 A Small Puzzle  Joe Fields
The site offers a visual proof that the sum of the first n consecutive odd numbers is n^2, the "L"decomposition.
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 Smarandache Notions  J. Castillo
A journal for papers related to the work of Florentin Smarandache, who in the 1960s proposed some new geometries: NonGeometry, CounterProjective Geometry, AntiGeometry, and Paradoxist geometry, which would generalize and unite Euclid, Lobachevsky/Bolyai/Gauss,
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 Software for Algebra and Geometry Experimentation  William Stein et al.
Free and open software for researching and teaching algebra, geometry, number theory, cryptography, and more. SAGE performs group theory and combinatorics (using GAP), symbolic computation and calculus (Maxima), commutative algebra (Singular), number
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 Software (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
An extensive collection of links to software, with abstracts and reviews, organized in four different ways: by platform (Macintosh, MSDOS) and then by subject; interactive texts (using a commercial package such as Mathematica, Maple or Mathkit to interact
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 The solving of Fermat's Last Theorem  Karl Rubin; Ohio State University Distinguished Lecture
Slides for a talk that tells the story of Fermat's Last Theorem for a general audience, including the history of the problem, the story of Andrew Wiles' solution and the excitement surrounding it, and some of the many ideas used in Wiles' proof.
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 Some Interesting references about LLL  François Koeune
Papers on the LLL algorithm and its applications, divided into: Understanding LLL; LLL as a Tool; Latticebased Cryptosystems; Refinements and Variants of LLL; and Interesting links.
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 Some Materials for Discrete Mathematics  E. Lee Lady, University of Hawaii
Files in PDF, DVI, and Postscript format. Contents include: an algorithm for solving linear Diophantine equations, the Chinese remainder theorem, mathematical induction and recursive algorithms, Change of base to Cantor representation, Dijkstra's algorithm
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 sortedsums  D. J. Bernstein
A collection of tools for enumerating small solutions to certain types of Diophantine equations. Includes links to the latest published sortedsums package, and to a paper explaining the algorithms used.
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 S.O.S. Mathematics  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
Internet courses/tutorials to help students do homework, prepare for a test, or get ready for a class. The material presented here reviews the most important results, techniques and formulas in college and precollege mathematics. The learning units are
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 Steve Fulling's Home Page  Stephen A. Fulling
Courses in Foundation Coalition Freshman Calculus, linearity, and other subjects offer objectives, assignments, solutions and reports, exams, and supporting documentation such as books (.pdf, .ps, and .dvi formats). The site also includes access to the
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 Steve Mayer's Web Pages  Steve Mayer
Intended for Mayer's students at Bournemouth & Poole College: syllabi, student web pages, assignments, homework, module notes, review material for the A Level Pure Mathematics curriculum, and more, including resources for the Norwegian students he
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 Steve's Math Site
"Mathematic memorabilia" by a Phoenix, Arizona high school student: binary numbers, factorials, calculations of 2^x from x=1 to x=200+, hand calculations of pi, logarithms and one radian, 3^x from x=1 to x=100+, and more.
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 Studies In Mathematics: Web Discussion  Breindel, Clair; University of Chicago
The University of Chicago's alternative course to calculus. The first quarter is number theory, and the second quarter is geometry and symmetry. When Bryan Clair taught the courses, he covered the history of number systems, different base number systems
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 Sum of squares  Dario Alpern
An applet that decomposes any integer number up to 1000 digits long into a sum of four or less perfect squares.
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 SysteMATHics  Sigurd Andersen
Based on a discipline started by John G. Bennett, systematics is an attempt to understand the meaning implicit in number. The three areas of mathematical exploration covered are triadic numbers; ngrams, number patterns expressed graphically using the
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 TaniyamaShimura Conjecture Proved (Math Chat)  Frank Morgan, MAA Online
A proof of the full TaniyamaShimura conjecture, partly included in Wiles's 1994 proof of Fermat's Last Theorem, was announced last week [June, 1999] at a conference in Park City, Utah, by Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor,
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 Taxicab Numbers  Simon Plouffe
A list of the smallest number that can be expressed as a sum of two positive cubes in n different ways, for n = 1 through 5.
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 Tewodros Amdeberhan's Electronic Headquarters
Tewodros Amdeberhan studies combinatorics, number theory, special functions, partial differential equations, computer algebra, algorithmic proof theory, and harmonic analysis. His articles on these topics, as well as some unpublished musings, are available
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 Things Impossible  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Essays on impossible things, including trisecting an angle, doubling a cube, squaring a circle, moving pegs five places in one direction (via checkerjumps), finding the center of a given circle with the straightedge alone, representing the square root
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 Three Years of Computing: Final Report On The Palindrome Quest  John Walker
A 1990 report on computations on the 196 problem: "Pick a number. Reverse its digits and add the resulting number to the original number. If the result isn't a palindrome, repeat the process. Do all numbers in base 10 eventually become palindromes through
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 Thue Equations  Clemens Heuberger
A special family of equations F(X,Y) = m, where F is an irreducible homogeneous form of degree n at least 3 and m is a nonzero integer. With a list of special cases that have been solved.
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 Tom's Mathematical Things  Tom Womack
Links to many elliptic curve subjects, including curves of given rank and small conductor, Mordell curves of large rank, and interesting torsion groups, from a secondyear postgraduate mathematician at the University of
Nottingham, supervised by John
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 Tomás Oliveira e Silva
From an assistant professor in the Electronics and Telecommunications Department of the University of Aveiro, Portugal. On the Collatz problem: maximum number tested (N): 91·2^50 = 102456891522678784.
