- The Wavelet Tutorial - Robi Polikar
The engineer's ultimate guide to wavelet analysis: a tutorial that explains basics of signal processing with a focus on the technique of wavelet transformations (WT). Basic concepts of importance in understanding wavelet theory; Short Term Fourier Transform
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- WebCalC - The WebMath Group
An on-line calculus course with easy to read text, fully worked examples, problem solutions, quizzes, and online linking. To view WebCalC, you need the software Scientific Notebook (a free viewer version is available). The site includes links to publications
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- Weighing the Evidence - Keith Devlin (Devlin's Angle)
Hundreds of thousands of years of evolution have equipped us with many useful mental abilities - our instinct to avoid many dangerous situations and our use of language are two obvious examples. However, evolution has not equipped us to handle statistical
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- Weird Dice (MatheMUSEments!) - Ivars Peterson (Math Muse for Kids)
In the dice game Piggy, you and your opponent take turns rolling a pair of ordinary dice. Your score is the sum of the face values of the dice, so if you roll a three and a four, you get seven points. The first player to reach 100 points wins. Suppose
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- Welcome to PERTH: PEerless on EaRTH - Dave Watson
Dave Watson's main interest is computational geometry, and he specializes in spatial interpolation. Books/software on Contouring (a survey of published bivariate contouring and interpolation methods), Tessellations, Spherical Tessellations, Isolines,
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- The Western Reserve Reading Project - The Ohio State University
With over four hundred pairs of twins participating in annual data collection sessions over the past ten years, the Western Reserve Reading Project (WRRP) explores how the environment affects children's ability to learn "by evaluating how genes and environmental
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- We Use Math - BYU Mathematics Department
From actuary to urban planner, read short descriptions of the scores of careers that use math -- or log in to submit your own career entry. Each occupation's write-up includes its salary range, educational background, the specific math courses it requires,
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- What Can Mathematics Do For The Businessperson? - Keith Devlin (Devlin's Angle)
In business, the ability to dig beneath the surface of a problem to see what
the real underlying issues are, and the capacity for clear and logical thought, can be extremely valuable. And learning mathematics provides an excellent way to develop that
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- What Does It Take to Be an Expert Problem Solver? - Annie and John Selden; Mathematical Association of America
Organized into five sections: Expert-Novice Studies Have Often Concentrated
on Textbook Problems; Solving Nonroutine Problems; Are Mathematicians Expert Problem Solvers? How Might One Teach Problem Solving? and The Importance of Affect. From the MAA's
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- What do we know about mathematics curricula? - Alan Schoenfeld, Journal of Mathematical Behavior
In the absence of either large-scale empirical proof of success or the existence of compelling and documentable standards, there is reason to be cautious. The traditionalists are nervous for good reason. It should be noted, however, that the resistance
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- What, How, and the Web - Cut the Knot!, Alexander Bogomolny
More on place value. "There is an obvious confusion there between two questions, what to teach and how to teach it. Does the failure of the New Math to present a specific topic necessarily imply that teaching this topic has no merit? The New Math has
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- What is the best way to lace your shoes? - Burkard Polster, Nature
"The two most popular ways to lace shoes have historically been to use 'criss-cross' or 'straight' lacing -- but are these the most efficient? Here we demonstrate mathematically that the shortest lacing is neither of these, but instead is a rarely used
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- What Is the Collaborative Classroom? (NCREL) - M.B. Tinzmann, B.F. Jones, T.F. Fennimore, J. Bakker, C. Fine, and J. Pierce
New learning and thinking curricula require collaboration. An article that addresses shared knowledge and authority among teachers and students; teachers as mediators; heterogeneous groupings of students; teacher and student roles; interactions; challenges
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- What Is Your Answer to That Question? - Cut the Knot!, Alexander Bogomolny, with Don Greenwell
The question - Why study mathematics? - appears in a multitude of guises and a plethora of variants... Mathematics is often compared to art. Like literature, mathematics has metaphor, ambiguity, paradox, and mystery. It has history. Mathematics has contributed
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- What's Going On During Mathematics Awareness Month - Keith Devlin (Devlin's Angle)
"This year's theme is mathematics and biology. Two important examples of how mathematics is used in biology are: in developing computer models of the human heart, which are helping us to understand how the heart works and, more importantly, how it goes
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- What Should I Look For in a Math Classroom? - Mathematical Sciences Education Board (MSEB)
A set of practical guidelines, with explanations of their relevance. From the Mathematical Sciences Education Board of the National Research Council.
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- What's Noteworthy on Learners, Learning & Schooling - Mid-continent Regional Educational Laboratory (McREL)
"The major challenges for educational reform today are putting the pieces together to create sustainable systemic change and scaling up systemic reform to encompass all schools, all programmatic areas, all levels of schooling and diverse social contexts."
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- What's Sophisticated about Elementary Mathematics? - Hung-Hsi Wu
"The characteristics of coherence, precision, and reasoning are not just niceties; they are a prerequisite to making school mathematics learnable." In this American Educator article originally published Fall, 2009, the author goes on to unpack whole number
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- What Will Be the Effect of a Standards-based Education on College Students? - Judith Roitman
This article, by Judith Roitman of the University of Kansas, appeared in the April 1995 FOCUS, the newsletter of the MAA. Among other things, Roitman discusses the need for dialog between K-12 teachers and their college counterparts, and difficulties
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- What Works Clearinghouse
Reviews of the effectiveness of educational intervention programs, products, practices, and policies. Among other curricula, the WWC has reviewed studies of the Middle School Math Curricula interventions Cognitive Tutor, Compass Learning, Connected Mathematics
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- When mathematics has to be theater - Keith Devlin (Devlin's Angle)
A mathematician's entry into the world of commercial multimedia - the creation of an interactive calculus textbook on CD-ROM.
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- When mathematics is plain sailing - Keith Devlin (Devlin's Angle)
In the ocean waters off New Zealand, an intense mathematical olympiad has just begun: The America's Cup - a yacht race, the premier international event in
ocean sailing. Competition is fierce. The technical challenges are enormous. And the costs are
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- 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 one-half 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 Back-to-School 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 middle-school 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 Cauchy-Weierstrass 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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