 The solving of Fermat's Last Theorem  Karl Rubin; Ohio State University Distinguished Lecture
Slides for a talk that tells the story of Fermat's Last Theorem for a general audience, including the history of the problem, the story of Andrew Wiles' solution and the excitement surrounding it, and some of the many ideas used in Wiles' proof.
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 Solving Rubik's Cube  David Lee Winston Miller
A "bestfast" Arity Prolog program and demonstration of an efficient heuristic search method to solve Rubik's Cube. Examine the cube's topography (its flat layout) and "submachines." Documentation includes "Understanding the problem," "Why this approach
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 Solving the Quintic by Iteration [PDF]  Peter Doyle, Curt McMullen
This paper, which appeared in Acta Mathematica, gives explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm
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 Solving the Quintic with Mathematica  Wolfram, Inc.
Solving the Quintic  The impossibility of solving general quintics in radicals, Tschirnhaus's transformation, Klein's approach to the quintic, Solutions based on series, Solutions based on differential equations, Equations of higher degree. Steps to
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 The Soma Cube Puzzle  Modvix
Purchase the Soma Cube. Piet Hein, a Danish poet and inventor, visualized the set of all irregular shapes formed by no more than 4 cubes, each of the same size, and realized that the seven simplest irregular combinations of cubes can form a larger Soma
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 Some disasters attributable to bad numerical computing  Douglas N. Arnold; Institute for Mathematics and its Applications
Real life examples of what can happen when numerical algorithms are not correctly applied: The Patriot Missile failure (rounding errors); The explosion of the Ariane 5 rocket (a simple overflow); The sinking of the Sleipner A offshore platform (inaccurate
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 Some Interesting references about LLL  François Koeune
Papers on the LLL algorithm and its applications, divided into: Understanding LLL; LLL as a Tool; Latticebased Cryptosystems; Refinements and Variants of LLL; and Interesting links.
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 Some Materials for Discrete Mathematics  E. Lee Lady, University of Hawaii
Files in PDF, DVI, and Postscript format. Contents include: an algorithm for solving linear Diophantine equations, the Chinese remainder theorem, mathematical induction and recursive algorithms, Change of base to Cantor representation, Dijkstra's algorithm
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 Some Materials for the Graduate Algebra Course  E. Lee Lady; University of Hawaii
Syllabus, course notes, and various proofs, in PDF, PostScript and dvi format. The course assumes that students know about groups, rings, and vector spaces, and covers all the topics in algebra commonly used by analysts and topologists, such as commutative
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 Some Mathematical Works of the 17th & 18th Centuries  Ian Bruce
This website has a number of books in PDF format translated from Latin, as well as papers by Euler, Bernoulli, etc. The books translated include Briggs' Arithmetica Logarithmica, Trigonometria Britannica, Gregory's Optica Promota, Harriot's Praxis, and
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 Some Planar Isospectral Domains  Buser, Conway, Doyle, Semmler
A paper on isospectral pairs of plane domains, and a particularly simple method of proving isospectrality. One example is a pair of domains that are not only isospectral but homophonic, showing that one really can't hear the shape of a drum. With a gallery
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 Some Problems in Matroid Theory  Thomas Zaslavsky
Sources of problems compiled by Zaslavsky, and problems he's found interesting: Bonin's Projective Bound; Maximum rFlat; Covering And Packing by Flats. For general sources of information on matroid theory, see Matroid Miscellany.
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 Some Problems & Puzzles  Nancy Casey
Problems inspired by math books (Instant insanity; Penrose rhombs) and friends Larry Copes and Mike Fellows (BikePed, Idaho  also known as Muddy City).
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 Some Psychological Aspects of Developing Computer Based Instruction in Undergraduate Advanced Mathematics  Mikhail Bouniaev
A summary of a presentation given at the Joint Mathematics Meetings, January 1013, 1996, Orlando, Florida. The paper deals with research on teaching advanced math using theory of stagebystage development of actions. Since this theory is not very well
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 Some Solid (Threedimensional) Geometrical Facts about the Golden Section  Ron Knott
Phi and threedimensional geometry  Dice Shapes; Coordinates and other statistics of the 5 Platonic Solids; The Greeks and the platonic solids; Quasicrystals and Phi; Footnotes on Plato and Euclid, and on shapes for fair dice.
