by Zack Almquist

The undergraduate honors thesis. Best described as chance to study something hard, with the help of a friendly professor. It is an amazing chance to supplement ones undergraduate education and learn a bit of the art of advanced math. With the help of Professor Shao I have just finished my honors thesis in probability. I will give presentation/defense on Friday May 27^th in Chapman 303. For anyone who is interested here is my abstract and title:

LOWER TAIL PROBABILITIES AND THE GAUSSIAN PROCESS

This paper is devoted to the study of the lower tail probabilities for Gaussian Process. It will begin with a brief summary of continuous probability theory, at least enough to allow an undergraduate math major of approximately the junior level to appreciate the theorem and examples presented. The proof of the so-called Slepian Lemma will follow the discussion of continuous probability theory and lead into a discussion of three applications that arise from the Slepian Lemma. The first example comes from Brownian pursuits; the second emerges from the study of real zeros of random polynomials and the third example results from the first passage time for the Slepian process. Some numerical analysis of the second two examples will conclude.

One of the most interesting aspects of the thesis for me was first working through a fairly hard proof (The Slepian Lemma), and understanding it well enough that I could write up a proof that made since to me, a very useful and interesting exercise.  Working on the simulations was also very educational, even if it was also amazingly frustrating. I was only able to make one of the simulations work and even then it only gave me ok results, but writing the programs (with the help of Rigo) was quite enlightening and then finding out how long those programs took to run was also a bizarre experience.

Founded in 1776, the Phi Beta Kappa Society is the oldest and most prestigious honorary society in the nation. Alpha of Oregon became the first chapter in this state in 1923. Although three private schools in Oregon now have chapters, the University of Oregon still has the only Phi Beta Kappa chapter in the public Oregon University System. The society honors students whose undergraduate academic records fulfill the objectives of a liberal arts education. Members are generally elected from the top 10 percent of a university's graduating class. 
The new math major members for this year are Jamie Curtis, Brian Grossmiller, Lars Hoernlein, Heidi Holly, Melissa Johnson, Zan Moore, Amanda Stout, Jason Zaklan, and Erin Keenan.
Congratulations!

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