Professor: Professor R. J. Williams, AP&M 7161.
Email: williams at math dot ucsd dot edu.
Office hours: Starting April 6, Mon 6.30-7.20pm, Wed 3.30-4.20 p.m. and by appointment.

Lecture time: MW 5-6.30 p.m.
Place: AP&M 5402. There will be no lecture on Wednesday, April 15 and no office hours that day. This lecture time is being made up with the extended class time of the other class meetings.

Teaching Assistant: Ching Wei Ho, AP&M 6414.
Office hour: Tues, 1.30-2.30 pm.

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, ergodic theory, Markov chains, Brownian motion, Markov processes, stable processes.


  • K. L. Chung and J. B. Walsh, Markov processes, Brownian motion, and time symmetry, Springer, 2005.
  • E. Cinlar, Probability and stochastics, Springer, 2011.
  • R. Durrett, Probability: Theory and Examples, Cambridge University Press, 4th edition, 2010.
  • T. Liggett, Continuous time Markov processes : an introduction, American Math. Society, 2010.

    HOMEWORK: For Math 280C homework, click here.


  • Krishna B. Athreya and Soumendra N. Lahiri, Measure Theory and Probability Theory Springer Texts in Statistics, 2006.
  • H. Bauer, Probability Theory and Elements of Measure Theory, Academic Press, New York, 1981.
  • P. Billingsley, Probability and Measure, Wiley, New York.
  • L. Breiman, Probability, Addison-Wesley, 1968.
  • Y. S. Chow and H. Teicher, Probability theory, Springer, New York, 1988.
  • K. L. Chung, A Course in Probability Theory, Revised Edition, Academic Press, New York, 2000.
  • B. Driver, Probability Tools with Examples, Lecture Notes, UCSD, 2014.
  • R. Dudley, Real Analysis and Probability, Cambridge University Press, 2002.
  • Allan Gut, Probability: A Graduate Course Springer Texts in Statistics, 2005.
  • Jean Jacod and Philip Protter, Probability Essentials, Springer, 1999.
  • Olav Kallenberg, Foundations of Modern Probability, Probability and its Applications, 1997.
  • David Pollard, A User's Guide to Measure Theoretic Probability, Cambridge University Press, 2002.
  • A. N. Shiryayev, Probability, Springer-Verlag, New York, 1984.
  • S. Resnick, A Probability Path, Birkhauser, Boston, 1999.
  • David Williams, Probability with martingales, Cambridge University Press, Cambridge, England, 1991.