MATH 275A: Fall 2020

MATH 275A: Fall 2026

Graduate Probability

lecturer: Marek Biskup
time and place: MWF 10-11 in MS 5138
office hours: 11-noon (tentatively) or by appointment

Scheduling:

The first class (Friday, September 25) will be held over zoom. The zoom link will be distributed directly to the enrolled students; others please request it via above email.

Homework:

HW#1 HW#2 HW#3

Board photos & lecture notes:

Here you will find board photos & lecture notes along with a brief description of material covered.

General information: This is the 1st quarter of the basic 3-quarter graduate probability sequence. In this quarter we aim to cover the following topics:

Basic setup of probability theory: measure and integration, random variables and their distribution
Infinite product spaces, independent random variables, Borel-Cantelli lemmas, etc.
Laws of Large Numbers (weak and strong) for independent random variables
Convergence in distribution, Central Limit Theorem (characteristic function, Lindeberg's and Stein's methods)
Stable laws, infinite divisibility, limit laws for heavy-tailed random variables, Levy-Khinchin formula, laws of types
Conditional expectation and probability (time permitting)

A key prerequisite for this course is a good knowledge of undergraduate analysis (up to Riemann integral); prior knowledge of measure theory will not be assumed.

Literature & resources:

Principal textbook: R. Durrett Probability: Theory and Examples, Cambrige Univ. Press. (see online version)

Other resources will be distributed as we go on.

Midterm exam: October 28, 2026 in class

Final exam: December 8, 2026 at 8-11AM, location TBD

Homework: A list of problems will be distributed weekly through this website. The submission of only a few problems will generally be checked.

Course credit & milestones:

For a successful completion of the course, the student should be able to demonstrate understanding of the material as detailed in the above bullet-point list at the level of technical skill required by typical homework assignments. The assessment will reflect on the quality of the completed homework (10%) and the performance on the midterm (20%) and the final exam (70%). Letter grading will be used.