MATH 6710 - Probability Theory I Fall 2013

Instructor: John Pike

Textbook:R. Durrett, Probability: Theory and Examples, 4th edition.

This is the first half of a year-long introduction to probability theory at the graduate level. We will begin by introducing some of the fundamental concepts (e.g. probability spaces, random variables, expectation) from a measure-theoretic perspective. Basic knowledge of abstract measure theory is assumed, but we will endeavor to keep the course as self-contained as possible. We will then discuss the notion of independence and move on to derive the laws of large numbers and some related results. Next we will introduce characteristic functions and weak convergence in order to prove the central limit theorem and various complements/extensions thereof. We will conclude with a look at stopping times, random walk, and conditional expectation.