 Digits, Squares, and Cycles  Ivars Peterson (MathTrek)
Fascinating patterns lurk among the digits of whole numbers. Pick a positive integer, such as 57. Square each of the digits, then add the squares together: 5^2 + 7^2 = 25 + 49 = 74. Do the same thing with the digits of 74: 7^2 + 4^2 = 49 + 16 = 65. Keep
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 Diophantine geometry in characteristic p: a survey  José Felipe Voloch
An article that appeared in Arithmetic Geometry, F. Catanese, ed., Symposia Mathematica XXXVII, Cambridge Univ. Press, 1997, pp. 260278. Introduction; Curves; Abelian varieties and their subvarieties; Diophantine Approximation in characteristic p; Omitted
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 Dipping math scores heat up debate over math teaching...  Bridget Murray, American Psychological Association (APA) Monitor
... psychologists differ over the merits of teaching children 'whole math'. An APA newsletter article that outlines the debate over the effectiveness of whole math, a demonstrative approach where manipulatives help children understand math concepts. "Some
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 Discoveries & Breakthroughs Inside Mathematics  American Mathematical Society (AMS)
Read articles and watch video news segments about the latest discoveries and applications of mathematics: "Do the Math Dance," "Mathematician Calms the Skies with Turbulence Detection Algorithm," "Become a Smarter Shopper," "The Science Behind Movie Magic,"
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 Discovering Geometry Newsletter  Key Curriculum Press
A free biannual publication providing information and teaching techniques for The Geometer's Sketchpad software package, the Discovering Geometry Newsletter is a resource for those interested in geometry and technology education. Download PDFs of past
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 Discover Magazine  The Walt Disney Company
The monthly magazine of science and technology. Covers space, biology, health, medicine, AIDS, computers, new technology, the environment, astronomy, ancient life, archeology, evolution, physics, mathematics, ecology, and more. Available online: selected
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 Discrete Fourier Series Transform  Eric Brasseur
A brief introduction to the discrete Fourier transform and its application to signal sampling. Also available in French.
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 Discussiones Mathematicae  Borowiecki; Technical University of Zielona Góra, Poland
Four journals: Differential Inclusions, Control and Optimization; General Algebra and Applications; Graph Theory; and Probability and Statistics. Information for each journal includes a general description, subscription information, list of editors,
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 Disorder in the Deck  Ivars Peterson (MathTrek)
About 30 years ago, tournament bridge players started using computershuffled rather than handshuffled decks. Almost immediately, there was an outcry protesting the apparently wild fluctuations in the distribution of cards of different suits in computerdealt
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 Distributed Maple  Wolfgang Schreiner; RISCLinz, Johannes Kepler Universität Linz
A system for writing parallel programs in the computer algebra system Maple, so that different computers in a network can perform parts of the same computation. The program may be downloaded here in .tar or .zip form. The manual, a README file, and papers
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 Divide and conquer for quantum computers  Ivars Peterson  Science News Online
In theory, quantum computations can be speeded up significantly by letting many quantum computers work together in parallel on data encoded as particles in an entangled quantum state.
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 Divisibility Criteria  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A definition of some divisibility criteria, and their derivation from modulo arithmetic, with links to related pages.
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 Division by Three [PDF]  John Conway, Peter Doyle
A formal proof that it is possible to divide by three. This assertion is easy to prove using the axiom of choice, but becomes a much more difficult problem if the axiom of choice is not allowed (as is the case here). From this proof, and the much simpler
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 D. J. Bernstein
Courses, research articles (in dvi format), and a list of available software, listed by a professor of mathematics and computer science at the University of Illinois. Pages are also listed by topic. Also at ftp://koobera.math.uic.edu/www/djb.html.
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 Dmitry Gokhman
Papers (Hardy fields; Differential fields of complex germs; Applied mathematics), Class lecture notes and summaries, code (IGF, LibPS 2, Python, Perl, TeXtool 2.12a), courses, translations, guests.
