 Real Functions  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to real functions studied in calculus classes; the focus here is on their derivatives and integrals, and general inequalities. This category includes familiar functions such as rational
functions. History;
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 A Really Friendly Guide to Wavelets  C. Valens
A tutorial in wavelet transforms and their applications to signal theory and image compression, aimed at engineers. The tutorial may be read online, or downloaded as a PDF or zipped PostScript file.
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 Realtime Fourier synthesis  Sound generation  Erich Neuwirth
An Excel application that will allow you to synthesize sounds. Mathematically speaking the sliders control the amplitudes of the overtones of the base frequency. Excel workbooks for different versions of Excel to download for Microsoft Windows. Realtime
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 The Real Y2K Problem (Math Chat)  Frank Morgan, MAA Online
Solution to the challenge: Every year in the millennium from 2000 to 2999 can be represented as the sum of consecutive integers, except one year. Which year cannot be represented as the sum of consecutive integers? New challenge: Where do you think you
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 Recherche dans MATHS France  Académie de Toulouse
Un moteur de recherche qui scanne tous les sites académiques en mathématiques.
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 Reciprocity Laws  Franz Lemmermeyer
Reciprocity Laws. From Euler to Eisenstein has just appeared in SpringerVerlag Heidelberg. It is an updated version of Chapters 1  11 as they used to be available at this site; the table of contents with ps and pdf files of Chapter 11 (corrected version)
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 Recognizing Numerical Constants (Organic Mathematics Proceedings)  David H. Bailey, Simon Plouffe
Article and presentation. Abstract: The advent of inexpensive, highperformance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining,
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 Recommended Mathematics Literature  International Mathematics Olympiad (IMO)
A page of readings recommended by the International Mathematics Olympiad in association with Amazon.com Books. Major sections include: Problem Solving; Collections of Mathematical (Competition) Problems; Anthologies and Surveys; Number Theory; Analysis;
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 The rec.puzzles Archive
The index of the rec.puzzles archive. Puzzles are categorized by subject area and include solutions compiled from various sources and supposed to be definitive. Subjects include: analysis, arithmetic, combinatorics, competition, decision, geometry, group,
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 The rec.puzzles Archive  Massachusetts Institute of Technology (M.I.T.)
A list of puzzles, categorized by subject area, from the newsgroup rec.puzzles. Puzzles include solutions compiled from various sources, supposed to be definitive. Subjects include analysis, arithmetic, combinatorics, competition, decision, geometry,
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 rec.puzzles FAQs by Newsgroup  Dept. of Computer Science, Universiteit Utrecht
Information on the following topics: crosswords, analysis, arithmetic, combinatorics, competition, cryptology, decision, geometry, group, induction, Instructions, language, logic, physics, Pickover (Cliff), probability, reallife, references, series,
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 Recreational Mathematics  David Eppstein, Theory Group, ICS, UC Irvine
Some Web resources for recreational math, including links to Eppstein's pages own (Number Theory, Combinatorial Game Theory, and The Geometry Junkyard) and to pages by others.
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 Recreational Mathematics  MAA Online
From the Mathematical Association of America's Basic Library List  a bibliography of articles (in print, not on the Web) on Recreational Mathematics: Games and Puzzles; Puzzle Collections; Contests and Problems; Martin Gardner; Miscellany.
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 Recreational Mathematics Topics  Steven Dutch; University of Wisconsin  Green Bay
Contents: Symmetry, Crystals, Polyhedra and Tilings: an extensive, illustrated collection including reflectional and rotational symmetry; repeating patterns in two and three dimensions; building crystal forms with unit cells; regular, Archimedean, radial,
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 Rectilinear Geometry (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric problems defined on squares and rectangles, higher dimensional boxes, cubes, and hypercubes, right triangles and other rightangled figures, and "taxicab geometry" in which distances are measured
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 Recursion in Space  21 Isometric Models  Ernest V. Miliauskas
Mathematical constructions, subassemblies or subsets of an infinite set, presented in a slide show that demonstrates the author's interest in symmetric threedimensional forms. From chalk talks in advanced spacial studies given at Ryerson University
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 Recursos de Matemáticas para 2º de Bachillerato y 1º de Carrera de Ciencias  Matemáticas de Bachiller
In Spanish: Libros que puedes hojear; videos que puedes ver introducción al Álgebra de lo Lineal, introducción al Cálculo Diferencial, introducción al Cálculo Integral, ejercicios de examen de Selectividad, Know How; Detector de Pardillos Matemáticos;
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 Recycling Topology  Ivars Peterson (MathLand)
It's hard to miss the triangle of three bent arrows that signifies recycling. It appears in newspapers and magazines and on bottles, envelopes, cardboard cartons, and other containers. But have you noticed that there are two versions of this ubiquitous
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 Redecorator Fractal Wallpaper Manager  Seraline P/L, Sydney, Australia.
