 A 27Vertex Graph That Is VertexTransitive and EdgeTransitive But Not 1Transitive [PDF]  Peter Doyle
A paper describing a 27vertex graph that is vertextransitive and edgetransitive but not 1transitive. While all vertices and edges of the graph are similar, there are no edgereversing automorphisms. PostScript, source, and PDF picture are available
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 Adventures in the MathZone  Ivars Peterson (MathTrek)
Ivars Peterson and his wife, Nancy Henderson, have written "a book that introduces children to a variety of ideas also of interest to today's mathematicians: knots, map coloring, Möbius strips and topology, prime numbers, chaos, fractals, and more. Our
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 Algorithms Project  Institut National de Recherche en Informatique et en Automatique (INRIA)
A small international group of people with interests in design and analysis of algorithms, computer algebra, combinatorial analysis and asymptotics. It aims at general methods in combinatorics and analysis, with which classes of problems can be treated
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 Application of Rayleigh's ShortCut Method to Polya's Recurrence Problem [PDF]  Peter Doyle
Doyle's Ph.D. thesis at Dartmouth College, June 1982. The goals of the presentation are to explain why Polya's theorem is true and to develop techniques for applying Rayleigh's method. The main results make sense of the notion that if two graphs look
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 Arbeitsgruppe Bachem/Schrader  University of Köln
A working group of the Center for Parallel Computing (ZPR) at Köln. Site includes a list of members and contact address; informative writeups on its projects, some in English. Topics include: Basic Research (meaning "pure" as opposed to "applied");
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 Arnd Roth  Arnd Roth, Institute for Theoretical Physics, Heidelberg, Germany
Arnd Roth studies computational physics and neuroscience. This page provides documentation and code for related Mathematica notebooks, and a notebook for the Knight's Tour chess problem, available online. Also links to abstracts or text of many of Roth's
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 Averting Instant Insanity  Ivars Peterson (MathTrek)
Once called "The Great Tantalizer," the puzzle looks innocuous and sounds quite simple. It consists of a set of four cubes with one of four colors on each of their six faces. Your goal is to arrange the four cubes in a row so that all four colors appear
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 The Best Two Points in a Square (Math Chat)  Frank Morgan, MAA Online
Solution to the challenge: Where do you think you should you place two points in a unit square to minimize the average distance in the square to the nearest of the two points? Computer calculations by Al Zimmermann yield configurations of 211 points
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 BHOSLIB: Benchmarks with Hidden Optimum Solutions for Graph Problems  Ke Xu
Benchmark graphs for testing several NPhard graph algorithms: maximum clique, maximum independent set, minimum vertex cover and vertex coloring. All instances are expressed in DIMACS format and are planted with hidden optimum solutions.
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 Books: Professional & Technical: Professional Science: Mathematics  Amazon.com
Browse bestselling math books from the Professional and Technical Bookstore at Amazon.com, in such categories as Applied; Chaos & Systems; Geometry & Topology; Mathematical Analysis; Mathematical Physics; Number Systems; Pure Mathematics; Transformations;
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 Brendan McKay
Software includes nauty, a program for computing automorphism groups of graphs and digraphs, which can also produce a canonical labelling; and plantri, a program for generating planar triangulations. Also, skeptical treatment of claims made of miraculous
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 Calculating Swarms  Ivars Peterson  Science News Online
Ant teamwork suggests models for computing faster and organizing better. Astonishing feats of teamwork emerge from a large number of unsupervised individuals following a few simple rules. This sort of selforganizing cooperative behavior among ants, bees,
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 Candy for Everyone  Ivars Peterson (MathTrek)
Several students are sitting in a circle. Each student has an even (though not necessarily the same) number of wrapped pieces of candy. On a signal, each student passes half of his or her trove to the student on his or her right. Between signals, the
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 Clickmazes  Gilbert, Mitchell
An extensive collection of interactive puzzles and mazes organized in the following categories: Maze gallery; Attic gallery; Maze of Life; HexaRoll; Oskar's fourbit mazes; 2D tilt mazes; Colourzone mazes; 3D tilt mazes; Tilt puzzles; NEWS and RULES;
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 The Clique Algorithm  Ashay Dharwadker
A polynomialtime algorithm for finding maximal cliques in a graph with new bounds on Ramsey numbers.
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 Colorful Mathematics  Claude Laflamme
An educational software series presenting advanced mathematical concepts to K12 students in a gameoriented approach. The five games offered use simple coloring and/or drawing techniques to illustrate mathematical concepts from graph theory. Downloadable
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 Coloring Penrose Tiles  Ivars Peterson (MathTrek)
One set of Penrose tilings consists of a pair of diamondshaped figuresone fat and one skinny. Attempts to color such Penrose diamond tilings led some people to conjecture that three colors suffice. Now, mathematicians Tom Sibley of Saint John's University
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 Coloring (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on coloring problems, including the Four Color Theorem and other graph coloring problems.
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 Combinatorics and Graph Theory  Department of Mathematics, Umeå University, Sweden
Home page of the Combinatorics Group. Members and research projects, seminars, archives of downloadable software, combinatorial and graph theoretical data, and preprints.
