 Dancing with Mathematics: Mathematics Related to Contra Dancing  Larry Copes
The mathematics of contra dancing. The essay has three sections  What's contra dancing? What mathematics is in contra dancing? and More abstractly  and links to figures illustrating contra dance symmetries and geometric transformations.
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 David Bruce Wilson
David Bruce Wilson researches probability, combinatorics, and theoretical computer science. Abstracts of his articles on these subjects are available on the web and may be downloaded in PostScript or .dvi formats. Software available for download includes
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 David Marius Bressoud
David Bressoud has written several undergraduate textbooks that use physics and the history of mathematics to motivate the study of multivariable calculus, number theory, real analysis. Other books include A Course in Computational Number Theory and
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 Dennis Stanton
Dennis Stanton is a professor at the University of Minnesota studying combinatorics and hypergeometric functions. Many of his papers are available online in PostScript and PDF formats. There are also exams and solutions from previous classes, and a complete
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 DIMACS Research and Education Institute (DREI)  Rutgers University
An institute from the Center for Discrete Mathematics and Theoretical Computer Science which takes the approach that research and education should work handinhand, that collaborations between researchers and educators are formed by understanding each
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 Discreta  Betten, Haberberger, Laue, Wassermann
A program to construct tdesigns with a prescribed automorphism group. Includes an explanation of the construction of tdesigns, a tutorial, a database of design parameter sets, publications, and source code to download.
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 Discrete and Computational Geometry  SpringerVerlag
An international journal of mathematics and computer science that accepts research articles of high quality in discrete geometry and on the design and analysis of geometric algorithms; more specifically, DCG publishes papers on such topics as configurations
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 The Discrete Mathematics Project  Dominic Peressini; University of Colorado at Boulder
Archived resources from the collaboration of the UC Boulder School of Education and Department of Applied Mathematics. Activities sketch goals, abstracts, brief problem statements, instructor suggestions, suggestions for curriculum integration and further
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 Discrete Mathematics & Theoretical Computer Science (DMTCS): An Electronic Journal  Jens Gustedt
DMTCS is an electronic journal published by the Maison de l'Informatique et des Mathématiques Discrètes, MIMD. It is a peerreviewed publication devoted to rapid publication of innovative research which covers discrete mathematics and theoretical computer
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 Discrete Math Problem of the Week (PoW)  Math Forum
Discrete math problems from a variety of sources, including textbooks, math contests, NCTM books, and puzzle books, and reallife situations, designed to reflect different levels of difficulty. From 1999 until 2002, this service challenged students with
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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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 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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 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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 Ejercicios y Problemas de Matemática  Pablo Mateus
Ejercicios y problemas de números (natural, entero, racional, real), estadística, ecuaciones, funciones, análisis combinatorio, probabilidad, trigonometria, geometria, y más. También, um glosario y consejo sobre pruebas
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 Electronic Journal of Combinatorics  McKay, Wilf, Eds.
A refereed allelectronic journal that welcomes papers in all branches of discrete mathematics, including all kinds of combinatorics, graph theory, discrete algorithms, etc. See also The Electronic Journal of Combinatorics and The World Combinatorics
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 Electronic Journals in Mathematics  Dept. of Mathematics, Univ. at Albany
Links to electronic journals for mathematics, and those publishing both electronically and on paper. Examples: The Electronic Journal of Combinatorics; The Electronic Journal of Differential Equations; Electronic Journal of Probability and Electronic
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 Encyclopedia of Combinatorial Structures  Virginie Collette; INRIA
A site designed to be similar to Sloane's Encyclopedia of Integer Sequences but with an emphasis on sequences that arise in the context of decomposable combinatorial structures. Like the EIS, the database is searchable by the first terms in the sequence,
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 Enumeration of the Binary Trees (Catalan Numbers)  Ivan Galkin
For each number of nodes, n, there is a certain number of possible binary tree configurations. These numbers form a sequence of integers with respect to n. A useful way to describe an integer sequence is to construct a generating function...
