Syllabus for Math 561

• Instructor: Renming Song
• Office: 338 Illini Hall
• Phone: (217) 244 6604
• email: rsong at math uiuc edu
• Home page: http://www.math.uiuc.edu/~rsong
• Office Hours: MWF noon-1pm or by appointment
• Class Hours: MWF 2:00-2:50 P.M.

Text:R. Durrett: Probability: Theory and Examples (3rd edition) Duxbury Press, 2005

Course Topics This is the first half of the basic graduate course in probability theory. The goal of this course is to understand the basic tools and language of modern probability theory. We will start with the basic concepts of probability theory: random variables, distributions, expectations, variances, independence and convergence of random variables. Then we will cover the following topics: (1) the basic limit theorems (the law of large numbers, the central limit theorem and the large deviation Principle); (2) martingales and their applications. If time allows, we will give a brief introduction to Brownian motion. The prerequisite for Math 561 is Math 540.

Grading Policy 50% of your grade will depend on homework assignment, and 50% will depend on a final exam.