This is the first semester of a year-long introduction to probability at the graduate level. The course assumes a knowledge of measure theory but some of the basic facts will be reviewed at the begining. We will follow Durrett's Probability: Theory and Examples (4th edition), covering these chapters:
Chapter 2. Laws of Large Numbers
Chapter 3. Central Limit Theorems
Chapter 4. Random Walks
Chapter 5. Martingales
Problem set 1, due Thurs 9/11
Problem set 2, due Thurs 9/25
Problem set 3, due Thurs 10/9
Problem set 4, due Thurs 10/23
Problem set 5, due Thurs 11/20
Problem set 6, due Thurs 12/4
Sign up for a presentation topic by Thurs 10/23. The sign up sheet with topics and dates is on my office door, 438 Malott.
Beamer slides courtesy of the large deviations group (Kun Dong, Daniel Freund, Matt Hin, Andrew Loeb, Aditya Vaidyanathan).