Mathematics and statistics

Product topology

The product topology, also called the Tychonoff topology, is the standard topology on a Cartesian product of topological spaces, the smallest one making every coordinate projection continuous.

Production part approval process

The production part approval process (PPAP) is an AIAG-defined evidence package by which a supplier demonstrates it can consistently produce parts meeting all design specifications at production rate.

Profile likelihood

The profile likelihood is a function derived from a multi-parameter likelihood by fixing the parameter of interest and maximizing over nuisance parameters, supporting confidence intervals and hypothesis tests.

Profile monitoring

Profile monitoring is a statistical process control method in which process quality is characterized by the relationship between a response variable and explanatory variables, observed as a curve at each sampling stage.

Profinite group

A profinite group is a topological group that is an inverse limit of finite groups, or equivalently a compact, totally disconnected group; Galois groups of infinite extensions are examples.

Profinite integer

A profinite integer is an element of the ring of profinite integers, the inverse limit of the residue rings of the integers modulo every positive integer.

Program evaluation

Program evaluation is a systematic process of collecting and analyzing data about programs, policies, and organizations to assess their effectiveness and efficiency, using designs such as randomized experiments.

Progression-free survival

Progression-free survival (PFS) is a clinical trial endpoint defined as the time from the start of treatment until disease progression or death, whichever comes first.

Progressive enlargement

Progressive enlargement is a construction in stochastic calculus that enlarges a reference filtration so a random time becomes a stopping time, developed from the late 1970s.

Projection (linear algebra)

A projection in linear algebra is an idempotent linear operator, meaning applying it twice gives the same result as once, sending every vector to a chosen subspace.

Projection lattice and comparison theory

The projection lattice of a von Neumann algebra is its complete lattice of projections, ordered by positivity, with Murray–von Neumann equivalence and comparison theory deciding when projections are equivalent.

Projection pursuit

Projection pursuit is a statistical technique that searches one- and two-dimensional projections of high-dimensional data for the most interesting views, making clusters, holes, and nonlinearity visible.

Projection pursuit regression

Projection pursuit regression (PPR) is a nonparametric regression method introduced by Jerome Friedman and Werner Stuetzle in 1981, modeling a response as a sum of smooth functions of linear predictor combinations.

Projective cover

A projective cover of a module M is a surjection from a projective module with superfluous kernel; unique when it exists, though not every module has one.

Projective dimension

Projective dimension is an invariant of a module over a ring, the minimum length of a projective resolution, measuring how far the module is from being projective.

Projective duality

Projective duality is a symmetry of projective geometry in which the roles of points and lines can be exchanged, so the dual of any true theorem is also true.

Projective geometry

Projective geometry is the branch of mathematics studying properties of figures that survive projection, keeping incidence and the cross-ratio while discarding distance, angle, and parallelism; it underlies perspective and computer vision.

Projective hierarchy

The projective hierarchy is a classification of sets of real numbers, built from the analytic sets by complementation and projection, introduced by Lusin and Sierpiński in 1925.

Projective line

The projective line is the one-dimensional projective space over a field K, formed by adding a single point at infinity to the ordinary affine line.

Projective module

A projective module, also called a finitely generated projective module in the finite case, is a module over a ring that behaves like a free module, characterized by the lifting property for homomorphisms.

Projective plane

A projective plane is a geometric structure of points and lines in which every pair of lines meets, achieved by adding points at infinity to parallel lines.

Projective representation

A projective representation of a group assigns operators to group elements that multiply only up to a scalar factor, classified by the second group cohomology H²(G, U(1)).

Projective resolution

A projective resolution of a module is an exact sequence of projective modules ending in it, the standard tool for computing derived functors such as Ext and Tor.

Projective space

Projective space, written KP^n, is the set of lines through the origin of a vector space, adding points at infinity so any two lines meet in one point.

Projective variety

A projective variety is a subset of projective space cut out by homogeneous polynomials, one of the two basic objects of classical algebraic geometry alongside affine varieties.

Prokhorov's theorem

Prokhorov's theorem is a result in probability theory stating that a family of probability measures on a Polish space is tight if and only if every sequence has a weakly convergent subsequence.

Promax rotation

Promax rotation is a two-stage oblique factor rotation in exploratory factor analysis, proposed by Hendrickson and White in 1964 as a fast alternative to analytic methods.

PROMETHEE

PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation) is an outranking method of multi-criteria decision analysis introduced in 1985, ranking alternatives by pairwise comparisons over several criteria.

Pronic number

A pronic number, also known as an oblong or heteromecic number, is a number that is the product of two consecutive integers; the sequence begins 0, 2, 6, 12, 20.