Dates: August 9-13 M-F 1:00 p.m.-4:00 p.m.
Location: University of Missouri-Columbia campus (exact location to be determined)
Instructor: Alex Iosevich, Associate Professor of Mathematics, University of Missouri-Columbia
Teaching assistant: (to be determined)
Fee: $100 (used to pay the assistant)
Contact information: iosevich@math.missouri.edu or iosevich@hotmail.com
Registration form: Please fill out the form enclosed below and send it to:

Alex Iosevich, Associate Professor
Department of Mathematics
University of Missouri-Columbia
Columbia Missouri 65211 USA

A check in the amount of $100 should be made out to:

Department of Mathematics University of Missouri-Columbia
 
 

Description of the program: The purpose of this program is introduce motivated high-school students to one of the most important problems in modern mathematics- the Besicovitch/Kakeya conjecture. While this problem has proved to be very difficult, it requires very little background and the basic concepts are easily accessible to high-school students. The BK conjecture says, roughly speaking that if a set determines lots of different slopes, then the set itself must be quite big. In spite of its apparent simplicity, this problem is still unsolved. It is my hope to convince you to think about this beautiful problem which, as you will see, is so easy to state, yet so difficult to solve.

We shall begin by discussing some basic counting techniques and methods for estimating sums. We shall then move on to the aforementioned Besicovitch/Kakeya problem and this is where the fun really begins!

Sructure of the program: On most days, we shall begin with a 50 minute lecture, from 1:00 p.m.-1:50 p.m., followed by a short break. A problem solving periiod of about one hour is followed by another break. We shall conclude each day by summarizing what we have learned up to that point and answering questions.

PLEASE SIGN UP! If you think you may be interested in the program, please send me an email! In addition to being lots of fun, this program will look great on your college application and even later.

A preliminary set of lecture notes will appear on my web page (http://www.math.missouri.edu/~iosevich/kakeyahs.pdf) by April 6, 2004. Please feel free to start reading and asking me questions. I will respond as promptly as I can.