Math/Stat 733 - Theory of Probability I.

Fall 2020

Meetings: TR 1pm-2:15pm (online)
Instructor: Benedek Valkó
Email: valko at math dot wisc dot edu
Office hours: Tu 4-5pm, F 3-4pm, or by appointment (online)

This page gives an overview of the course, all relevant information and resources will be provided in the official Canvas page.

Course description

This is the first semester of a two-semester graduate-level introduction to probability theory and it also serves as a stand-alone introduction to the subject. The course will focus on the basics of probability and cover at least the following topics: foundations (probability spaces and existence of processes), independence, zero-one laws, laws of large numbers, weak convergence and the central limit theorem, conditional expectations and their properties, and martingales (convergence theorem and basic properties).


Richard Durrett: Probability: Theory and Examples, 5th edition, 2019

There are several good textbooks on probability and it might help to have a look around. Here is a list of textbooks that could be used for extra reading:


Measure theory is a basic tool for this course. A suitable background can be obtained from Math 629 or Math 721. Chapter 1 in Durrett covers the measure theory needed. We will very briefly review some measure theory at the beginning of the semester, but it will be expected that all students in the course are familiar with the basics. Prior exposure to elementary probability theory could be useful, but it is not required.

Course content

We cover selected portions of Chapters 1-4 of Durrett. This is a rough course outline:

Weeks 1-2: Foundations, properties of probability spaces
Weeks 3-5: Independence, 0-1 laws, strong law of large numbers
Weeks 6-10: Characteristic functions, weak convergence and the central limit theorem
Weeks 11-15: Conditional expectation, Martingales

The course continues in the spring semester as Math 734 covering topics such as Markov chains, stationary processes, ergodic theory, and Brownian motion.


Course grades will be based on biweekly home work assignments (25%), class participation (15%), a midterm exam (30%) and the final exam (30%). (See the Canvas page for more information.)


We will be using Piazza for class discussion.  The system is catered to getting you help fast and efficiently from classmates and myself.  Rather than emailing all questions to me, I encourage you to post your questions on Piazza. If you have any problems or feedback for the developers, email
You can access our Piazza page from the Canvas page of the course.

Instructions for homework assignments

If you would like to learn more probability...

Check out the Probability Seminar, the Graduate Probability Seminar and the Statistics Seminar for talks that might interest you. Have a look at the wiki page of our probability group to learn more about the probabilists at UW-Madison. Consider attending the 2020 Midwest Probability Colloquium  (this will be held online this year).