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 Some Things I've Written  Jennifer Gutbezahl
Research from the author's doctoral studies in social psychology. Gutbezahl's dissertation focused on how attributions for success and failure in mathematics affect how well students do in math class: "How Negative Expectancies and Attitudes Undermine
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 Some Thoughts on Measurement  Harold Brochmann
All measurements inherently have limited precision; it isn't sensible to give credence to measurements if you are dealing with a piece of ordinary paper and an ordinary wooden or plastic ruler, no matter how careful the person measuring has been. This
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 Some (Unsolved) Mathematical Problems  Jörg Winkelmann
A collection of some analysis questions the author encountered in the context of his own research.
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 Some Variations on the Theme of Polyominos  Recmath
Patterns that illustrate how the squares of polyominos are connected to each other. Examples of polyominos with a grid superimposed to illustrate the individual squares; with a line that joins the midpoint of two adjacent square if the squares are connected.
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 Sommer Cube  Michael Sommer
The faces of the modular Sommer Cube (S3) feed into twisted conduits that comprise a threedimensional, tunnelling maze. The website provides example arrangements and construction questions such as "Given that a ball must exit at the lowest S3 level and
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 A Song About Pi  Ivars Peterson (MathTrek)
A short biography of Irving Kaplansky, Director Emeritus of the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA, and his analysis of the structure of complex songs.
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 sortedsums  D. J. Bernstein
A collection of tools for enumerating small solutions to certain types of Diophantine equations. Includes links to the latest published sortedsums package, and to a paper explaining the algorithms used.
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 S.O.S. Mathematics  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
Internet courses/tutorials to help students do homework, prepare for a test, or get ready for a class. The material presented here reviews the most important results, techniques and formulas in college and precollege mathematics. The learning units are
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 The Source of UK Facts and Figures  Government Statistical Service, Office for National Statistics, UK
The information you need to access UK statistics. Links to: The Campion Fellowship in Official Statistics; Population Trends 98  reference and report tables; Quarterly Civil Service Staff in Post; UK in Figures 1999; Scottish Statistics Publications;
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 Source Panel Integrals / Java Matrix Solver  Marc Gerritsma, Jamie Grier
The source panel integrals Javascript can be used to calculate the integrals and the matrix elements of the source panel method (see sec 3.17 of Fundamentals of Aerodynamics, 2nd edition, by J.D. Anderson, jr.). The Java matrix solver can be used to solve
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 Southeast Applied Analysis Center (SAAC)  School of Mathematics, Georgia Tech
A centralized location to coordinate activities in applied analysis in the
Southeastern United States, fostering academic research, applied mathematical research in industrial settings, and educational innovations. The present departmental strengths
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 Southwest Journal of Pure and Applied Mathematics  Ioannis Argyros, EditorinChief
The Southwest Journal of Pure and Applied Mathematics (SWJPAM) is an electronic journal devoted to all aspects of pure and applied mathematics, and related topics. Electronic issues date back to 1995, and are available for download in postscript, compressed
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 Space Science and Engineering Center (SSEC) Visualization Project  Bill Hibbard
The SSEC Visualization Project makes the Vis5D and VisAD systems freely available over the Internet. Vis5D provides interactive visualization of the output of numerical simulations of the Earth's atmosphere and oceans. VisAD enables scientists to interactively
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 SpaceTime  Chris and Stephen DeSalvo
SpaceTime develops mathematics software for personal digital assistants (PDAs) and other mobile devices such as Pocket PCs, Palm Pilots, and smartphones. Play JavaScript and Flash games in the arcade: ArithmeTick, Math Scramble, Math Mountain, Snake,
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 Space Time Travel  Ute Kraus and Corvin Zahn (Theoretische Astrophysik Tübingen)
Black holes and travel at nearly the speed of light: Visualization of the theory of relativity. Online papers, images, movies and paper models. English version of the German site.
