6,052 articles
Regular polygon
A regular polygon, also called a regular 2-polytope, is a plane polygon with all sides and all interior angles equal, one existing for every side count from 3 up.
Regular semigroup
A regular semigroup is a semigroup in which every element a has an inverse b satisfying a = aba, including groups, inverse semigroups, and matrix semigroups.
Regular sequence
A regular sequence is a sequence of ring elements where each is a nonzerodivisor on the module left by the earlier ones, used to define depth.
Regular space
In topology, a regular space is one where each point and closed set not containing it lie in disjoint open sets, a separation axiom between Hausdorff and normality.
Regular tetrahedron
A regular tetrahedron is the simplest of the five Platonic solids, with four equilateral triangular faces, four vertices, and six edges, described by the Schläfli symbol {3,3}.
Regular variation
Regular variation is a property of measurable functions describing power-law asymptotic behavior, introduced by Jovan Karamata in 1930 and standard in probability and extreme value theory.
Regularization (mathematics)
Regularization in mathematics is the construction of stable approximate solutions to ill-posed problems by adding constraints, introduced by Tikhonov in 1963 and central to ridge regression and the lasso.
Regularized regression
Regularized regression adds a penalty term to least-squares fitting, shrinking coefficients toward zero to lower prediction error; ridge and the lasso are the canonical cases.
Regulation (EC) No 223/2009 on European statistics
Regulation (EC) No 223/2009 is the EU regulation establishing the legal framework for developing, producing, and disseminating European statistics, in force since 2009 and amended in 2024.
Reidemeister move
A Reidemeister move is one of three local changes to a knot diagram that do not change the knot, proved complete by Kurt Reidemeister in 1926.
Relation algebra
Relation algebra is an algebraic structure whose elements represent binary relations, equipped with Boolean operations, composition, and converse; Tarski axiomatized it in 1941, building on De Morgan, Peirce, and Schröder.
Relative consistency
Relative consistency is a property of formal theories: a theory S is consistent relative to T when Con(T) implies Con(S), since strong theories like ZF cannot prove their own consistency.
Relevance logic
Relevance logic, also known as relevant logic, is a family of non-classical logics developed to avoid the paradoxes of material and strict implication by requiring content connection.
Relevant type theory
Relevant type theory is the substructural type system with exchange and contraction but no weakening, so every variable is used at least once; it corresponds to relevant logic and the λI-calculus.
Reliability engineering
Reliability engineering, also called systems reliability, is a branch of systems engineering that ensures products perform their intended functions without failure, using probability, statistics, and testing across the product lifecycle.
Remainder
A remainder is the integer left over when one integer is divided by another and only whole multiples are subtracted; dividing 14 by 3 leaves a remainder of 2.
Renewal process
A renewal process is a stochastic point process in which interarrival times between successive events, called renewals, are independent and identically distributed, so the process restarts at each event.
Renewal theory
Renewal theory is the branch of probability theory that studies renewal processes, counting events such as failures and replacements, with applications in reliability, queueing, and epidemiology.
Repeated measures ANOVA
Repeated measures ANOVA is a statistical method testing whether means of several measurements from the same subjects differ across time points or conditions, using fewer participants than between-subject designs.
Repeated random subsampling validation
Repeated random subsampling validation, also known as Monte Carlo cross-validation or repeated holdout, is a model-validation method that averages test errors over many random train/test splits.
Repeating decimal
A repeating decimal, or recurring decimal, is a decimal in which a digit or block of digits repeats endlessly; it is exactly equivalent to the number being rational.
Reporting guidelines for medical research
Reporting guidelines for medical research are checklists and flow diagrams, including CONSORT, STROBE, and PRISMA, that specify the minimum items a study report should contain.
Representation ring
The representation ring R(G) of a group is the Grothendieck ring of its finite-dimensional representations, with addition from direct sums and multiplication from tensor products.
Representation theory
Representation theory, also called mathematical representation theory, is the branch of mathematics that studies abstract algebraic structures, chiefly groups, by representing their elements as linear transformations of vector spaces.
Representation theory of finite groups
The representation theory of finite groups studies how finite groups act on vector spaces, pioneered in the late 1800s by Frobenius, Schur, and Burnside, with Maschke's theorem its central structure.
Representation theory of Kac–Moody and affine algebras
The representation theory of Kac–Moody and affine algebras studies how infinite-dimensional Lie algebras act on vector spaces; for affine algebras, integrable representations carry a level, and the Weyl–Kac character formula yields number-theoretic identities.
Representation theory of semisimple Lie algebras
The representation theory of semisimple Lie algebras, or Cartan–Weyl theory, classifies how semisimple Lie algebras act linearly on vector spaces, with every irreducible determined by its highest weight.
Representation theory of SL2(R)
The representation theory of SL2(R), the non-compact simple Lie group of 2 × 2 real matrices with determinant 1, studies its unitary representations, classified by Bargmann in 1947 into principal, complementary, and discrete series.
Representation theory of SU(2)
The representation theory of SU(2) classifies how the special unitary group SU(2) acts on vector spaces, with irreducibles labeled by spin and dimension 2s + 1.
Representation theory of the Galilean group
The classification of how the Galilei group, the nonrelativistic space-time symmetry group, acts on quantum systems; its ray representations, classified by Bargmann in 1954, carry mass as a central charge.