2000 MATH CAMP ABSTRACTS

Monday, July 17
 
Computers, Codes, and Pails of Water - Prof. Richard Blecksmith
How do CDs 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.
 
Fractals on the Internet - Dave Giacobbe & Dan Kostopoulos
Explore several websites where you can create your own fractal drawings.
 
How to Draw Tessellations Like M. C. Escher? - Prof. Richard Blecksmith
Draw white fish swimming to the right with identically shaped black fish in the background swimming to the left.
 
Submarine Hunting - Steve Haptonstahl
How to blow stuff up! Actual hands-on exercises practiced in the military.

Tuesday, July 18
 
The Solitaire Army Problem - Prof. William Blair
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.
 
Competition Sessions Beginning, Advanced, & Olympiad
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.
 
Dynamic Geometry or How to Get the Computer To Do Your Homework - Suzanne Riehl, Bob Hein, and Jill Shahverdian
Learn how to use the computer program "Geometer's Sketchpad" to answer questions such as: What is the sum of the angles of the tips of a 5-pointed star? or How to draw with vanishing points.
 
Cracking Codes and Searching for Extra-Terrestrials on the Internet - Dr. Eric Behr
A computers can do a lot more than just display roving eyes when it shuts down for the night.

Wednesday, July 19
 
A Mathematician Wins at Nim and Krypto - Prof. David Rusin
There are some games that you can always win if you know how. Other games have strategies but no guarantee of success.
 
Question 999 - Prof. Richard Blecksmith
Investigate the question, Does .99999...=1?
 
The Solitaire Army Solution - Prof. William Blair
See Tuesday, July 18
 
Pythagorean Triples - Prof. Richard Blecksmith
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?

Thursday, July 20
 
How to Detangle Knots Using Fractions - Prof. Richard Blecksmith
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 4th grade.
 
Playing With Knots - Matthias Weiss
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.
 
Finite Braided Groups - Prof. Harold Ellers
Explore an algebraic structure different from the real numbers. This algebraic system will help us to understand when braids that look different can be disentangled so they look the same.  
It's Just Math - Prof. Alan Zollman
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.
 
Hands-On Geometry and Algebra - Prof. Alan Zollman and Shannon Fields
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.
 
A Career in Physics, Mathematics, and Computer Programming - Simcha Brudno
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 has discovered several interesting mathematical formulas.

Friday, July 21
 
Non-Euclidean Geometry Models - Prof. Harvey Blau
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.
 
What Godel Did - Prof. Richard Blecksmith
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.
 
Michael Jordan and Perfection - Prof. Richard Blecksmith 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.