Art of Problem Solving

A site for gifted math students, especially those planning to participate in various math olympiads. Created by former olympiad winners, the site offers an online school, a variety of forums and improvisational problem solving sessions guided by Art of Problem Solving instructors.

Stella - Polyhedron Navigator

Great Stella is by far the most comprehensive tool around for exploring the fascinating world of polyhedra. Select from over 200 built-in models (including Platonic, Archimedean, Kepler-Poinsot and all other uniform polyhedra, Johnson solids and Stewart toroids), or create endless new ones using advanced tools such as duality, stellation, faceting, and augmentation. Also comes with a library containing hundreds of additional models so you can take advantage of the power without learning all the ins and outs. Nets can be printed for any polyhedron created, allowing you to build your own physical models with a bit of cutting, folding and gluing. Photos of many models built using the program also appear on the site, as well as a published paper about the features of the program, and a glossary of polyhedral terms.

An Interactive Real Analysis book.

An excellent text on Real Analysis which, being available on-line, offers several unique extras. Access to the information is through a (nested) table of content and Glossary and, of course, a wisely used network of hypertext links. Real abundance of problems with solutions available at a press of a button. A few Java applets illustrate successfully such concepts as continuity and uniform continuity and present parameterized graphs of several curve families.

Eric Weisstein's World of Mathematics (Formerly, Eric's Treasure Trove of Mathematics.)

A rare and, probably, the most comprehensive collection of mathematical information available on the Web. This is a dynamic extension of Eric's hardcopy Encyclopedia of Mathematics. There are close to 9,000 entries each with book references and links to related Web sites. Some topics are covered better than others, but in most cases you may expect to glean a good deal of information on a huge variety of topics in Mathematics.

The site underwent several major revisions. In its latest incarnation, it features an exemplary user interface with multiple entry points and a powerful search engine.

Mathematics Archives

One of the most comprehensive Web resource sites. Teaching material, Math related sites, Journals and Magazines, Government Institutions, Societies and Colleges, Math Departments.

Frequently Asked Questions in Mathematics.

A collection of mathematical assays maintained at the University of Waterloo. Covers many topics in history, algebra (mostly higher), number systems and Number Theory and more. Special pages describe Famous problems in Mathematics. The site is a valuable on-line source of information but not as comprehensive or well organized as Eric's Treasure Trove. But there is a promise hence the hope.

MathSoft

creators of Mathcad, maintain a puzzler page. The software is fantastic and fits better into everyone's budget than Mathematica. Puzzles are assumed to be solved using Mathcad. Often it's OK. I would describe Mathcad as a "program as you write" software. Indeed, one often programs a solution while dotting down a description of a problem. However, they do not pursue the difference between a deduction and a demonstration. The equality sign (=) is often (and I think misleadingly) used in lieu of an approximate equality (). However, once you know what you are doing, this software piece (which also offers symbolic, i.e. exact computation) proves both an outstanding problem solving tool and a source of delightful pastime. The Favorite Mathematical Constants page is truly remarkable.

MacTutor History

Mathematical archives. A most remarkable and well organized site. Plenty of information not all of which is actually historical. Information can be accessed (and, therefore, searched for) in a variety of ways - several indices, chronologies, birthplace map. There is also a page of Famous curves that uses Java extensively.

The Mathematical Association of America

Where else would you look for mathematical resources? Information on their publications - books and periodicals, meetings, etc. The site features MathTrek - a most valuable column by Ivars Peterson with an archive of older issues available online. There are three more columns. Devlin's Angle by Keith Devlin, Dean of Science at Saint Mary's College and the author of several exceptional popular math books. Math Chat by Frank Morgan, professor of mathematics at Williams College. And Cut The Knot by yours truly. The Read This! - an Online Book Review section - is an ever expanding collection of book reviews that highlights the books almost as soon as they get out of print.

American Mathematical Society

An informative page from the foremost mathematical organization. Most valuable is their Digest of popular articles of mathematical interest.

Virtual Library: Mathematics

A place where one can spend hours traveling back and force between various links. Information is organized into several categories: Specialized Fields (there are quite a few specialized fields indeed. Suits any taste), Mathematics Department Web Servers (check to see if any college was missing), General Resources (links to sites all over the world), Math Education and more.

David Eppstein's Home Page

By a professor of Information and Computer Science at the UC Irvine. A very respectable collection of problems, articles and applications available on the Net. Much of it created by the author himself. The page is split into several topics: The Geometry Junkyard, Number Theory, Recreational Mathematics, Combinatorial Game Theory. Each one of these would qualify the page for any list of Net resources. Here you can also find selected links to other personal pages with math content.

National Council of Teachers of Mathematics

In a very short time this site underwent a remarkable transformation. You can find here conference and membership information and online publications with plenty of entertaining math activities. Valuable resources are provided at 4 corners: for teachers, family, leaders, and researchers. The latest version of the NCTM Standards has been conveniently made available online.