A wallpaper manager, or randomizer, and image creator for Windows 95/98/NT/2000. Redecorator can change your desktop wallpaper as often as you like, creating seamless tiles and fractals.
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 The REDUCE Computer Algebra System  Anthony C. Hearn
An interactive program designed for general algebraic computations of interest to mathematicians, scientists and engineers. Capabilities include: expansion and ordering of polynomials and rational functions; substitutions and pattern matching; automatic
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 The REDUCE Computer Algebra System  Anthony C. Hearn; RAND
An interactive program designed for general algebraic computations of interest to mathematicians, scientists and engineers. Its capabilities include:
expansion and ordering of polynomials and rational functions; substitutions and pattern matching in
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 Reference Notes  Department of Mathematics, Cal. State U. San Bernardino (CSUSB)
Notes on set theory, symbolic logic, methods of proof, basic proofs, functions, relations, binary operations, and groups. Also, Math Tools for practicing modular arithmetic and truth tables, or for solving Diophantine equations. Search the Notes, or scan
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 Reflections on Deep Blue  Keith Devlin (Devlin's Angle)
We generally assume that the ability to play a good game of chess requires intelligence when it comes to people. Why not for chessplaying machines as well? Well, here is one argument that shows that things are not so simple. One aspect of human intelligence,
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 Reform Calculus Resources  Harel Barzilai
Many printable activities and worksheets, some with solutions, longterm student projects, capsules and tutorials, and resources for instructors including a sample secondsemester calculus course with inclass groupwork activities, projects, and student
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 Regression Applet  R. Webster West, Dept. of Statistics, Univ. of South Carolina
An applet designed to teach students the effect of leverage points on a regression line. Students may add points to the plot by clicking the mouse button. By adding points far from the existing line, the regression line changes considerably. This is particularly
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 Regression Tools
Online, Flashbased regression tools for linear, logarithmic, exponential, power, polynomial, multiple linear, multiple polynomial, and nonlinear regression.
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 RegressIt  Robert Nau
This free Excel addin macro (xlam) performs multivariate descriptive data analysis, multiple linear regression (with forecasting), and variable transformations. Fitting models with up to 50 variables at one time and up to 32,000 rows of data, RegressIt
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 Regular Graphs  Markus Meringer
Tables of simple connected kregular graphs on n vertices and girth at least g with given parameters n,k,g.
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 Relatively Prime  Samuel Hansen
A series of audio shows "all about the stories behind mathematics," as gathered from interviews with Fields Medalists, composers, "standup mathematicians," and others. Listen to hourlong segments "from the mathematical domain" such as "Chinook," about
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 Relativity and Gravitational Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to relativity and gravitational theory: differential geometry, analysis, and group theory applied to physics on a grand scale or in extreme situations (e.g. black holes and cosmology). History; applications
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 Reliable Expert: Math and Statistics Homework Help
Homework help service: send your question, with a fee offer and deadline, and if Reliable Expert accepts your offer, you'll get your answer when you need it.
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 Religious schools inspire math reasoning  B. Bower  Science News Online
Students at ultraorthodox Jewish schools, who study mainly holy texts, outperform most students at mainstream schools on tests of geometric reasoning, perhaps because of the emphasis on reflection and considering different perspectives.
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 The Remarkable Number 1/89  Robert Miner
An overview of the Fibonacci series, interesting facts about it, and a sketch of the proof of why the decimal expansion of the fraction 1/89 contains all the Fibonacci numbers expressed as a sequence of decimal fractions, a fact discovered by Cody Birsner.