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 The Erdös Number Project  Jerry Grossman
Paul Erdos wrote hundreds of mathematical research papers in many different areas, many in collaboration with others. His Erdos number is 0. Erdos's coauthors have Erdos number 1. People other than Erdos who have written a joint paper with someone with
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 Erich's Combinatorial Geometry Page  Erich Friedman
Famous and infamous problems with diagrams and some solutions and proofs. Includes: tree planting problems; circles through points; maximizing squares; triangulating squares; triangulating triangles; lines avoiding squares; lines avoiding points; points
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 Erich's Packing Center  Erich Friedman
A huge collection of packing problems, each explained with graphics. 2D examples include Triangles in Squares, Circles in Squares, Squares in Squares, Triangles in Triangles, Circles in Triangles, Squares in Triangles, Triangles in Circles, Circles in
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 A Fair Deal For Housemates  Ivars Peterson (MathTrek)
Four friends move into a house and find they must choose among four rooms of different size and quality. Instead of sharing the rent equally, they decide to divide the total so that each person ends up satisfied with his or her combination of room and
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 The Fair Division Calculator  Francis Su
An interactive Java applet designed to help you determine how to divide among n people: a desirable object (such as a cake); an undesirable object (such as a set of chores); or a set of indivisible objects (rooms, desirable) with payments (rent, undesirable).
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 Fair Shares (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The birthday party is over, and one chunk of thickly frosted, richly decorated cake is uneaten. Your mother insists that you and your sister slice the cake into two equal pieces, so that she doesn't have to listen to you fight over which is bigger. What
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 Focus on Student Practice  Suzanne Alejandre
Article about how students worked on the Problem of the Week (PoW) "Wooden Legs" in a way that developed the Common Core State Standards (CCSS) Mathematical Practice of "making sense of problems and persevering in solving them." This article, originally
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 Folding Maps  Ivars Peterson (MathTrek)
Erik D. Demaine of the computer science department at the University of Waterloo
in Ontario and his coworkers have developed an efficient method for recognizing when a creased sheet is foldable into a flat package (results are reported in an unpublished
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 Formulas for fairness  Ivars Peterson  Science News Online
Applying the math of cake cutting to conflict resolution: researchers turn to the mathematics of cake cutting and point allocation to develop improved methods for people to use to settle disputes.
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 Four Numerical Triangles in Nexus  Len Smiley
Three wellknown combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that
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 Fragments of the Past  Ivars Peterson (MathLand)
Historians of mathematics now generally agree that scholars in China, India, and the Islamic world produced remarkably sophisticated mathematics between the fifth and the fifteenth centuries. However, most would probably still argue that Europeans in
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 Frank Garvan
Frank Garvan is a mathematics professor at the University of Florida. His combinatorics research articles are available for download in PostScript and .dvi formats. A Maple package for qseries may also be downloaded. One may also find the syllabi
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 Frédéric Chyzak's Mgfun Project
Mgfun is a group of Maple packages intended for calculations with multivariate generating functions, in particular for their symbolic summation
and integration, and for the proof of special function and combinatorial identities. These packages include
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 Freaky Links  Cut the Knot!, Alexander Bogomolny with William A. McWorter Jr.
Mathematics impinges on itself and the sciences in unexpected and bizarre ways. This page is a small illustration of this phenomenon, taking up recreational mathematics and the game of Chinese checkers, the strategy game called Hex, quasigroups, and block
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 Frederic Chyzak
Frederic Chyzak researches combinatorics and computer algebra, specifically holonomic functions. His thesis and other articles are available as abstracts and as PostScript files. Slides for a series of talks on holonomic functions and computer algebra
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 From Polychords to Polya: Adventures in Musical Combinatorics  Mike Keith
A book that explores the various connections between the basic musical building blocks  chords, scales, and rhythms  and the area of mathematics known as combinatorics, which is concerned with counting and classifying configurations of objects. Questions
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 Front for the Mathematics ArXiv  Univ. of California, Davis
U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex
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 The Fruit Game
An interactive game in which players take turns removing fruit from the table according to the rules. The player who removes the last fruit from the table loses. Based on the mathematical puzzler known as the game of Nim.
