Spring 2027
Kasper Larsen
Subtitle:
Course Description:
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; (iv) Convergence in distribution and the Central Limit Theorem; (v) conditional Ex-
pectation; (vi) Martingales in discrete-time; (v) Brownian motion.
Textbook:
David Williams’ book "Probability with martingales"
Prerequisites:
642:501
Spring 2025
Kimberly Weston
Course Description
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.
Prerequisite:
Real Analysis (640:501 or equivalent)
Textbook:
Graduate Probability lecture notes by Richard Bass