ESP Biography

Stanford Splash is part of a growing movement of Splash programs at universities around the country, including Chicago, Duke, Boston College, and the original at MIT. Come learn about the present and future of all those Splash programs, how Splash fits into the national education picture, and how you can make your mark on it. You should absolutely take this class if you've ever entertained the thought of starting your own Splash when you get to college. That level of ambition isn't necessary, of course--this class is not just about how to start new Splash programs.

The Banach-Tarski Paradox is the consummate example of mathematics behaving badly. It states that, given a perfect sphere, it's possible to cut it up into 5 pieces, rearrange those pieces rigidly (no stretching, twisting, etc.), and end up with 2 copies of the sphere you started with. We will prove the Banach-Tarski Paradox. The proof is long, intricate, and often fascinating, which means we'll have to skip some boring parts to save room for digesting the main ideas. Along the way we'll see rudiments of abstract algebra, talk about some very deep set theory, and come out with an understanding of why cutting up perfect spheres is not the same as cutting up apples. This class is the first of two parts; make sure to catch the second as well if you want the whole proof!

The Banach-Tarski Paradox is the consummate example of mathematics behaving badly. It states that, given a perfect sphere, it's possible to cut it up into 5 pieces, rearrange those pieces rigidly (no stretching, twisting, etc.), and end up with 2 copies of the sphere you started with. Disturbing? Well, it's supposed to be. NOTE: This is the second part of a class that sets out to prove the Banach-Tarski Paradox. For more info, see Part I.

A brief look at technology that allows bomb squads, airports, and soldiers abroad to detect explosives, nerve gases, and other dangerous chemicals from a distance. We'll focus on two different sensors, which are made from polymers (long repeating chains of atoms) that conduct electricity. If you enjoy chemistry, you will enjoy this class.

What does it it look like to wander around on a fractal? In this class, we'll take a look at the basic math of the hyperbolic plane, a space where there are infinitely many parallel lines through a point off another line, instead of just one like we're used to. As a result, you get a weird and beautiful piece of math, where fractals fit comfortably and area doesn't work the way it should. If you like having your mind gently bent or like mathematical pictures, and have a good ability to thjnk about unusual new concepts, you'll enjoy this class.

How do you detect a bomb without a metal detector, x-ray equipment, or any kind of search? The answer lies in chemical sensors, which are extremely sensitive devices that can pick up traces of TNT, nerve gas, or other dangerous chemicals from several meters away. We'll examine the inner workings of chemical sensors that rely on polymers that conduct electricity, which currently give the most sensitive equipment known to man. If you like chemistry, you'll iike this class. Incidentally, a good background in chemistry--say, a year of it in school--is pretty necessary to understand what's going on here.