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 DNA Adds Up  Ivars Peterson (MathLand)
Calculating that 0 + 0 = 0, 1 + 0 = 1, and 0 + 1 = 1 is normally no big deal. When the calculations are done in the lab using DNA molecules, however, these elementary manipulations look considerably more interesting. In the July 12 [1996] Science, a team
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 DNA, Computers, and Killer Apps  Ivars Peterson (MathLand)
When computer scientists look at DNA, they see information storage and processing. They view the four bases of DNA as something akin to the zeros and ones of the binary code by which computers store and process information. They look for algorithms, theorems,
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 Does March Madness need a timeout?  J. Travis  Science News Online
Suggestions about the effects of circadian rhythms, daily cycles of physiological activity that every organism experiences, and changes in time zone (causing 'jet lag'), on sports teams.
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 Dominique Foata
Dominique Foata is a mathematician specializing in combinatorics. Abstracts of his papers are available online, and they may be downloaded in .dvi, PostScript, or TeX formats. The site also contains a summary and errata for the textbook Calcul des Probabilités,
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 Doodling and Miracles  Cut the Knot!, Alexander Bogomolny
Almost 100 years ago, Frank Morley proved a curious theorem from elementary geometry that had remained unknown until 1899. With time, the theorem became known in mathematical folklore as Morley's Miracle (Morley's Trisector Theorem is a more mundane term.)
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 Doron Zeilberger's Electronic Headquarters
Doron Zeilberger researches combinatorics using computer programs. The site is notable for his Opinions page; these opinions are wideranging but touch upon mathematics education, the use of computers, and the value of incomplete proofs. All of Zeilberger's
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 Do software engineers need mathematics?  Keith Devlin (Devlin's Angle)
Software engineers don't use their college mathematics, but they make use of their college mathematics education every day. Brains are perhaps the world's best examples of an adaptive system. When we subject the human brain to an extended educational
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 Do the Math  Slate
A topical series about math in culture, politics, psychology, and other popular themes, many written by math professor Jordan Ellenberg. Articles, which date back to June, 2001, have included "Barry Bonds and the Placebo Effect," "Algebra for Adulterers,"
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 Dot Patterns and Sierpinski Gasket  Cut the Knot!, Alexander Bogomolny
How many ways are there to define the Sierpinski gasket (also, the Sierpinski triangle)? The author has counted a respectable 9 but would be happy to learn of more. An applet with rows of digits or circles with colors corresponding to the digits shows
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 Dots and Boxes  Ivars Peterson (MathTrek)
The familiar pencilandpaper game of DotsandBoxes can be played on several different levels of sophistication. Elwyn Berlekamp posits that the game can be played on at least four different levels. "Players at any level consistently beat players at
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 Double Bubble Conjecture Proved (Math Chat)  Frank Morgan, MAA Online
Four mathematicians have announced a mathematical proof of the Double Bubble Conjecture: that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. In an address to the Undergraduate Mathematics Conference
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 Doubling the Cube  MacTutor Math History Archives
Linked essay covering the history of and some solutions to the classical
problem in Greek mathematics of doubling or duplicating the cube, also called the
Delian problem; and on proving the impossibility of constructing a solution using only ruler
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 Downloadable Articles, Papers & Materials  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
Articles by Villiers related to geometry and geometry education some in PDF format, including: An Extended Classification of Quadrilaterals; A Mathematical Treasure Hunt; Place Kicking Locus in Rugby; Sketchpad Solutions and Results; A Dual, and Generalizations,
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 Do You Know That...  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of short essays about over 60 curious mathematical facts and terminology, mostly linked to explanatory or exploratory essays, drawn from various parts of Bogomolny's site, CuttheKnot. See page two and page three.
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 A Dozen Reasons Why Schools Should Avoid Filtering  From Now On (FNO)
Why schools should not block access to particular sites: filters may not work very well;. they may work too well; they may increase attention to SMUT and spur motivation; their ongoing cost may block better programs from your students; they may create
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 The Drills To Play  Cut the Knot!, Alexander Bogomolny
An exploration of a detail found at the beginning of Kurt Godel's biography by John Dawson, how repetition and practice constitute an integral and necessary part of the learning process; that, by implication, one first conceives an idea, then proves it
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 Dr Len Fisher: Opening the Door to Science  Len Fisher
Fisher concentrates on the science of the everyday and making science accessible. His latest book is Rock, Paper, Scissors: Game Theory in Real Life. The site contains excerpts from his books as well as descriptions of his talks, articles about his work,
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 Drums That Sound Alike  Ivars Peterson (MathLand)
Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normalmode vibrations. He outlines the progress made on Mark Kac's
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 The Dynamical Systems and Technology Project at Boston University  Robert L. Devaney; Dept. of Mathematics
An NSFsponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process.
