Mathematics and statistics

Actual and potential infinity

Actual and potential infinity are two conceptions of the infinite: an unending process that stays finite, versus a completed totality, a distinction Aristotle drew and Cantor made mathematical.

Actuarial notation, formally the International Actuarial Notation, is the standardized symbol system used in actuarial science to write quantities involving interest, mortality, life insurance, annuities, and premiums.

Actuarial science

Actuarial science, also called actuarial mathematics, is the discipline applying mathematics, statistics, and financial theory to the financial consequences of risk and uncertainty, principally death, illness, and property loss in insurance.

Acute and obtuse triangles

An acute triangle has all three interior angles less than 90 degrees, while an obtuse triangle has exactly one angle greater than 90 degrees; both are oblique triangles.

Acyclic orientation

An acyclic orientation of a graph is an assignment of a direction to each edge with no directed cycle, making the result a DAG; counting them is #P-complete.

Adaptive design

Adaptive design is a clinical trial design permitting prospectively planned modifications, like altering sample size or dropping treatment arms, based on accumulating data from subjects in the trial.

Adaptive finite element method

The adaptive finite element method (AFEM) solves partial differential equations by repeatedly refining the finite element mesh where the solution is least accurate, guided by computable error estimates.

Adaptive importance sampling

Adaptive importance sampling (AIS) is a Monte Carlo technique that repeatedly adjusts the proposal distribution using previous samples, widely used in rare-event simulation and Bayesian computation.

Adaptive logic

An adaptive logic is a formal logical system that adapts its consequence relation to a premise set, treating formulas as abnormal unless the premises force otherwise; it was created by Diderik Batens.

Adaptive neuro fuzzy inference system

The adaptive neuro fuzzy inference system (ANFIS), introduced by Jyh-Shing Jang in 1993, is a Sugeno fuzzy inference system whose rules and membership functions are tuned from data by neural learning.

Adaptive quadrature

Adaptive quadrature is a numerical integration method that computes a definite integral to a requested accuracy by recursively subdividing the domain where the integrand varies most.

Adaptive sampling

Adaptive sampling is a family of survey designs in which the choice of sampling units depends on data already collected, used mainly for rare and clustered populations.

Adder (electronics)

An adder, also known as a binary adder, is a digital logic circuit that adds numbers, typically in binary, serving as a building block of processors and ALUs.

Addition

Addition is the basic arithmetic operation combining two summands into a sum, written a + b; it is commutative and associative, with subtraction as its inverse.

Addition-chain exponentiation

Addition-chain exponentiation is a method for computing a power of a group element using an addition chain for the exponent, with one multiplication per step, minimizing multiplications in cryptography.

Additive basis

An additive basis is a set of integers from which every integer can be written as a sum of a bounded number of elements, studied in additive number theory.

Additive category

An additive category is a category in which morphisms between any two objects form abelian groups and finite direct sums exist, the setting for algebraic K-theory and abelian categories.

Additive combinatorics

Additive combinatorics, also called arithmetic combinatorics, is a branch of mathematics studying combinatorial properties of algebraic objects such as Abelian groups, rings, and fields, centered on sumsets and small doubling.

Additive function

An additive function, or additive arithmetic function, is an arithmetic function satisfying f(mn) = f(m) + f(n) for relatively prime integers m and n; log n is completely additive.

Additive hazards model

The additive hazards model is a survival analysis regression model in which the hazard is the sum of a baseline hazard and covariate terms, so coefficients are hazard differences.

Additive inverse

The additive inverse, also called the opposite number, of a is −a, the number added to a to give 0; subtraction is addition of the inverse.

Additive model

The Additive model is a regression technique where the effect of each predictor is the sum of its separate contributions. It is a core structure of Generalized Additive Models (GAMs).

Additive regression

Additive regression is a nonparametric regression method that models a response as a sum of smooth functions of individual predictors, keeping linear-model interpretability while learning curved relationships.

Additive smoothing

Additive smoothing, or Laplace and Lidstone smoothing, adds a small constant α to every count so unseen categories get nonzero probability in naive Bayes and language models.

Address-based sampling

Address-based sampling (ABS) is a survey sampling method that draws probability samples of households from postal address databases, most often the USPS Computerized Delivery Sequence file, and recruits them by mail.

Adele ring

The adele ring, or ring of adeles, is the locally compact topological ring built from all completions of a global field, central to class field theory.

Adjoint functors

Adjoint functors, also called an adjoint situation, are a pair of functors related by a natural bijection of morphisms, introduced by Daniel M. Kan in 1958.

Adjoint method

The adjoint method computes the gradient of a scalar objective with respect to many parameters via one adjoint solve, costing 2 to 5 times one objective evaluation; in neural networks it is known as backpropagation.

Adjoint representation

The adjoint representation is the canonical representation of a Lie algebra on itself, with each element acting as the bracket map, and it encodes the Killing form and root system.