National Education Association

A lot of information is available to help make schools and classrooms a better place to study. You'll find a cybertour of schools with established Web sites, learning resources and discussions of innovative approaches to restructuring school learning and modern educational technology, advice and instruction of how to create and use a school Web site. There is also a Recess forum for teachers to share funny moments from their experience. (Remark (3/18/97): my opinion of the site was somewhat shattered when I discovered they actively promote a document that hinges test performance of students on the degree of teachers' unionization. I am ashamed. It's simply too cheap. At the beginning of 2002 I discovered that the document is no longer available. But it was there.)

This is MegaMathematics!

A site from Los Alamos National Laboratory. Hands-on lessons and resources in Knot and Set Theories, Coloring problem, Algorithms and Finite State Machines. The presentation is very substantive but elementary. One might only wish for a longer list of covered topics.

The Math Forum

Originally a fundamental undertaking by Swarthmore College, the Math Forum is now part of the School of Education at Drexel University. Resources for students and teachers. Internet programs and activities. Ask Dr. Math. Teacher2Teacher, Math Tools. Math Fundamentals, Pre-Algebra, Algebra and Geometry Problems of the Week. Topics in Math Education. Dynamic Geometry software experience. The site is the hub of the math education activity on the Web.

Peanut Software for Windows

A Web site by Rick Parris from Phillips Exeter Academy. Candidly, I know little about the Academy, much less about Rick Parris. To boot, the site offers very little in the way of HTML programming. However, one can download from the site several free Windows and DOS programs. All of them are worthy at least some time looking into and figuring out what they can be used for. The simplest one, Winarc, is a collection of games including variations on the Rubik cube. And these I loved immensely. You can choose from 1x1, 2x2, 3x3, 4x4 Rubik cube, Tetrahedron, Pyracube and Dodecahedron. Another program, Winfeed, explores fractal sets (Mandelbrot, Julia, IFS and more). By clicking at a point from the Mandelbrot set you pop up a window with emerging Julia set corresponding to the point. I was really enchanted.

Mathmania

Known also as Erdös for Kids this site offers unsolved problems. Students should not be intimidated by the fact the problems are yet unsolved. There is so much background information you'll learn something anyway. Information is presented in a modern (html and animation) yet very rational form. Separate pages for students and teachers. I especially enjoyed their Knots section. Other sections are devoted to the Graph Theory, Finite State Machines and Network Sorting.

Virtual Polyhedra.

A site by George Hart of Hofstra University. Internet at its best. VRML models of all kinds of polyhedra. About 850 in all. Direction how to create one's own paper models.

Cornell Theory Center Math and Science Gateway

A collection of links to various math resources on Internet. I'll be for ever grateful to the links I discovered there. One was Rick Parris' site, another MuPAD Computer Algebra System. In addition to Mathematics the site actually lists links to other scientific locations: Astronomy, Physics, Computers, Engineering, Museums and more.

Symbolic Sculpture And/Or Mathematics

A very graphical site from the Center for Popularization of Mathematics, University of Wales. The pictures are indeed beautiful including several animated gif files. I modestly hope that my avi files presenting formation of knots and the Moebius Strip are no less entertaining. Among many others there's a visualization of the Gordian Knot. Do I have a different vision of this knot.

Knot A Braid of Links

A page by Canadian Mathematical Community. Every week they present a new selection weaving a braid of math sites on the Net. I think it's quite imaginative to associate a Web page by the Canada's Math Community with a camel instead of a husky. This page provides information on the International Mathematical Olympiads and links to other sites in other countries with IMO websites.

POPMathematics

A list of math related sites maintained by The Mathematics Archives. In their own words: Did you ever wonder what made your teacher get so excited about some topic in Mathematics? On this page, we will try to collect items about Mathematics one of which hopefully may explain this weird behavior.

Abstract Algebra On Line

The site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. It is based on the two books Abstract Algebra and Abstract Algebra, II by by John A. Beachy and William D. Blair. Plenty of information.

On-line Dictionary of Combinatorics

A site maintained by Joe Fields, U. Illinois at Chicago. Combinatorics must be a comprehensive field for the 'A' section includes Affine Hull and Affine Plane and Abelian groups. The author also accepts inquiries for new entries.

Famous Mathematicians

A site from the Department of Mathematics at the University of Venezuela. So far the count stands at 29 biographies of which five are marked as new. Each article is accompanied by a list of sources which is helpful for more extended research.

Quantum

A site from the National Science Teachers Association. Quantum is a bimonthly magazine; partly translated from Russian, partly augmented with articles collected in the USA. I have not read it recently. But if the publisher succeed in preserving its flavor, and if the flavor and quality of the magazine has not changed since I last read many years ago, the magazine could be a valuable resource for a curious high school or college student and for a concerned teacher looking for unusual, supplemental topics. The site maintains The CyberTeaser page with a series of delightful problems. Problem archive is also available.

