Mathematics and statistics

Numbering (computability theory)

A numbering in computability theory is a surjective map from the natural numbers onto a countable collection of objects, such as the partial computable functions or the computably enumerable sets.

Numeral system

A numeral system, also called a scale of notation, is a system for representing numbers using digits and rules for combining them, either additively or by place value.

Numerical algebraic geometry

Numerical algebraic geometry (NAG) is a tool set for approximating solutions to polynomial equation systems using numerical algorithms, initiated by Andrew Sommese and Charles Wampler.

Numerical analysis, also called numerical computation or numerical mathematics, is the study of methods used to obtain approximate solutions to mathematical problems, together with their analysis for accuracy, stability, and speed.

Numerical continuation

Numerical continuation, also known as homotopy continuation, is a family of numerical methods that traces solution curves of parameterized nonlinear equations as a parameter varies, forming the basis of bifurcation analysis.

Numerical integration

Numerical integration, also called numerical quadrature, computes definite integrals approximately when no closed-form antiderivative exists, by summing weighted samples of the integrand at chosen points.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations, also called numerical solutions of ordinary differential equations, are algorithms that approximate solutions step by step, judged by accuracy, stability, and cost.

Numerical stability

Numerical stability is the property of an algorithm whose rounding errors and small input perturbations do not grow unboundedly, central to scientific computing and numerical linear algebra.

NumPy

NumPy, or Numerical Python, is the primary open-source array programming library for Python, first released in 2006 and serving as the foundation of the scientific Python ecosystem.

Nyquist stability criterion

The Nyquist stability criterion is a graphical test that determines whether a closed-loop feedback system is stable by counting encirclements of −1, introduced by Harry Nyquist in 1932.

Nyquist–Shannon sampling theorem

The Nyquist–Shannon sampling theorem, also called the Nyquist theorem, states that a bandlimited signal can be perfectly reconstructed from samples taken at more than twice its highest frequency.

o-minimality

O-minimality is a tameness condition in model theory requiring every definable set to be a finite union of points and intervals, introduced by van den Dries.

Oaxaca–Blinder decomposition

The Oaxaca–Blinder decomposition is a statistical method that splits the mean difference between two groups, such as a wage gap, into explained and unexplained parts, introduced in 1973.

Oblate spheroidal coordinates

Oblate spheroidal coordinates are an orthogonal system of curvilinear coordinates whose constant-coordinate surfaces are oblate spheroids, adapted to flattened bodies like Earth and charged disks.

Oblique projection

Oblique projection, or oblique view, is a parallel projection in technical drawing where the front face is shown true size and depth is drawn at an angle.

Observability

Observability is a property of dynamical systems, introduced by Rudolf Kalman in 1960, stating whether the full internal state can be inferred from measured outputs.

Observational study

An observational study, as defined by William G. Cochran in 1965, investigates cause and effect without assigning exposures, making it possible where randomized trials would be unethical but leaving it vulnerable to bias.

Obstacle problem

The obstacle problem is a constrained variational problem in partial differential equations, modeling an elastic membrane resting on an obstacle, the prototype of free boundary problems.

Obstruction theory

Obstruction theory is a family of methods in algebraic topology, codified by Samuel Eilenberg around 1940, that tests whether a partial map or section can be extended.

Occupancy model

An occupancy model is a hierarchical statistical model used in ecology to estimate the probability that a species occupies a site, while separately estimating detection probability.

Occupancy modeling

Occupancy modeling is a statistical method in ecology that estimates the probability a species occupies a site from detection-nondetection survey data, while correcting for imperfect detection.

Octagon

An octagon is a polygon with eight sides and eight angles; a regular octagon has 135° interior angles and is the shape of the stop sign.

Octahedron

An octahedron, also called a square bipyramid, is a polyhedron with eight triangular faces, six vertices, and 12 edges; the regular form is one of the five Platonic solids.

Octal

Octal, also known as base 8, is the numeral system using the digits 0 through 7, where each digit corresponds to three binary bits, used in Unix file permissions.

Octonion

Octonions, also known as Cayley numbers, form an 8-dimensional normed division algebra over the real numbers, described by John Graves in 1843 and published by Arthur Cayley in 1845.

Octonions

The octonions, also known as Cayley numbers or octaves, are an eight-dimensional number system whose multiplication is neither commutative nor associative, the largest of the four normed division algebras.

Odds

Odds are a way of expressing how likely an event is as a ratio of the chance that it happens to the chance that it does not happen.

Odds ratio

The odds ratio (OR), also called the log odds ratio, is a biostatistical measure of association computed as the ratio of odds of an outcome between exposed and unexposed groups.

Office for National Statistics

The Office for National Statistics (ONS, Swyddfa Ystadegau Gwladol) is the United Kingdom's recognized national statistical institute, producing official statistics on the economy, population, and society.