Textbook:         Resnick, S. A Probability Path, Birkhauser, 1999.

Homework:      There will be weekly homework assignments due at the start of class on Wednesday.  No late homeworks will be accepted.

Description: Math 280ABC is the fundamental graduate probability sequence. It covers measure theoretic probability essential for the pursuit of research in probability or in fields in which probability is used in applications. Topics to be covered include:

1. Measure and integration from a probabilistic perspective.

2. Basic probabilistic notions of random variables, expectation, independence.

3. Limit theorems: laws of large numbers, convergence in distribution, central limit theorems.

4. Martingale theory: conditional expectation, convergence theorems, optional stopping.

5. Stochastic processes: a selection from random walk, Markov chains, Brownian motion, Markov processes, statistical mechanics, stable processes, stochastic integration.

Topics 1, 2, and parts of 3 will be covered in Math 280A. The remainder of topic 3, and topics 4 and 5 will be covered in the subsequent two quarters of Math 280B, C. The text below will be supplemented with class lecture notes.