How do CD’s play correctly even when they are scratched? Obviously, they have some capability to detect and correct errors. How secure are encryption methods used by the government and over the Internet? These secret codes are surprisingly easy to understand once you know some fundamental secrets about the integers.

Draw white fish swimming to the right with identically shaped black fish in the background swimming to the left.

A challenging combinatorial puzzle, involving "checker-type" moves on a grid, will be used to show how elementary algebra can be used in a surprising way with powerful results.

How often do you take a math test just for fun? Take a Freshman/Sophomore or Junior/Senior exam based on questions from the regional Math Competitions held at NIU and other locations throughout Illinois. Afterwards, strategies and short cuts to the solutions will be discussed. Work in groups on sample Olympiad questions given in worldwide Math Competitions.

Learn how to use the computer program "Geometer’s Sketchpad" to answer questions such as "What is the sum of the tips of a 5-pointed star?" and "How to draw with vanishing points."

Computers can do a lot more than just display roving eyes when it shuts down for the night.

There are some games that you can always win if you know how. Other games have strategies but no guarantee of success.

A triangle whose sides have the lengths 3, 4, 5, is a right triangle. Are there other examples? Could we find them all? What do we know about similar problems involving other powers besides squares?

Based on an idea by John Conway, four people tangle two ropes by repeating two basic operations: knot and turn. Learn how to straighten any complicated tangle using the fractions learned in the 4^th grade.

Learn concepts such as "isomorphism" and "algebraic invariant" using knots. Only a basic command of arithmetic with variables and polynomials, as well as some intuition, are needed.

How we learned to add, subtract, multiply, and divide in the early grades of elementary school is how we also add, subtract, multiply, and divide fractions, decimals, integers, and algebraic equations.

Such things as "Saws and Ladders," "Algebra Blocks," "Factor Blocks," and "Paper Folding" demonstrate many of the basic ideas and theorems of high school geometry and algebra.

Simcha Bruno spent a decade at MIT working in a high-energy research laboratory, has been an invited guest at Los Alamos National Laboratory in New Mexico (before hard drives containing nuclear secrets were missing), and is discovering several interesting mathematical formulas.

The world of geometry consists of some far out models way different than the Euclidean plane taught in high school geometry class. You can actually construct and view these strange worlds, where parallel lines may not exist and triangles can have three 90-degree angles.

At the turn of last century, mathematicians believed that every mathematical statement either had a proof or a counter-example until eccentric logician, Kurt Godel, proved them wrong.

The divisors of 12 (not counting 12 itself), "1, 2, 3, 4, 6," add up to 16, which is larger than 12, while the divisors of 10, "1, 2, 5," add up to 8, which is smaller than 10. The divisors of 6, "1, 2, 3," add up to 6, which is the integer itself. Such numbers are called, "perfect." Michael Jordan’s jersey number, "23," is intimately connected with a search for other perfect numbers.