 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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 Speed Arithmetic  Jim Loy
Faster ways of adding and multiplying from left to right.
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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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 Stan's Library  Stanislav Sykora
A library including a section of mathematical articles, reviews, etc..
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 Stardust Equations  Keith Devlin (Devlin's Angle)
On Sunday, February 7, at 4:04 PM, a Lockheed Martin Delta II rocket lifted off from Cape Canaveral carrying an unmanned spacecraft about the size of an office desk, having the romantic name of Stardust. If all goes well, on January 15, 2006, the spacecraft
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 State Institute of Statistics (SIS)  Republic of Turkey
The agency in charge of collecting statistics for the country of Turkey. Includes tables and charts of key social, economic, and environmental statistics and a dictionary of important statistics and economics terms arranged by subject. Some articles
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 Statistical Assessment Service (STATS)
STATS is a nonprofit, nonpartisan resource on the use and abuse of science and statistics in the media. Its goals are to correct scientific misinformation in the media and in public policy resulting from bad science, politics, or a simple lack of information
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 Statistical Mechanics, Structure of Matter  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to statistical mechanics, structure of matter, the study of largescale systems of particles, including
stochastic systems and moving or evolving systems. Specific types of matter studied include fluids,
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 Statistics  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to statistics: the science of obtaining, synthesizing, predicting, and drawing inferences from data. Elementary calculations of mean and standard variation suffice to summarize a large, finite,
normallydistributed
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 Statistics Finland
The Finnish statistics office; includes news and press releases, important socioeconomic and election data, and publications, including a report on Finnish education. Finnish and Swedish versions also available, as well as Finlande en chiffres in French.
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 Statistics Iceland
The statistics ministry of the government of Iceland. Key socioeconomic figures; press releases; monthly statistics in PDF format; methodological information. Site also available in Icelandic.
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 Statistics Indonesia (Badan Pusat Statistik)  Republic of Indonesia
The statistics collection department of the government of Indonesia. Glossary of statistical terms, key socioeconomic figures for Indonesia by subject and region, census results, methodology information, and links to regional offices. Recent economic
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 Statistics Lithuania
The agency that collects statistics for the country of Lithuania. The site includes: a timeline of statistics in Lithuania dating to 1528, tables of geographic, population, and economic data, press releases, list of recent publications  some may be
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 Statistics Netherlands
A government organization that collects, interprets, and presents information about Dutch society. Tables of key socioeconomic figures for the Netherlands; publications and press releases, which may be ordered or downloaded in PDF format; introduction
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 Statistics Norway
The agency that collects Norwegian statistics. Includes articles about data, tables of recent economic and population statistics, and list of publications; many publications and research papers may be read or downloaded in PDF format. The site also
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 Statistics & Probability (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on probability and statistics, covering: average, Babson, demography, mode, Neumann, probability, queuing theory, statitics, and vital statistics.
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 Statistics Singapore
The Singapore Department of Statistics page includes key economic and social indicators, a glossary of economics and statistics terms, press releases, a list of publications, and the Statistics Singapore newsletter in PDF format.
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 Statistics Sweden
Provides official statistics for the country of Sweden: population, key socioeconomic figures, press releases, and graphs of important data. More information, including an order form for timeseries information, is available in the Swedishlanguage version
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