Probability and Random Processes (Grimmett and Stirzaker) (PDF)
Introduction to Probability (Blitzstein and Hwang) (PDF)
High Dimensional Probability (Vershynin) (PDF)
Additional Resources
Aug 26 2026: Course overview
Aug 31 2026: Probability Spaces
Sep 02 2026: Reasoning with probability
Sep 07 2026: Random variables and distribution functions (Labor Day, class still meets)
Sep 09 2026: Law of Averages and Monte Carlo
Sep 14 2026: Multiple random variables, independence, Buffon’s needle
Sep 16 2026: Expectations of random variables
Sep 21 2026: Variance and common random variables
Sep 23 2026: Expectation, variance, and independence
Sep 28 2026: Moments of random variables, moment generating functions
Sep 30 2026: MGFs of sums of independent random variables
Oct 05 2026: Fall reading days (no class)
Oct 07 2026: The limit theorems: WLLN and CLT
Oct 12 2026: Midterm review
Oct 14 2026: Midterm exam
Oct 19 2026: Conditional probability distributions, conditional expectation and variance
Oct 21 2026: More conditional probability, simulation
Oct 26 2026: Stochastic processes, intro to Markov Chains
Oct 28 2026: Stationary distributions and Ergodic Theorems
Nov 02 2026: Markov Chain Monte Carlo and Metropolis Hastings
Nov 04 2026: MCMC examples and applications
Nov 25 2026: Thanksgiving recess (no class)
Dec 07 2026: (last class meeting)
Dec 18 2026: Final exam 2:00 pm - 5:00 pm
Final grades will be computed using the following weighting of assignments and exams:
Grading scale:
Note that a B- is the lowest satisfactory grade for graduate credit.
Homework assessments
You should expect that homework will be assigned each Wednesday and due the following Wednesday. Homework assignments will consist of a PDF posted to Canvas containing exercises for you to solve. There will be 6-8 exercises per homework assignment, and you can expect that there will be 10 homework assignments over the course of the semester.
Subject to the Academic Integrity conditions below, homework problems may be completed in any manner you see fit. While I strongly encourage you to write out your solutions in some form (e.g. pen and paper, LaTeX) you are not required to turn in your completed homework solutions. Instead, homework will be assessed in class as follows:
The first 10 minutes of each class session on Wednesdays will be reserved for homework assessment. I will provide you with a sheet of paper containing 1 exercise from the week’s homework assignment (or sub-problems thereof), and you will write your solution on it. You will not know which exercise will be selected for assessment in advance. However, to make this a fair and fruitful learning exercise, I will provide scaffolding when necessary to ensure that the solution can be written in 10 minutes. Scaffolding may include hints, reminders of useful facts, or even partial solutions where you fill in what remains.
To provide flexibility for weeks in which life circumstances do not permit the completion of your coursework to the best of your ability, your two lowest homework assessment grades will be dropped.
Class Attendance
Attendance in this class is mandatory. If you need to miss a class for any reason, please email me in advance. Part of attending class is attending all of the class meeting time. Please be respectful of me and your fellow classmates by showing up on time.
With respect to both attendance and tardiness, there are no fixed penalties associated with a single missed class or a single late entry. There are legitimate reasons to miss class or to be late to class. Making either of these a habit, though, will result in deductions from your attendance grade.
While you are ultimately responsible for keeping up with any lecture material you may miss by consulting classmates, reading lecture notes, reading the course textbooks, etc., I am also happy to work with you during office hours or by appointment to help you stay on track.
Extenuating Circumstances
Students are expected to communicate with me as soon as possible regarding extenuating circumstances and how their participation in the course, including attendance and completion of homework assessments, may be affected by them.
Academic Integrity
I encourage collaboration among students to complete homework assignments. The purpose of collaborating is to help yourself and your classmates learn the material more effectively.
Do not cheat. Cheating circumvents the learning process and deprives you of the chance to gain expertise in your discipline. It also puts you in a position to fail in-class exams, for which you will not be able to use resources outside of your own problem solving ability.
I ask that you:
If an action you are considering is not covered by one of these specific asks, please use your own sense of right and wrong to determine whether it constitutes cheating.