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 Remote Interactive Optimization Testbed (RIOT)  Industrial Engineering and Operations Research, UC Berkeley
Interactive educational and research tools for optimization problems. Applications: Learn about practical applications of optimization technology to Major League baseball, openpit mining, computer network design, and modular parts fixturing. Experiment
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 Repeated Prisoner's Dilemma Applet  Mike Shor
A repeated prisoner's dilemma game in which the user plays for twentyfive
rounds against each of five different (unknown) 'personality types'. Demonstrates the value of cooperation and the ability to take advantage of
some simple rules.
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 Replacing Iowa and New Hampshire (Math Chat)  Frank Morgan, MAA Online
Answer to the challenge: Propose a new system for selecting Presidential candidates. Winning answer by Joe Shipman: a year before the primaries start choose five congressional districts at random to have a primary the last week in
January and five more
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 Representations and Cohomology Preprints  Dave Benson
An alphabetical list of dvi and ps files, by author.
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 The Republic of Mathematics  Gary E. Davis
The Republic of Mathematics™ was founded "to promote happy and productive mathematical experiences for all learners, democratize the learning and teaching of mathematics, and help empower students and teachers in their engagement with mathematics."
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 Resampling Stats
Resampling is a statistical method of drawing repeated samples from the given data to determine the value of a parameter of interest. Resampling Stats is a computer program offered for sale (30day free trial, discount for personal or academic use). The
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 Research and Expository Papers by Charles Wells and others  Charles Wells; Case Western Reserve University
Research and expository publications concerning mathematical writing, such as Communicating Mathematics: Useful Ideas from Computer Science; Varieties of Mathematical Prose; Communicating Logical Reasoning; and Handbook of Mathematical Discourse, which
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 Research Experiences for Undergraduates (REU) Program in Mathematics  Cornell University
During the summers of 1996, 1997, and 1998 undergraduates worked on research projects under the direction of Cornell University Mathematics Department members: Analysis on Fractals; Dynamical Systems.
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 Research Group in Mathematical Inequalities and Applications (RGMIA)  RGMIA and Victoria University, Australia
The Research Group in Mathematical Inequalities and Applications disseminates results via publication (both in print and electronic form) and conferences; creates an awareness of the theory of inequalities and support seminars and visiting academics;
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 Research Group on Graph Theory and Combinatorics  Universitat Politècnica de Catalunya (UPC)
A group of about twentyfive members whose research belongs to the area, developing research projects and/or conducting works directed toward Ph.D. dissertations. Includes a searchable publication database and a page on The (Degree,Diameter) Problem for
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 Research in Math Education  Mathematics Education at The Math Forum
Research into the learning and teaching of mathematics: methods; K12 and college undergraduate education (articles, conference sessions); bibliographies; centers; studies; special interest groups; organizations and journals.
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 Research in Practice  Ben BlumSmith
A "math education research digest" by a former teacher, private tutor, and faculty member of Bard College's Master of Arts in Teaching program who went on to pursue his doctoral degree from the Courant Institute of Mathematical Sciences at New York University.
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 Research Interests  Godfried Toussaint
Links to resources, mainly in computational geometry, e.g., mobility of objects in space, degeneracies, quadrangulations, tomography, triangulation, proximity, facility location, and polygonal approximation.
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 Research Interests  Richard Mollin
Notes reflecting the author's interest in the interrelationships between continued fractions and ideal theory. This paper generalizes some independent seminal results by Chowla and Schinzel, later developed by Friesen.
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 Research in Undergraduate Education  1996 AMS/MAA Joint Meetings  The Math Forum
Listings from the AMSMAA Special Session on Research in Undergraduate Mathematics Education.
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 Research Papers  The Geometry Center
Scientific papers written at the Geometry Center that use the unique aspects of hypertext to present information in a nonlinear fashion. Many include movies or interactive pictures. A Tight Polyhedral Immersion of the Real Projective Plane with one Handle
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 Research  Peter Alfeld; University of Utah
Researchrelated materials: An interactive applet that lets you explore the BernsteinBézier form of a bivariate polynomial; recent papers, complete bibliography, recent talks, computer graphics (illustrating various mathematical concepts: US Global Positioning
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