Materials

This is a collection of materials developed for and used at various math circles for teachers and students. Handouts and worksheets used specifically for math teachers' circles are marked by

. We continue working on further refinement and enhancing of most of these notes, so it will be periodically updated--keep visiting. We would welcome any addition to this list!

General Problem Solving

Fractions, Decimals, Ratios, Percents, Proportions (Tatiana Shubin)
Introduction to Problem Solving (Joshua Zucker)
Problems to Tease and Teach (Tatiana Shubin)

Mathematical Games

Mathematical Card Tricks (Tom Davis)
One-Player Games (Joshua Zucker)

Combinatorics

Catalan Numbers (Tom Davis)
Combinations and Permutations (Tom Davis)
Combinatorial Problems (Tom Davis)
Counting Things (Tom Davis)
Derangements (Brian Conrey & Tom Davis)
Euler Characteristic & Worksheet (Sam Vandervelde)
Exploring Pascal's Triangle (Tom Davis)
Game of Criss-Cross & Worksheet (Sam Vandervelde)
Graph Theory Problems (Tom Davis)
Magic, Latin, and Sudoku Squares (Matthias Beck)
Polya's Counting Theory (Tom Davis)
The Mathematics of Sudoku (Tom Davis)
Tilings (Sam Vandervelde)
Parking Functions (Matthias Beck)

Geometry

Classical Geometric Construction (Tom Davis)
Curves in Computer Graphics (Tom Davis)
Euler's Theorem (Tom Davis)
Four Points on a Circle (Tom Davis)
Geodesic Domes (Tom Davis)
Geometry and Geography (Tom Davis)
Homogeneous Coordinates for Computer Graphics (Tom Davis)
Introduction to Matrices (Tom Davis)
(Mostly) Plane Geometry Problems (Tatiana Shubin)
Pick's Theorem (Matthias Beck)
Pick's Theorem (Tom Davis)
Polyhedral Symmetry (Sam Vandervelde)
Practical Calculation of Polygonal Areas (Tom Davis)
Projective Geometry (Tom Davis)
The Mathematics of Zome (Tom Davis)

Number Theory

Codes, Ciphers, and Secret Messages (Matthias Beck)
Coins, M&M's, and Generating Functions (Matthias Beck)
Cryptography (Tom Davis)
Divisibility Tests (Matthias Beck)
Introduction to Diophantine Equations (Tom Davis)
Primes, Divisibility, and Modular Arithmetic (Joshua Zucker)
RSA Encryption (Tom Davis)
Prime Number Card (Paul Zeitz)

Miscellanea

Big Numbers (Tom Davis)
Conway's Rational Tangles (Tom Davis)
Fractions and Decimals (Tom Davis)
Infinity (Tom Davis)
Permutation Groups and Rubik's Cube (Tom Davis)
Practical Probability (Tom Davis)

Math Circles for Students

mathcircles.org contains Sam Vandervelde's book Circle in a Box, a wonderful resource for people interested in creating their own math circle program, as well as links to existing math circles in North America.

General Math Resources

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