 Department of Mathematics and Computer Science  North Carolina School of Science and Mathematics (NCSSM)
Learning materials for teachers and students include resources on algebra, advanced functions, and mathematical modeling; data sets used with the NCSSM textbook Contemporary Precalculus Through Applications; the AP Calculus Web Center; and Mathematics
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 Department of Science & Mathematics Education: Research and Development  Univ. of Melbourne, Australia
Read faculty research and learn about their projects and interests: children's understanding of statistical and probabilistic concepts; the negotiation of meaning in mathematics & science classrooms (The Classroom Project); the expression of algorithms
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 Dept. of Statistics  University of Illinois at UrbanaChampaign
Web pages generated by statistics courses; biographical sketches of faculty, staff, lab members, and graduate students; department newsletter. Graduate program admission requirements, degrees offered, courses, statistical consulting services, and The
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 Derivatives Page  Financial Pipeline
Derivatives are financial securities whose value is derived from another "underlying" financial security. Options, futures, swaps, swaptions, and structured notes are all examples of derivative securities. Derivatives can be used in hedging, protecting
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 Design, Analysis, Implementation, and Evaluation of Graph Drawing Algorithms  Petra Mutzel
Automatic Graph Drawing is a relatively new field in Computer Science. The task is to draw diagrams of objects and their relations in such a way that they are easy to read and understand. Applications are, e.g., animation of algorithms, data and flow
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 Design Ideas  Julie Coghill
A series of articles that discuss quilt design using proportion, asymmetry, and Pythagorean triples.
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 Designing a Sustainable Standardsbased Assessment System  Don Burger; Midcontinent Regional Educational Laboratory (McREL)
Designing and implementing a sustainable standardsbased system that consistently yields high student achievement involves more than setting and measuring academic goals. Changing to a standardsbased system provides an
opportunity to reexamine the
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 Designing Effective Professional Development: Lessons from the Eisenhower Program  U.S. Department of Education
The second report of the National Evaluation of the Eisenhower Professional Development Program, Part B (State and Local Activities), a multiyear evaluation being conducted by the American Institutes for Research (AIR) under a contract with the U.S.
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 Determinación Geométrica de los Números Primos y Perfectos  Omar E. Pol
Un breve ensayo en que "se describe la geometría que determina la distribución exacta de los números primos y también de los números perfectos. Se ilustra el texto con diagramas originales; se muestra el modelo principal
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 Detracking America's Schools: The Reform Without Cost?  Brewer, Rees, Argys; Phi Delta Kappan
The practice of grouping school students by level of ability, known as tracking, has long been used in American public schools. In recent years, opponents of tracking have argued that belowaverage students are hindered by being grouped together, while
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 Developing Algebraic Thinking  Suzanne Alejandre
Teacher lesson plan and student kinesthetic activities on the Traffic Jam activity and applet, as originally published in the inaugural (Fall, 2002) issue of ONMath, an electronic journal of the National Council of Teachers of Mathematics (NCTM).
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 The Development of Group Theory  MacTutor Math History Archives
Linked essay describing the rise and progress of group theory from the 18th through the 19th centuries, with references (books/articles).
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 Dice and Valentine's Day Symmetries (Math Chat)  Frank Morgan; Christian Science Monitor
A dice challenge from S. H. Logue: The six faces of four dice have these numbers on them: A 1 1 5 5 5 5 B 4 4 4 4 4 4 C 3 3 3 3 7 7 D 2 2 2 6 6 6. You and your opponent each choose one die to use throughout the game. Each round you both roll, and the
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 Dien dàn Toán hoc.net
A math site in Vietnamese.
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 Difference and Functional Equations  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to functional equations, those in which a function is sought which is to satisfy certain relations among its values at all points. For example, we may look for functions satisfying f(x*y)=f(x)+f(y) and
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 Differential Geometry  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to differential geometry, the language of modern physics and an area of mathematical delight. Typically, one considers sets which are manifolds (that is, locally resemble Euclidean space) and which come
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 Different Ways to Represent Numbers  Chad Lake
Online paper that discusses and illustrates counting in bases other than 10; converting to decimal; the Snake Algorithm (the algorithm, summary of binarytodecimal Snake Algorithm, decimaltobinary Snake, extending the Snake to other bases, and summary
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 Digital Manipulatives: New Toys to Think With  Resnick, Martin, Berg, Borovoy, Colella, Kramer, Silverman; MIT Media Laboratory
Manipulative materials such as Cuisenaire Rods and Pattern Blocks enable children to explore mathematical and scientific concepts such as number and shape through direct manipulation of physical objects. Resnick et al. have developed a new generation
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 Digital Mathematical Performance  Gadanidis, George; Borba, Marcelo; Hughes, Janette; et al.
Watch video, liveacted dramatic storyboards, and animations of how people "perform" mathematics: Flatland, "Help Me, Fermi," Should Parallel Lines Never Meet," "The Pleasure of Making 10" (linear equations), "The Waiter" (the missing dollar problem),
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 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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