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 Frustration Solitaire  Doyle, Grinstead, Snell
A paper on the rankderangement problem, which asks for the number of permutations of a deck of cards such that each card is replaced by a card of a different rank, and which arises when computing the probability of winning the game of 'frustration solitaire'.
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 The Game of Go  JeanClaude Chetrit
A page for Go players interested in mathematics or abstract reasoning. How many static positions exist and how many are legal? This is purely an exercise in counting (combinatorics). See also Chetrit's conjectures about playing Go on a 2 by 2 board and
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 gamepuzzles: for the joy of thinking  Kadon Enterprises, Inc.
Board games and the like: Combinatorial puzzles, tessellations, math manipulatives for all grades. Handson sets and some online exemplars of polyominoes, polyforms, color tilings. Source for classics like Archimedes' Square (Stomachion), Penrose tiles,
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 Giacomo Lorenzoni
Download the author's programs, which include ThermalWall, for calculating fundamental dynamic thermal characteristics of walls composed of multiple homogeneous layers; and PEEI, for the numerical solution of systems of partial differential equations.
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 Gordon Royle's Homepage: Research  Gordon Royle
Catalogues and tables of interesting combinatorial objects: small graphs, cubic graphs, symmetric cubic graphs, vertextransitive graphs, Cayley graphs (by group), vertextransitive cubic graphs, cubic cages and higher valency cages, planar graphs, cubic
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 Gowers's Weblog  Timothy Gowers
Blog by a Cambridge University professor interested in analysis, combinatorics, arithmetic combinatorics, and "general questions about mathematics, and how it is discovered and transmitted  hence this blog." Posts, which date back to September, 2007
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 Groups & Graphs Home Page  Bill Kocay
A software package for graphs, digraphs, combinatorial designs, and their automorphism groups. Features include automorphism group computation; graph certificate which identifies a graph uniquely up to isomorphism; Hamiltonian cycles; planarity test and
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 The Hadamard Maximal Determinant Problem  Will Orrick, Bruce Solomon
The site lists the largest known determinants of {1,1} matrices. It also has links to other online
sources of large determinant matrices and references to the literature.
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 Handbook of Combinatorial Designs  CRC Press
Home page for the Handbook. Contains the Table of Contents (postscript and text); Acknowledgments; New Results that have appeared since the Handbook was sent to press; Errata; and Ordering Information.
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 Handson Math: Activities for the Elementary Classroom  Janine Parker
Lesson plans for children in grades one through six about topology, number patterns, and geometry. Handouts for each lesson may be downloaded in PostScript form or as GIF files, and a zipped DOS program to display Platonic solids, Archimedean solids,
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 HarvardMIT Math Tournament  Early, Owen
The HarvardMIT Math Tournament is an annual math tournament for high school students. Categories of tests typically include algebra, calculus, combinatorics (formerly "advanced topics"), geometry, general, oral, team, and guts; minievents include Buzz
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 Helmut Prodinger
Helmut Prodinger researches analysis of algorithms, combinatorics, tree enumeration, and number theory. Many of his papers on these subjects are available online in PostScript, .dvi, and/ or TeX form.
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 Herbert Wilf
Herbert Wilf is a combinatorialist. The entire text of his books generatingfunctionology, A = B, and Algorithms and Complexity may be downloaded in PDF format, as may his "East Side, West Side" lecture notes on combinatorial objects and Maple programming.
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 iCoachMath.com  HighPoints Learning, Inc.
iCoachMath.com coaches students online; and provides teachers with student performance reports, customized test papers, and math resources such as lesson plans aligned to state and national standards. The site freely offers an illustrated dictionary of
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