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 Combinatorics, Probability & Computing  Cambridge University Press
Now published bimonthly, the journal covers combinatorics, probability theory, and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial
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 Combinatorics Research Group  Pure Maths Department, The Open University
A group interested in graph theory, design theory, the history of combinatorics, and combinatorial computing. The Group runs the Open University Winter Combinatorics Meeting near the end of January each year.
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 A compendium of NP optimization problems  Crescenzi & Kann
A continuously updated catalog of approximability results for NP optimization problems. Because no NPcomplete problem can be solved in polynomial time (unless P=NP), many approximability results (both positive and negative) of NPhard optimization problems
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 Computer Lab Courseware  University of Toronto
Courseware to help in the teaching of various mathematical concepts. Most is made up of Mathematica notebooks and packages, but some consists of C programs written to run under XWindows. A lab manual in TeX beginning with an introduction to UNIX and
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 Counting Hamilton Cycles in Product Graphs  Frans Faase
Exploration of Hamilton paths through a program which draws a snake that starts at one place in a box, and then extends itself until it cannot go further, after which it shrinks again, to seek another path. The author coded these snake programs in Fortran,
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 A Course on the Web Graph  Anthony Bonato
A comprehensive introduction to stateoftheart research on the applications of graph theory to realworld networks such as the web graph. It is the first mathematically rigorous textbook discussing both models of the web graph and algorithms for searching
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 Cutting Corners  Ivars Peterson (MathLand)
Go to just about any college campus or public park and you're bound to see two kinds of trails: "official" paths defined by paved or gravel surfaces and "unofficial" routes trodden into the grass or dirt marking where pedestrians have preferred to walk
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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 Sumner's Home Page  David Sumner
Study guides, exams, quizzes, problem sets, exam review materials, utilities, programs and simulations, syllabi, and other materials for courses such as calculus, sequences and series, graph theory, number theory and cryptography, and probability. The
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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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 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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 discretemath  Math Forum
A discussion group for subject matter concerning teaching and researching of discrete mathematics at all levels. It began as a closed list for the researchers and educators who participated in the Rutgers University Discrete Math 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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 Discussiones Mathematicae  Borowiecki; Technical University of Zielona Góra, Poland
Four journals: Differential Inclusions, Control and Optimization; General Algebra and Applications; Graph Theory; and Probability and Statistics. Information for each journal includes a general description, subscription information, list of editors,
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 Discussiones Mathematicae Graph Theory  Borowiecki; Technical University of Zielona Góra, Poland
The journal publishes articles in English on all aspects of graph theory, especially concerning: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties,
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 The Distribution of the Knight  the Theoretical Research Institute
For every given starting point in the knight's tour problem, evaluate every
possible path that visits each square exactly once, and then count how many
solutions exist. Illustrations and calculations of the distribution of solutions
and dead ends across
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 Division by Three [PDF]  John Conway, Peter Doyle
A formal proof that it is possible to divide by three. This assertion is easy to prove using the axiom of choice, but becomes a much more difficult problem if the axiom of choice is not allowed (as is the case here). From this proof, and the much simpler
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 Elementary Math Enrichment  Beth Schaubroeck
Free mathematics enrichment materials for accelerated 4th and 5th graders. The 70 lessons, grouped into 12 different units, include solutions and teacher guides: Ancient Mathematics (Mayan math, in base 20; and Egyptian math, which lacks zero), Baseball
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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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 Five Triangles mathematics blog
This blog, which dates back to April, 2012, posts problems for middle and junior high school students. Topics have ranged from ratios and fractions to area and paths to quadratic equations and linear equations.
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 Four Coloring Maps  Mario Stefanutti
Personal notes and ideas from a computer software engineer in pursuit of a "very easy pencil and paper proof of the four color problem." Posts, which date back to January, 2011, have included "Four color theorem: slow motion maps" and "Counting maps."
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 FourColor Map Theorem  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about the fourcolor map theorem, such as explanations, proofs, and extensions to higher dimensions and to the mobius strip.
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 Four Colors Suffice: How the Map Problem Was Solved  Robin Wilson; Princeton University Press
"On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in historyone that would confound thousands of puzzlers for more than a century. This is the
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 The Four Color Theorem  Robertson, Sanders, Seymour, Thomas; Georgia Tech
A brief summary of a new proof of the Four Color Theorem, with a fourcoloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas, illustrated using a map of the United States. Contents: History; Why a new proof?; Outline
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 Four Travelers Problem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Four roads on a plane, each a straight line, are oriented so that no two are parallel and no three pass through the same point. A traveler walks along each road at a constant speed. The speeds, however, may not be the same. Traveler 1 meets Travelers
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 Fun, Puzzles, Travel  Paul Bourke
Brain twisters, arranged by approximate level, and designed for the most part to require no particularly advanced mathematical skills. Illusions include impossible triangle, MullerLyer, bad box, and Colours.
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 Games on Graphs (MegaMath)  Nancy Casey; Los Alamos National Laboratory
Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problemsolving situations and communicate the reasoning used in solving these problems. Graphs, stories and games provide
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 Geometry of Fullerenes  Slavik Jablan, Mathematical Institute, Belgrade
Fullerenes (Buckminster Fuller) are considered from the points of view of geometry, graph theory and knot theory. Contents: Introduction; General fullerenes, graphs, symmetry and isomers; 5/6 fullerenes; Knot theory and fullerenes; "Perfect" fullerenes;
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