HAKMEM

I ran into this site while looking for Internet coverage of continued fractions. As far as I understand, it's a collection of facts and documented ideas generated at the AI Lab of M.I.T. under a grant from ARPA. Thus whatever you find there is free for the taking. The collection is very stimulating. What do they think about there? Geometry, Age bra, Calculus, Recurrence relations, Boolean Algebra, Random numbers, Number Theory, Primes, Probability, Automata Theory, Games, Continued fractions (of course), - nah, I just can't enumerate everything.

NRICH project from University of Cambridge that finally joined the fracas. The project aims to promote the fun of maths via the web. They publish a monthly magazine, on the 1st of each month. The magazine, called 'Interact' contains articles, puzzles, interesting problems and challenges that can be used for maths clubs. They also publish solutions from school children. There is a Bulletin Board to pose questions, Ask a Mathematician. However, everyone interested may post an answer. Subscription is free.

maths online

A well organized collection of topics each illustrated by one or more applets. A gallery of topics from introductory Calculus that are suitable for high school students and teachers and college freshmen. The design of the applets and the pages in general is admirably consistent. The authors have even managed to illustrate the notion of derivative with simple but entertaining puzzles.

International Newsletter on the Teaching and Learning of Mathematical Proof

A bimonthly online newsletter with bibliography and Web links related to the various aspects of mathematical proof, teaching and philosophy. Very informative.

  Puzzles.com

A collection of links and original puzzles from Binary Arts including a simulation of their famous Rush Hour sliding blocks puzzle. Three new layouts of the puzzle are added every week.

  Who’s Counting?

A free wheeling column by John Paulos from Temple University. Paulos is the author of Innumeracy, Beyond Numeracy, Mathematician Reads a Newspaper and several other popular books. Always humorous and enjoyable articles of a keen observer of the world around him with a mind sharpened by mathematical practice.

  On-Line Encyclopedia of Integer Sequences

Have you ever come across a number sequence in your work (or play) - such as 1, 1, 2, 3, 6, 11, 23, 47, ... - and wanted to find out what was known about it (or even simply the next term)? This is the place to find out.

Contact person: N. J. A. Sloane

A novel edition of Euclid's Elements

It promises to be the best so far. Among the tools used is The Geometry Applet which is getting improved all the time. I have not checked every Proposition but the ones I saw have been illustrated with this Java applet and the experience was enjoyable. The hypertext cross-references that accompany every proof are absolutely invaluable. The illustration for the Proposition VI.31 (better known as the Pythagorean Theorem). It's quite different from the one I have conjured up.

  Darij Grinberg

A high school student (not for long now), Darij Grinberg already has several publications to his credit. His site offers several ingenious solutions to various geometric problems which are both pleasant and edifying.

  ENCYCLOPEDIA OF TRIANGLE CENTERS, Clark Kimberling

A focal point site for every one interested in Triangle Geometry. The site classfies hundredth of remarkable points, lines, circles related to the triangle. New ones are added on a regular basis. The site is an online expansion of Clark Kimberling's book Triangle Centers and Center Triangles.

 M. de Villiers

A former mathematics teacher and currently a professor of mathematics and math education, Michael de Villiers is a pioneer of using dynamic geometry software in research and instruction. His site offers a remarkable collection of generalizations of classical results obtained with the help of the newly available tools.

 Terry Stickels' site

Author and speaker Terry Stickels has dedicated his life to the pursuit of improving one's mental flexibility and creative problem solving skills . . . and making it fun. His books, calendars, card decks and newspaper columns are filled with fun and challenging puzzles that stretch the minds of even the best thinkers. At the site one can play with samples of Terry's creations and purchase many of his books.

 Age of Puzzles by Serhiy Grabarchuk.

AgeOfPuzzles.com is a web part of a puzzle-book-web project entitled Age of Puzzles. The project makes a comprehensive mosaic of puzzles created by different people in different time and at different places. It's a Colorful Journey through Endless Patterns of Quick Wits!

 International Slide Rule Museum; Mike Konshak, curator

The site displays scans of over 1000 different slide rules and scans of down-loadable slide rule instructions and manuals. It also has a very informative SR encyclopedia as well as other data of interest to slide rule collectors and educators. There are several sets (up to 25) of matching SR's that are available as loaners to teachers wishing to introduce SR's to students.

 BrainBashers.com

Brain teasers, puzzles, optical illusions and games by Kevin Stone, IQ 151, a member of Mensa for over 18 years.

 GameIntellect.com

Well known and unique downloadable games and puzzles, free online Flash and Java games. Some games, for example, Nim, Super Nim, Always 100 have a clear mathematical content and can be used for a meaningful and entertaining practice.

A partner site, Sapphire Games offers even more entertainment, both online and for download.

 visualmathlearning.com

Visual Math Learning - A Free Online Interactive Mathematics Tutorial