 Where to Start?  Cut the Knot!, Alexander Bogomolny
A discussion of math education: the intent of the NCTM Standards, reflections on the history of constructivism, classroom practices (with a link to Marilyn Burns' Math Solutions page), and a simple applet for solving linear equations. An interactive column
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 Where Will the New Millennium Begin? (Math Chat)  Frank Morgan; Christian Science Monitor
Assuming the third millennium arrives on January 1, 2001, where on Earth should the celebration begin?
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 Which Countries Are Most Like Stars? (Math Chat)  Frank Morgan, MAA Online
Which countries in the world have a point such that the shortest line from
every other point in the country stays inside the country? (ignore mountains and valleys). Mathematicians call such countries starlike. Are there any countries such that the shortest
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 Which One Is Older? (Math Chat)  Frank Morgan, MAA Online
Creative solutions to the challenge: how can two people determine which is older without revealing their ages? Math videos available from the Mathematical Sciences Research Institute via the MAA. "Mathematics in Arcadia," "Fermat's Last Theorem," as seen
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 Whips and Dinosaur Tails  Ivars Peterson (MathTrek)
The loud crack of a deftly flicked bullwhip is a small sonic boom, generated when the whip’s thin, highly flexible tip exceeds the speed of sound. Sauropod dinosaurs of the family Diplodocidae have enormous tails that gradually narrow to thin, delicate
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 Whistler Alley Mathematics  Paul Kunkel
Kunkel's Geometer's Sketchpad lessons convey a conceptual understanding, usually without rigorous proof, with questions and suggestions for extensions: Buffon's Needle (an old probability exercise); Chinese Handcuffs (questions with applications for geometry,
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 White Narcissus  Ivars Peterson (MathTrek)
The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical
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 Who's Counting  John Allen Paulos
Columns by Prof. John Allen Paulos, the author of Innumeracy, Mathematician Reads a Newspaper, and other popular books. Humorous and enjoyable articles by a keen observer of the world around him whose mind has been sharpened by mathematical practice.
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 Who's Really Ahead?  Ivars Peterson (MathTrek)
The winding down of the current baseball season seems an appropriate time to take a look at a curious inconsistency that sometimes appears in team standings... Once in a while the team with the higher winning percentage may be at least onehalf a game
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 Who's Really No. 1?  Ivars Peterson (MathTrek)
It happens every fall. Fierce arguments erupt over which U.S. college football team is the best in the nation. As the season progresses, this frenzy of head scratching and navel gazing mounts until the climactic bowl games at the end of the year (more
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 Who Wants to Be a Mathematician  American Mathematical Society
In the game show "Who Wants to Be a Mathematician," high school students compete for cash and prizes by answering multiple choice mathematics questions. Read about past performances of the game; view videos of games played in Danvers, MA, at Danvers High
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 Who Wants to be a Millionaire? (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: On ABC TV's "Who Wants to be a Millionaire," to maximize your expected winnings how sure should you be of your answer to the $500,000 question to answer? Somewhere from about 22.5% to about 46.5%, probably closer to the latter.
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 Who was Marin Mersenne?  Luther Welsh
It was not until the mid 20th century that Mersenne became known primarily for his Prime Number Conjecture. Historically, he was much better known for his correspondence with leading scientists of the day. Interested in optics, he also been called the
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 Why 2001 Won't Be 2001  Keith Devlin (Devlin's Angle)
"It's a good story... But how realistic is the behavior of HAL? We don't yet have computers capable of genuinely independent thought, nor do we have computers we can converse with using ordinary language. True, there have been admirable advances in systems
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 Why Does BacktoSchool Imply Back to Math?  Keith Devlin (Devlin's Angle)
...in a world where everyone can afford a pocket calculator and a great many people seem to be successful in life with little or no mathematical ability or knowledge of science, why do we place so much emphasis on math and science?
