 Algebra Through Problem Solving  Hillman, Alexanderson
A nontraditional Algebra text (high school and early college levels) placed on the Web by the Science Education Team at Los Alamos National Laboratory. Browse it on the Web or download a PDF version. Chapter headings include: The Pascal Triangle; The
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 AMOF: The Amazing Mathematical Object Factory  Frank Ruskey
Combinatorial objects are everywhere. How many ways are there to make change for $1 using unlimited numbers of coins of all denominations? Each way is a combinatorial object. AMOF is part encyclopedia and part calculator, a teaching tool that generates
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 Card Games  John McLeod
Rules and information, including probabilities, about card and tile games. Indices by alphabetical order, classified by mechanism and by objective (including a list of children's games), arranged by country and the types of cards. Also, commercial, solitaire,
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 Changes of Mathematical State  Ivars Peterson  Science News Online
A discussion of constraintsatisfaction problems, more specifically the logic puzzle in theoretical computer science known as the satisfiability (SAT) problem (e.g. working out a seating plan), the current state of research on computational "phase transitions,"
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 Classic Problems  Math Forum; Ask Dr. Math FAQ
Classic problems from the Ask Dr. Math FAQ (Frequently Asked Questions) files, including: age word problems, birthday probability, boy or girl?, camel and bananas, coin problems, doubling pennies, grazing animals, liars and truthtellers, the missing dollar,
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 Conteúdos Digitais em Matemática para o Ensino Médio  Kaleff, Ana Maria; and Humberto José Bortolossi  Universidade Federal Fluminense
Educational Java applets and lesson plans in Portuguese. Topics include real functions, algebra, permutations, polygons, tangrams, conic sections, solids of revolution, and other two and threedimensional geometry, which includes the Englishlanguage
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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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 Disorder in the Deck  Ivars Peterson (MathTrek)
About 30 years ago, tournament bridge players started using computershuffled rather than handshuffled decks. Almost immediately, there was an outcry protesting the apparently wild fluctuations in the distribution of cards of different suits in computerdealt
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 An essay on patterns in musical composition, transformation, mathematical groups and the nature of musical substance  Bill Hammel
An article on music composition and history, with a discussion of the organizing principles of various musical scales as they affect musical composition and links to related sites.
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 The Expected Number of Rising Sequences After a Shuffle [PDF]  Peter Doyle
A paper taking up Brad Mann's derivation of his simple expression for the expected number of rising sequences in a deck after a shuffle, which involved lengthy gymnastics with binomial coefficients. Doyle provides a short derivation. A PostScript file
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 Family or Child First?  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
In a twochild family, one child is a boy. What is the probability that the other child is a girl? Discusses the difference between choosing the child first and choosing the family first, and why they're mathematically different.
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 The Family Photo and Counting on One Hand (Math Chat)  Frank Morgan; Christian Science Monitor
From Norman Goodwin: A photographer wants to line up the 11 members of the Goodwin family from shortest to tallest (left to right), starting with anyone, adding someone else on either side, and continuing by always adding someone next to those already
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 Fast Food Combinations  Math Forum, Ask Dr. Math FAQ
How many possible combinations can be made from a special menu of eight items?
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 A Formula for C(n,k)  Jay's Corner
We would like to obtain a formula to calculate C(n,k) without writing down Pascal's triangle (although, to be honest, it is generally faster to write down Pascal's triangle than it is to use this formula, especially if you need a number of these binomial
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 Google Calculator
Google's calculator feature evaluates math expressions. The google.com and the Google Toolbar search boxes now handle queries such as: 56*78, half a cup in teaspoons, (G * mass of earth)/(radius of earth ^ 2), and 1.21 GW / 88 mph. Google provides instructions
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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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 How Many Handshakes?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions such as "There are 40 people in a room. They shake each other's hands once and only once...."
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 How to Play Fair With Loaded Dice (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: For some reason you need a standard fair die (with the numbers from 1 to 6 on the six faces). All you have is an unfair "loaded" die. How can you use the loaded die to fairly choose random numbers from 1 to 6? ... Roll the die
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 Hummer's Mind Reader  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Java simulation of a magic trick invented in the 1950s by the magician Bob Hummer. Choose one of three coins. Swap the other two, then swap as many pairs as you like. When you're done, the computer will announce your selection. The explanation includes
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 Institute of Mathematical Geography (IMaGe)  Sandra Lach Arlinghaus
Archives of SOLSTICE: An Electronic Journal of Geography and Mathematics. Chapters, notes, and book reviews dating from 1986, in variously jpg, pdf, html, or simple text formats. Sample articles include "Extension of Barr's Problem to the Set of Platonic
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 Juggling Drops and Descents (Organic Mathematics Proceedings)  Joe Buhler, Ron Graham
A discussion of the permutations f of the integers Z satisfying $f(x) \ge x$, with applications to juggling patterns. Demonstrations are included and the site includes QuickTime movies.
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 Magic Cube Generator  Dwane H. Campbell, Keith A. Campbell
This site offers a generator for magic squares, cubes, and hypercubes, along with history, overview of basic concepts, and statistics, and downloads and references. The authors focus primarily on a set of 8 by 8 by 8 magic cubes that are often called
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 Magician's Solution From Math Olympiad (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge from the 2000 International Math Olympiad: A magician has one hundred cards numbered 1 to 100. He puts them into three boxes, a red one, a white one and a blue one, so that each box contains at least one card. A member of the audience
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 Magic of Perfect Shuffles  Ivars Peterson (MathTrek)
S. Brent Morris likes to say that he's the only person with a doctorate in card shuffling. A mathematician at the National Security Agency (the world's largest employer of mathematicians) in Fort Meade, MD, he is also a showman, specializing in card tricks.
