noncommutative Hopf algebra that deforms the structure of a group or Lie algebra, introduced by Drinfeld and Jimbo in the 1980s.

Quantum plane

The quantum plane, also called the Manin plane, is a noncommutative algebra generated by x and y with xy = qyx, introduced by Yuri Manin in 1988.

Quantum trace

The quantum trace is a categorical generalization of the trace of a linear map, defined in ribbon categories and used to build knot invariants from braid representations.

Quartic function

A quartic function is a polynomial function of degree four, solved generally by Lodovico Ferrari's method in 1540. It is the highest degree solvable by radicals.

Quartile

A quartile is one of three cut points dividing ordered data into four equal groups: Q1 at the 25th percentile, Q2 the median, and Q3 the 75th.

Quasi-isometry

A quasi-isometry is a map between metric spaces that preserves distances up to a multiplicative factor and additive constant, the central notion of geometric group theory.