 Sliding Pi  Ivars Peterson (MathTrek)
"The entrance to the Downsview subway station in Toronto presents visitors with a striking vista. A vast mosaic of square tiles sweeps across a curved wall, inviting viewers to trace its lines and ponder intriguing irregularities
in its color scheme
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 Small Group Interactions (Learning and Mathematics)  Susan Bobbitt Nolen; Math Forum
In this 1991 article, "Smallgroup interactions as a source of learning opportunities in secondgrade mathematics," Yackel, Cobb, and Wood, of Purdue University Calumet, Vanderbilt University, and Purdue University, respectively, describe an experiment
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 A Small Puzzle  Joe Fields
The site offers a visual proof that the sum of the first n consecutive odd numbers is n^2, the "L"decomposition.
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 SMART Catalog  Science and Math Advancement and Resources for Teachers (SMART)
A searchable list of professional development and resource providers for mathematics, science, and technology, organized alphabetically or according to the California Math and Science Frameworks. Articles spotlight professional challenges and successes.
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 SMART: Science and Mathematics Advancement and Resources for Teachers  Los Angeles Educational Partnership
A program designed to help teachers in Los Angeles County (California, USA) develop their professional teaching skills and content knowledge. Links for Teachers, Students, Businesses and Institutions, Parents, and Community Members. Includes the SMART
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 Só Matemática  Só Matemática
Material para ensino fundamental, médio e superior, além de provas online, biografias de matemáticos, trabalhos de alunos, um acervo de softwares matemáticos, artigos, jogos, curiosidades, histórias, fóruns de
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 Séminaire Lotharingien de Combinatoire
An electronic journal on combinatorics. Abstracts of the papers are available online, and the full articles can be downloaded.
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 Soap Films and Grid Walks  Ivars Peterson (MathLand)
A simple, physical demonstration of a mathematical truth can produce a lasting impression  one that inspires new questions and speculations. For Christopher C. Chang, a student at Henry M. Gunn Senior High School in Palo Alto, Calif., and one of 40 finalists
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 Society for Mathematical Biology
A forum for discussion of research in biology, mathematical biology, and mathematics applied to or motivated by biology  interdisciplinary research such as biophysics, computational biology, and many other similar realms. Information on membership and
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 Sociological Foundations Supporting the Study of Cultural Diversity  Hugh Mehan, Univ. of California at San Diego
In order to understand the barriers to educational equality faced by lowincome cultural and linguistic minority youth, we need to understand the ways in which social class and ethnicity interact with language and culture. This paper examines various
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 The Socratic Method: Teaching by Asking Instead of by Telling  Rick Garlikov
An example and explanation of how to use students' (including young children's) inherent reasoning abiltiy to guide them gently and easily into an understanding of difficult ideas.
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 Soft Mathematics: The Mathematics of People  Keith Devlin
Keith Devlin describes the blending of mathematics with other disciplines, an approach that is increasingly being adopted in the study of people and their actions.
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 Software's Origin  Ivars Peterson (MathTrek)
Librarian Fred R. Shapiro of the Yale Law School in New Haven, Conn., searched for the word software among scholarly journals electronically archived in the JSTOR database and found that the term software used to describe computer programs dates back
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 Solitairey Sequences  Ivars Peterson (MathTrek)
Solitaire on the computer screen  called Klondike or Idiot's Delight, this form of solitaire has resisted mathematical analysis. Partly because Klondike involves player choice, no one has yet been able to construct a mathematical model of the game from
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 Solomon Papers  Sorin Solomon
Links to papers on microscopic representation of stock markets, and some papers on clusters and multiscale, artificial creativity and novelty emergence, Vision, psychophysics, and cognitive development, Sand piles, and Lattice QCD.
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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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 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 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 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 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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 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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 Southwest Educational Development Laboratory (SEDL)
The regional education laboratory serving Arkansas, Louisiana, New Mexico, Oklahoma, and Texas. Conducts applied research and development, delivers training, and provides technical assistance to K12 educators and decision makers. Topics: Improving Classroom
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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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 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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 Spatial Intelligence and Learning Center
The Spatial Intelligence and Learning Center (SILC) researches spatial learning and develops educational programs and technologies. Every month, the SILC showcase highlights research by different members, who include cognitive scientists, psychologists,
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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 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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 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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 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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 Spreading Memes  Cut the Knot!, Alexander Bogomolny
First of a series of interactive columns for MAA Online that use Java applets to simulate a puzzle or mathematical problem, one not stated directly since the applets are intended to be such that the right answer to an as yet unstated problem should be
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 Spreading Rumors  Ivars Peterson (MathLand)
Three people take longer to share their gossip than four people! This curious result arises out of the following mathematical problem: A group of friends love sharing their gossip. Each gossiper initially knows something that no one else in the group
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 Spreading the Word  Keith Devlin (Devlin's Angle)
History of and commentary on early calculus texts. "The first calculus text hit the shelves in 1696. They have been growing steadily in size (if not mathematical content) ever since. That first genresetting volume was Guillaume Francois Antoine de l'Hospital's
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 Spreadsheets, Mathematics, Science, and Statistics Education  Erich Neuwirth
Information about spreadsheets with an emphasis on mathematics and statistics education. Spreadsheets in Education: Recommended Books; Papers about Spreadsheets in Scientific Journals and Books; Example Spreadsheets and Projects (mostly Excel 5.0); Further
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 Springing a Physical Surprise  Ivars Peterson (MathTrek)
Consider a weight hanging from a spring, which in turn is suspended by a piece of string from an identical spring attached to the ceiling. Cutting the connecting string would send the weight and the lower spring plummeting to the floor. Now add two "safety"
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 Sprouts for Spring  Ivars Peterson (MathLand)
The game of sprouts has a way of growing on you. This twoperson, pencilandpaper game is simple enough that children can play it. Yet its intricacies provide much food for mathematical thought. The players start with a certain number of dots scattered
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 Square of the Hypotenuse  Ivars Peterson (MathTrek)
Some history of the legend of the discovery of the Pythagorean theorem: in his textbook The History of Mathematics, Roger Cooke of the University of Vermont describes how the Babylonians might have discovered the Pythagorean theorem more than 1,000 years
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 Square Wheel (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
A square wheel may be the ultimate flat tire. There's no way it can roll over a flat, smooth road without jolting the rider again and again. Stan Wagon, a mathematician at Macalester College in St. Paul, Minnesota, has a bicycle with square wheels. It's
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 Squaring the Circle  MacTutor Math History Archives
Linked essay covering the problem of squaring the circle in the form which we think of it today, which originated in Greek mathematics: given a circle, construct geometrically a square equal in area to the given circle. This article discusses the history
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 Standards for School Science and Mathematics: Background, Purposes, Goals, Principles  Lynn Arthur Steen, St. Olaf College
A "sidebar" on background of the standards movement in science and mathematics
education prepared for the National Science Foundation's "Indicators" study for 1995. In 1994 Indicators of Science and Mathematics Education. Washington, DC: National Science
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