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 Topics in Arithmetic and Elementary Mathematics  E. Lee Lady; University of Hawaii
Materials used in a university course for prospective elementary school teachers, to teach them how to be interested in mathematics. Materials are in PDF and DVI, and include: representing numbers in other bases, divisibility tests, periodic decimal expansions,
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 Trimathlon
Site centered around a book featuring activities from number theory and geometry beyond the realm of the typical school curriculum. The site features a discussion forum, a sample online game (with others promised), and a periodic puzzler with hint.
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 Understanding Mathematics: A study guide  Peter Alfeld, University of Utah
A resource and source of encouragement, with questions and Alfeld's comments (Are you frustrated working through heaps of meaningless problems that are all alike? Does the thought "I can look it up if I have to" occur to you frequently? Do you feel that
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 University of South Carolina High School Math Contests  David Sumner
Problems from the University of South Carolina (USC) High School Math Contests, since 1994. Walk step by step through illustrated solutions to each problem using the "next step" button. The delivery of questions is designed for competitive timing. Also,
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 Unsolved Problems in Number Theory, Logic, and Cryptography  Tim Roberts
This site "concentrates only on problems which are easily understandable to the amateur.... explainable on a single screen (perhaps 200 words), using simple terminology." Read brief descriptions of open problems such as the Chromatic Number, the Collatz
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 Vasiliu Lucilius Homepage  Vasiliu Lucilius
Lucilius offers books of his research work in mathematics and mathematical physics.
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 VeryPrime  Mathematical Search Engine  Marian Olejar, Jr.
Search engine based on text analysis and focused on mathematics and math terms. Includes a dictionary.
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 Victor Shoup's Home Page
Download research papers on cryptographic protocols and on algorithms for solving problems in the area of number theory and algebra. The Courant Institute researcher freely offers a standard for publickey encryption, a simple LaTeX class for preparing
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 Video Lectures in Mathematics  Jerry Farlow
An online pinboard gathering thousands of visual links to a broad range of math videos. Categories include applications of math; famous mathematicians; math education; math humor; math on TV, movies; STEM math initiatives; and "instructional: K12." Farlow
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 Vignettes on automorphic forms, representations, Lfunctions, and number theory  Paul Garrett
Shoft downloadable "vignettes" in postscript format, and some with overviews in html. Also some vignettes on functional analysis.
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 Vi Hart  Vi Hart
Blog, videos of math "doodling," instructions for slicing food mathematically, and more from the selfdescribed recreational mathemusician who considers math a hobby, with "special interests in symmetry, polyhedra, and surreal complexity. This usually
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 The Virtual High School
The Virtual High School project is a collaborative of high schools from around the country. In exchange for contributing a small amount of teaching time, a school in the collaborative can offer its students webbased courses ranging from advanced academic
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 Virtual Math Tutor
A new problem just about every day since October, 2010, with discussion and hints to follow.
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 A Virtual SpaceTime Travel Machine  JeanFrançois Colonna, École Polytechnique
Still Pictures and MPEG Animations (Images Fixes et Animations MPEG): Art and Science, Artistic Creation, Astrophysics, Celestial Mechanics, Deterministic Chaos, Deterministic Fractal Geometry, Fluid Mechanics, From the Infinitely Small to the Infinitely
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 Visible Euclidean Algorithm: finding greatest common divisors  Paul Garrett
Enter two positive integers, and click the button to see the operations of the Euclidean Algorithm.
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 Waring Experiments  Ivars Peterson (MathLand)
You might suspect that, at some point, four squares would no longer be enough to express a given whole number. This reasonable supposition was overturned in seventeenth century, when Pierre de Fermat proved that every positive whole number can be expressed
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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 1+1?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about what 1+1 is in decimal and binary, how to prove it with Peanos Postulates, as well as a false proof that 1 + 1 = 1.
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 What is Mod?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about modular arithmetic, including the method of casting out nines.
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 Wiles' proof of Fermat's Last Theorem  Paul Hewitt; University of Toledo
An overview, following Glenn Stevens' article in Modular Forms and Fermat's Last Theorem (SpringerVerlag, 1997). Notes from a series of three 1998 lectures.
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 Wiles, Ribet, ShimuraTaniyamaWeil and Fermat's Last Theorem  Dept. of Mathematics and Statistics, The University at Albany
An archive of FLT material from conferences, lecture, meetings, newsgroups, and Web sites. Much of the material that seeded this archive was copied from the former gopher archive pertaining to "Fermat's Last Theorem"at emath.ams.org.
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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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 WIMS (WWW Interactive Mathematics Server)  Université de Nice  Sophia Antipolis
Interactive mathematical applications, also available in French, with documentation. The server's exercises and programs are designed to find a polynomial with given values; find the Taylor expansion of a function; find a polynomial from its curve; given
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 Wireless Philosophy
Free videos on the practice of philosophy — teaching viewers how to develop critical thinking skills and do philosophy, rather than simply learn what philosophers have thought. See, in particular, Wi Phi's categories of videos on the philosophy
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 The Wolfram Demonstrations Project  Wolfram Research, Inc.
A web collection of freely available demonstrations in math, science, and many other areas. Interact with the demonstrations directly in your browser. Each Demonstration contains a set of related links to sites such as MathWorld, The Wolfram Functions
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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 of Words, Numbers, and Notes  Mike Keith
Mostly original diversions in the areas of mathematics, word play, and music, including a Cadaeic Cadenza, a long pi mnemonic. Also, Ailihphilia (literature and word play) and Scitamatics (mathematical diversions): the recreational study of words, numbers
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