6,052 articles
Roth's theorem on arithmetic progressions
Roth's theorem on arithmetic progressions is a 1953 result of Klaus Roth that any set of integers with positive density contains a three-term arithmetic progression.
Rough path
A rough path is a continuous but irregular path, such as Brownian motion, enriched with the iterated integrals needed to solve differential equations, introduced by Terry Lyons in the 1990s.
Rough path theory
Rough path theory is a branch of analysis, introduced by Terry Lyons in 1998, that studies differential equations driven by irregular signals too rough for classical calculus.
Round-off error
Round-off error is the difference between an exact mathematical result and its finite-precision computed form; small errors can accumulate, and cancellation is a principal hazard.
Rounding
Rounding is the replacement of a number with a nearby value that has a shorter, simpler representation, such as an integer or fewer decimal digits, following a rounding rule.
Routh–Hurwitz stability criterion
The Routh–Hurwitz stability criterion, also known as the Routh stability criterion, is a mathematical test that determines whether all roots of a real-coefficient polynomial have negative real parts.
Row and column spaces
The row and column spaces of a matrix are the subspaces spanned by its rows and by its columns, also called the range of a matrix.
Row echelon form
Row echelon form is a staircase matrix shape produced by Gaussian elimination, used to solve systems of linear equations and to read off a matrix's rank.
Royal Statistical Society
The Royal Statistical Society is a British learned society and professional body for statistics, founded in London in 1834 as the Statistical Society of London.
RSA Factoring Challenge
The RSA Factoring Challenge, also known as the RSA Challenge, was a competition run by RSA Laboratories from 1991 to 2007 offering cash prizes for factoring large numbers.
RSA numbers
RSA numbers: large semiprimes (RSA-100 to RSA-2048) published by RSA Laboratories' 1991–2007 Factoring Challenge for cash prizes up to $200,000; factored via GNFS up to RSA-250 (2020), with RSA-896 and above unfactored.
RStudio
RStudio is an integrated development environment for the R programming language, developed by Posit and available as a desktop application or as a server version reached through a web browser.
Rubik's Cube group
The Rubik's Cube group, also called the Rubik group, is the mathematical group of all legal positions of the Rubik's Cube, with about 43 quintillion elements.
Rubin causal model
The Rubin causal model, also called the potential outcomes framework or Neyman–Rubin causal model, defines causal effects as contrasts between potential outcomes, only one of which is observed per unit.
Rule 110
Rule 110 is an elementary cellular automaton, one of 256 rules numbered by Stephen Wolfram in 1983, proved computationally universal by Matthew Cook in 2004.
Rule 30
Rule 30 is a chaotic elementary cellular automaton introduced by Stephen Wolfram in 1983, named for its Wolfram code number and used as a random number generator in the Wolfram Language.
Rule of division (combinatorics)
The rule of division, also called the division principle, is a combinatorics counting rule: count an over-counted collection, then divide by the number of times each object was counted.
Rule of inference
A rule of inference, also called an inference rule, is a syntactic schema in logic that licenses a proof step from premises to a conclusion.
Ruled surface
A ruled surface is a surface swept out by a moving straight line, so a straight line lies on it through its points; examples include the plane, cone, and helicoid.
Rumor spreading model
A rumor spreading model is a mathematical model, adapted from epidemic theory, describing how rumors and misinformation spread through a population, with individuals classed as ignorants, spreaders, and stiflers.
Runge–Kutta methods
Runge–Kutta methods are one-step numerical algorithms for solving ordinary differential equations, introduced by Carl Runge in 1895 and shaped into a general family by Wilhelm Kutta in 1901.
Runge–Kutta–Fehlberg method
The Runge–Kutta–Fehlberg method is an adaptive-step numerical method for ordinary differential equations, introduced by E. Fehlberg in 1968; its best-known instance, combining fourth- and fifth-order formulas, is RKF45.
Runs test
The runs test, also called the Wald–Wolfowitz runs test, is a non-parametric statistical test that checks whether a two-valued sequence was produced in random order, comparing observed runs with the expected count.
Ruslan Stratonovich (Руслан Леонтьевич Стратонович)
Ruslan Stratonovich (Руслан Леонтьевич Стратонович), born in 1930, was a Soviet physicist and mathematician at Lomonosov Moscow State University known for the Stratonovich integral and nonlinear filtering.
Russell's paradox
Russell's paradox is a contradiction in naive set theory, found by Bertrand Russell around 1901, concerning the set of all sets that are not members of themselves.
S-construction
The Waldhausen S-construction is a simplicial construction in algebraic K-theory that Waldhausen introduced in 1985, generalizing Quillen's Q-construction and producing the Waldhausen K-theory spectrum of a Waldhausen category.
S-estimator
The S-estimator is a robust regression estimator introduced by Peter Rousseeuw and Victor Yohai in 1984. It minimizes a robust measure of residual scale, withstanding up to 50% data contamination.
S-procedure
The S-procedure is a control theory device converting quadratic implications into linear matrix inequality conditions on multipliers, sufficient in general and lossless for a single constraint.
S5 (modal logic)
S5 is a system of modal logic, introduced by Lewis and Langford in 1932 and commonly used as the logic of necessity and of knowledge.
Sacks splitting theorem
The Sacks splitting theorem is a 1963 result in computability theory: every noncomputable c.e. set splits into two disjoint c.e. sets, each of low degree.