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 Mathemagic Activities  Cyberspace Middle School (CMS)/Larry Dennis, Florida State University.
Tricks based on simple mathematics, but which to those who don't understand the mathematics may seem magical. Since these tricks are based on mathematics, they are relatively easy to do and are pretty close to foolproof. Book recommendations and trick
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 Mathematical Induction  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A brief discussion of mathematical induction, with proof, and other examples also proven by mathematical induction, including: Splitting piles; Continued Fractions; Linear Functions; Groups of Permutations; Inequality between arithmetic and geometric
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 Mathematical Problems  Torsten Sillke
Some in German, most in English. Topics include graph theory, number theory, combinatorics (enumerations), geometry, algorithms and complexity, recreational mathematics, tiling and packing, dissections, probability, algebra, analysis. Also links to "MathNews"
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 Math Made Simple  Tom Henry
Videos that explain math concepts and then provide stepbystep solutions to example questions. Lessons cover prealgebra, algebra, trigonometry, exponents and logarithms, permutations and combinations, sequences and series, coordinate geometry. Each
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 Nonsexist Solution of the Menage Problem  Bogart, Doyle
A paper that appeared in the American Mathematical Monthly. The ménage problem asks for the number of ways of seating couples at a circular table, with men and women alternating, so that no one sits next to his or her partner. The paper presents
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 Now College  Online Math Courses and Tutorials  Now International
An online learning company. Products are designed with video instruction, "realtime" whiteboard handwriting, graphics, animations, graphs, tables, and math notation. A complete highschool math program is planned. Currently, courses in trigonometry
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 Online Resources  Georgia Tech School of Math
Syllabi, course notes, problems, and Maple worksheets for single and multivariable calculus, linear algebra, statistics, and a Math for Management course (statistics, probability, sets, and some calculus). The site also contains sample exams for calculus
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 On the Evolution of Islands  Doyle, Mallows, Orlitsky, Shepp
On islands and seas: an island is a maximal set of adjacent marked cells in a ring or row; a sea is a maximal set of adjacent unmarked cells. An inductive proof and a countingargument proof. A paper that appeared in the Israel Journal of Mathematics.
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 On the Puzzles with polyhedra and numbers  Jorge Rezende
Several articles in PDF format, with related links: one on a set of didactic puzzles published by the Portuguese Mathematical Society (SPM); "Jogos com poliedros e permutações", an article in Portuguese describing puzzles with polyhedra
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 Party Games  Ivars Peterson (MathTrek)
You're one of six people at a dinner party. You would undoubtedly find that the dinner party includes either a group of at least three people who all know one another or a group of at least three people who don't know one another. The reason for this
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 Pentomino Relationships  Adrian Smith
The site describes how pentominoes (twelve pieces of wood, each a different shape and each made of five cubes) fit together into rectangles or cuboids, as well as the subsequent challenge of finding as many other solutions as possible from the one just
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 Phenomenological Pizza (SMILE)  Robert Foote, Disney Magnet School
A lesson for the middle grades designed to teach students to calculate the area of a circle, find how many twotopping pizzas can be made using 14 toppings, and determine cost per square inch. From the Geometry and Measurement section of a collection
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 PowerMath: the Virtual Reality Mathematics Teacher  Alexandre Menezes, PowerClassroom Software, LLC
Modular, studentcentered instruction software for Windows, based on visualization of mathematical ideas. Available in licenses from one to unlimited users. Demo CD available. Pricing and topics listed on web site.
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 Probability in the Real World  Math Forum, Ask Dr. Math FAQ
An introduction to the uses of probability in everyday life, including: weather forecasting, flipping coins, batting averages, lightning strikes, and the lottery.
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 Problems in Topological Graph Theory  Dan Archdeacon
An ongoing list of open questions in topological graph theory, to which the author invites contributions. Classical questions on genus; coloring graphs and maps; drawings and crossings; paths, cycles, and matchings; symmetries; locally planar embeddings;
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 Squares in a Checkerboard  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about how many squares or rectangles there are in a checkerboard or in an NxN square.
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 TheMathPage: Topics in Precalculus  Lawrence Spector; Borough of Manhattan Community College, CUNY
Topics in precalculus include the formal rules of algebra; rational and irrational numbers; functions and functional notation; graphs; the vocabulary and roots (zeros) of polynomial functions; completing the square; the factor theorem and integer root
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 Too Much to be a Coincidence? (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: In the September ACBL Bridge Bulletin, Noreen Wurdemann of the Bahamas reports that the two bridge hands below were dealt out at her club. She says that she is "100% certain there was no hankypanky." What is the probability of
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 Topics in High School Mathematics  Martin Cohen
Lesson ideas on geometric series, mathematical induction, Pythagorean triples, combinatorics, continuity, modular arithmetic, rotations and revolutions, and more.
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 Tricky Crossings  Ivars Peterson (MathLand)
Have you heard the one about an itinerant entertainer traveling with a wolf, a goat, and a basket of cabbages? The showman comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can't leave the wolf
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 Venn Diagrams  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about Venn diagrams and using them to model sets, intersections, and unions.
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 WebMath: Instant Solutions to Math Problems
Instant solutions to math problems: look over the various links on the home page until you find a topic that seems to describe the math problem you're working on. Select a link then another and you will be presented with a blank form into which you can
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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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 World Population and Four Dice (Math Chat)  Frank Morgan; Christian Science Monitor
Answers to the old challenge (Estimate what fraction of the people who have ever lived on Earth are alive on Earth today.) plus a new challenge and an additional problem and answer (courtesy S. H. Logue: Ann learned that her old dotmatrix printer can
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