Kimberly Weston
Introduction to Probability using Measure Theory
This course will be an introduction to the issues and techniques of probability theory, at the graduate level. The topics covered will include: (i) The measure theoretic framework of modern probability theory; probability spaces and random variables; (ii) Independence and zero-one laws; (iii) Laws of large numbers and Kolmogorov's three series theorem; (iv) Convergence in distribution and the Central Limit Theorem; (v) Conditional Expectation; (vi) An introduction to martingales in discrete-time and applications to Markov chains. Time permitting, we will try to give brief introduction to large deviations and Brownian motion.
not decided yet
Real Analysis (640:501 or an equivalent) and an undergraduate course at the level of Ross's text, A First Course in Probability.