Whatever the answer,
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 Why Do Math?  The Society for Industrial and Applied Mathematics (SIAM)
A showcase for exciting mathematical and computational science topics at an introductory collegiate level. Short popular science articles that illustrate the innovative uses of math in yachting, cochlear implants, neuroscience, space travel, tomography,
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 The Why Files  University of Wisconsin
An electronic exploration of the issues of science, math, and technology that lurk behind the headlines of the day, presenting those topics in a clear, entertaining and accessible manner. Provides a bimonthly feature on the science of everyday life, archived
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 Why Isn't There a Nobel Prize in Mathematics?  Peter Ross
Ross writes that Garding and Hormander state, "The true answer to the question (of the title) is that, for natural reasons, the thought of a prize in mathematics never entered Nobel's mind." Nobel's final will of 1895 bequeathed $9,000,000 for a foundation
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 Why is the Mathematician So Messy? (Math Chat)  Frank Morgan, MAA Online
A physicist and a mathematician can clean a house in 6 hours; an engineer and the mathematician in 3 hours; and the physicist and the engineer in 1 hour and 12 minutes. How long would it take the physicist alone?
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 Why It's Hard to Fold a Triangle in Half (Math Chat)  Frank Morgan, MAA Online
For a circular piece of paper, the lines along which you can fold it "in half" (with half the area on each side) are precisely the lines through the center. What other shapes work the same way? This works for lots of shapes, such as rectangles, parallelograms,
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 Why Not Geometry?  Cut the Knot!, Alexander Bogomolny
An exploration of the validity of teaching algebra at the middleschool level, testing, mathematics ewducation reform, the goal of education, and a suggestion that geometry might be a more important starting point.
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 Why Teach Mathematics?  Harold Brochmann
A series of articles addressing the questions Why do we have to learn this stuff? Why do we teach mathematics? Is the mathematics we teach relevant? Why is teaching mathematics so difficult?
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 Wikipedia Mathematics
The free encyclopedia's entries on mathematics. A wiki is a collection of interlinked web pages, any of which can be visited and edited by anyone at any time. Many pages also available in a range of foreign languages.
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 Will it rot my students' brains if they use Mathematica?  Theodore W. Gray and Jerry Glynn
Excerpts from the introduction to The Beginner's Guide to Mathematica V4. Jerry: "I have young students who reach for their calculators to get the answer to 5×6. My response, when I see that, is to explain that such behavior is socially unacceptable,
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 Will the real continuous function please stand up?  Keith Devlin (Devlin's Angle)
A description and a more rigorous CauchyWeierstrass definition that "forms the bedrock of modern real analysis and any standard 'rigorous' treatment of calculus," with a discussion of how the formal definition involves a major shift in conceptual model
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 Wilson's Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A description and proof of Wilson's Theorem, another consequence (Fermat's Little Theorem being one) of Euclid's Proposition VII.30, with related links.
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 A Winning Division  Ivars Peterson (MathTrek)
A farmer plans to divide a triangular piece of land evenly between his son and daughter. Because he wants to be scrupulously fair, he would like the two pieces to have not only equal areas but also equal perimeters. Where should he draw the line? This
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 Winning Partitions  Ivars Peterson (MathLand)
The simple idea of partitions has developed into a significant branch of number theory. Indeed, "any time the number of ways of writing a number as the sum of other numbers arises, the theory of partitions can't be far off," says number theorist George
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 The Winning Voting System (Math Chat)  Frank Morgan, MAA Online
Results submitted to the challenge: What do you think is the best voting system among three or more candidates? Joseph DeVincentis suggests a version of approval voting in which each voter has three choices: approval (+1), no opinion (0), or disapproval
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 Women in Math Project  Marie Vitulli; Department of Mathematics, University of Oregon
Information on all aspects of women and math, including bibliographies of publications (with a search engine), an extensive collection of biographies, links to associations, job, grant, and scholarship opportunities, conferences, workshops and programs,
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 Women & Mathematics  Key Issues in Mathematics at the Math Forum
Find sites relevant to women, girls, and gender equity in the Math Forum's Internet Mathematics Library.
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 Women, Minorities, and Persons with Disabilities in Science and Engineering: 1994  Division of Science Resources Studies (SRS), National Science Foundation (NSF)
An NSF report that describes the status of groups traditionally underrepresented in science and engineering, and documents factors important to choice of study and to success in pursuing science and engineering.
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 Women, Minorities, and Persons With Disabilities in Science and Engineering: 1996  Division of Science Resources Studies (SRS), National Science Foundation (NSF)
This report presents data on participation of underrepresented groups in science and engineering, and documents factors important to success in science and engineering in precollege education, undergraduate and graduate education, and employment. The
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 Wonders of Ancient Greek Mathematics  Timothy Reluga; Tufts University
An arbitrary collection of interesting solutions to geometric problems discovered and solved by the Greeks, limited to intuitive, elegant, or beautiful solutions and some that do not meet these requirements, serving as reminders of the level to which
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 Wordplay  John Langdon
On the application of ambigrams (words as art) in various fields of study. Most ambigrams are based on one form of symmetry or another; most of Langdon's ambigrams exemplify rotational symmetry.