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 Dynamical Systems on the Torus  Paul Trow
An illustrated essay introducing dynamical systems on the torus.
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 dynamicalsystems.org
An interactive laboratory on dynamical systems, in particular on particle systems. Software, Documents, and Links. Animated features include: Nonlinear chain; Forced Pendulum; Fermi system; Vlasov billiards; Vortex motion; 3 Body Problem; Convex Billiards;
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 Dynamic Geometry  Goldenberg, Scher; Education Development Center, Inc.
To understand how students construct mathematical ideas in "Dynamic Geometry" environments (tools like Geometer's Sketchpad and Cabri), one needs clear characterizations of the mathematical "raw materials" embodied in the software and how students use
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 Dyscalculia.org  R. M. Newman
Learn about dyscalculia: definitions, cognitive research, symptoms, diagnosis and best practices, classroom techniques, home learning aids, legal questions, papers such as "Developmental Perspectives on Dyscalculia: Implications for Teaching in the Middle
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 Dyslexia Symptoms & Dyslexia Signs  Benetta Strydom
A resource on the symptoms of dyslexia, including the possible effects of
this disorder on math and handwriting.
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 Early Career Profiles: Recent bachelorslevel graduates in the mathematical sciences  American Mathematical Society
A collection of profiles of alumni from a variety US colleges and universities who majored in mathematics. Each profile includes statements of what the alumnus or alumna now does, the math each uses on the job, the recent graduate's educational background,
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 Early Mathematics Education Project  Erikson Institute
"A solid early introduction to the 'big ideas' in mathematics can help a child succeed in school later on...." Read about Erikson Institute's teacher education workshops for foundational math, pedagogical research on the whole teacher approach by JieQi
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 Easymaths SA  Maggie Verster; Mathematics Web Association of South Africa
A free South African site for teachers, parents, and students, with lessons, tests, articles, worksheets with answers, study skills information, and more.
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 Economic and Game Theory  David K. Levine, Department of Economics, UCLA
A site that uses the tools of modern economic theory and game theory to explore how the interaction of intelligent goalseeking individuals determines social outcomes. The site offers general interest material, undergraduate and graduate course material,
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 Economic Research Service (ERS)  U.S. Department of Agriculture
This agency studies agriculture, food and nutrition, the environment, rural development, and international trade. Research reports, press releases, commodities reports, books, and other publications available online or for download in PDF format, with
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 Ed Dickey's Home Page  Ed Dickey
Syllabi for courses on teaching in middle/high school (mathematics), teaching mathematics with manipulatives (grades 712), graphics calculators in high school mathematics, computers in mathematics education, technology to support instruction, technology
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 Ed Laughbaum, Ohio State University
Research papers include Developmental Algebra with Function as the Underlying Theme; Graphing Technology  Tool of Choice for Teaching Developmental Mathematics; Using Data to Promote Mathematical Understanding; Sharp Corners, Rates of Change, Systems
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 Educação Matemática e Novas Tecnologias  Gravina, Barreto; Universidade Federal do Rio Grande do Sul (UFRGS)
Discusses new technologies as resources for the learning of Mathematics:
software descriptions, lesson plans, articles. In Portuguese.
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 Educational Resources Information Center (ERIC)  National Library of Education
A national information system designed to provide users with ready access to an extensive body of educationrelated literature. ERIC Sites links to clearinghouses, support components, and publishers of ERIC material. Special Projects include the Education
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 Educational Technology Center (ETC)  Harvard Graduate School of Education
The Educational Technology Center was formed in 1983 to explore two hard issues: topics or broad areas of concern for educators deemed difficult for learners; and issues of implementation, broadly conceived. What are the obstacles and sources of support
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 Education.Au Limited  Education Network Australia (EdNA)
Australian author of various publications on: Access and Equity; Adult and Community Education; Communication Technologies; CDROM Technology; Educational Television; Evaluating ComputerBased Education; Home Based Workers; Information Economy; Learning
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