Syllabus Math 561

Math 561. Theory of Probability I

Prerequisite: Math 540

Textbook used in recent years: R. Durrett: Probability: Theory and Examples (4th edition) Cambridge University Press, 2010

1. Basic concepts: random variables, distributions, expectations, variances, independence and convergence of random variables

2. Limit theorems: weak law of large numbers, strong law of large numbers, weak convergence, central limit theorem and large deviation principle

3. Discrete times martingales and their applications

4. Radom walks and Markov chains