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 Spanky Fractal Database  Noel Giffin
A collection of fractals and fractalrelated material for free distribution on the net. Most of the software has been gathered from various ftp sites on the Internet and is freeware or shareware. Contents: An index of Fractal material; General information;
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 Spatialised Prisoner's Dilemma: Evolution Simulator  Wayne Davis
Spatialised version of the Iterated Prisoner's Dilemma game theory that allows the users to set their own strategies and simulate evolution of strategies: Coded in Javascript by Wayne Davis.
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 Speakeasy  Speakeasy Computing Corporation
A userfriendly computational software package that enables novice and
experienced users to solve realworld problems. An intuitive computational language provides a natural way to communicate with your computer.
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 Speaking of Mathematics (Computing Science)  Brian Hayes, American Scientist
An article about AsTeR (Audio System For Technical Readings), a computing system for rendering technical documents in audio.
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 Special Functions  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to special functions, specialized functions beyond the familiar trigonometric or exponential functions. The ones studied (hypergeometric functions, orthogonal polynomials, and so on) arise very naturally
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 Special Functions  D. Lozier; Applied and Computational Math Division, NIST
This area of numerical computation has the property that input to its software is of small dimension, so highaccuracy reference software that produces test data with guaranteed error bounds is feasible. Library developers need illustrations of anomalous
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 Special Functions in WolframAlpha  Michael Trott
Special functions describe a large number of phenomena in mathematical physics and other disciplines. Michael Trott posts here about WolframAlpha's treatment of these functions. In particular, there are some with two forms: a simpler version that makes
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 Special Interest Groups: American Educational Research Association (AERA)  College of Education, Arizona State University
Index and complete list of AERA SIGs, which provide a forum within AERA for the involvement of individuals drawn together by a common interest in a field of study, teaching, or research when the existing divisional structure may not directly facilitate
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 Special Relativity  MacTutor Math History Archives
Linked essay describing the history of special relativity from Newton's laws through Lorentz and Einstein, with 12 references (books/articles).
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 Special Relativity Theory Made Intuitive  Sylvain Poirier
A paper. The author describes it: "Presentation of the deep mathematical concepts of Special Relativity theory, written like a philosophical analysis with few formulas, and based on a transfer of the Euclidean geometry tools and intuition to the pseudoEuclidean
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 Spherical Geometry  Dave Rusin; The Mathematical Atlas
Posts on spherical geometry. Applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; selected topics; other web sites with this focus.
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 Spherical Geometry Demo  John M Sullivan, University of Illinois
An applet demonstrating several features of spherical geometry, among them the parallel transport of tangent vectors, and the fact that the angles of triangles may not sum to 180 degrees.
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 Spidron System  Daniel Erdely
Erdely calls a planar, planefilling object a Spidron. Upon threedimensional deformation subject to specific constraints, the planar system generates a regular, dynamic, geometrical construction. Erdely's experiments have led to the idea of creating
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 SPIMSOW: Swarthmore Summer Project for the Implementation of Mathematical Software on the Web  Bouttenot, Parlikar; Mathematics & Statistics Dept., Swarthmore College & Math Forum
The product of a 1998 summer project investigating current Weboriented mathematical software. The site explores the capabilities of the new Web versions of Mathematica, Maple, and MathView, offering tutorials on configuring the software and creating
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 Spinning to a Rolling Stop  Ivars Peterson (MathTrek)
The underlying mathematics of spinning disks. Spin a coin on a tabletop. As it loses energy and tips toward the surface, the coin begins to roll on its rim, wobbling faster and faster. Toward the end, the coin generates a characteristic rattling sound
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 Spinozistic Calculus  Joseph B. Yesselman
Spinoza's Insights expressed in a Calculus format.
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 Spirals of Primes  Bryan Clair, University of Chicago
This page will generate a spiral of numbers, with the primes marked as stars, and the composites as dots. The center of the spiral is marked with an 'X'. Specify the number at the center of the spiral below, and the width (and therefore also the height)
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 Spirals (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on spirals of all kinds.
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 splib/wavelets  Rice University
Rice Digital Signal Processing (DSP) wavelet resources: links to wavelet research groups around the world.
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 SPLUS: Statistics and Data Mining Software  TIBCO Software Inc,
A suite of software products based on the "S" programming language created specifically for data visualization and exploration, statistical modeling and programming with data. It provides an objectoriented environment designed for interactive data discovery
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