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 Working Group Mathematical Logic
 LudwigMaximiliansUniversität, Munich, Germany
In English and German. Contact information, staff, conferences, seminars, and workshops, Ph.D. program, links, articles.
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 The Work of Robert Langlands  Mathematics Dept., University of British Columbia, Canada
A selection from Langlands' professional correspondence, previously unpublished work, and published work now out of print. Thesis, papers, manuscripts, letters, and bibliography.
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 World Mathematical Year 2000
On May, 6th, 1992, in Rio de Janeiro, the International Mathematical Union declared that the Year 2000 will be the World mathematical Year. The Declaration of Rio sets three aims: the great challenges of 21st Century; mathematics, a key for development;
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 World Population and Four Dice (Math Chat)  Frank Morgan; Christian Science Monitor
Answers to the old challenge (Estimate what fraction of the people who have ever lived on Earth are alive on Earth today.) plus a new challenge and an additional problem and answer (courtesy S. H. Logue: Ann learned that her old dotmatrix printer can
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 World's Fastest Man  Ivars Peterson (MathTrek)
The 1998 edition of The Guinness Book of World Records features an article about Donovan Bailey, billed as the fastest man alive. The article begins: "Canadian Donovan Bailey rocketed into the record books when he set a new world mark of 9.84 seconds
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 The World Wide Web and Pedagogy  Mathematics Education at The Math Forum
Examples of the hypertextual, hypermedia, communications capabilities of the Web in education: articles, courses, conferences, and model Web units.
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 Writing a Math Phase Two Paper  Steven L. Kleiman, with Glenn P. Tesler; MIT
A discussion of the kind of writing appropriate in a paper submitted to the math department to complete Phase Two of MIT's writing requirement: a review of the general purpose of the requirement and the specific way of completing it for the math department;
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 Writing Assignments in Calculus  Tommy Ratliff; Dept. of Mathematics & Statistics, Wheaton College, Norton, MA
Imaginative paper proposals for SingleVariable and Multivariable Calculus courses cover subjects from "Confusion in Beverly Hills" (geometry, trigonometry) to "The XFiles Makes Me So Angry" (optimization of a function of two variables)  and many more.
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 Writing for a Math Class  B. Sidney Smith, Wendy Hageman Smith; Math Academy Online/Platonic Realms
A "minitext" concerning written communication in mathematics classes, for both students and teachers. Teachers' section discusses possible formats and assessment, and gives sample lessons; students' section gives practical tips on approaching a written
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 Writing in Mathematics  Dr. Annalisa Crannell; Franklin & Marshall College
Dr. Crannell's Guide to Writing in Mathematics, the checklist she uses, and writing assignments from her PreCalculus and Calculus I, II, and III classes. Contents include: Why Should You Have To Write Papers In A Math Class?; How is Mathematical Writing
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 Writing Proofs  Leslie Lamport
PostScript, DVI, and LaTeX versions of each (but no HTML) are available. How to Write a Proof: A method of writing proofs is proposed that makes it much harder to prove things that are not true. The method, based on hierarchical structuring, is simple
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 Writings for a General Audience  Marcus Jaiclin
PDF articles on popular and recreational mathematics by Jaiclin, an Assistant Professor at Westfield State University: Notes on Mathematics of Voting Methods; Fractals, Pascal's Triangle, and the padic Numbers; Airplane Passenger Seating Problem; No
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 Writings from the MegaMath Project (MegaMath)  Casey, Fellows, Koblitz; Los Alamos National Laboratory
Documents containing classroom materials and discussions of mathematics pedagogy. The Los Alamos workbook; Lessons for math teachers; An hour in the classroom; Literacy lessons and mathematics learning; Computer science in elementary school; Combinatorially
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 Writing to Develop Understanding: The Math Forum @ Drexel's PoWs  Suzanne Alejandre
What can we ask students about their problem solving that will help them the most? This article, originally published in the December, 2006, issue of the CMC ComMuniCator, journal of the California Mathematics Council, addresses that question by examining
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 www4teachers
A center for practical ideas about technology in education. Articles published online, updated monthly: teacher interviews on firsthand classroom technology; interviews with educational technology leaders; interviews with kids; howto columns on classroom
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