- Instructor: Jordan Bryan ([email protected])
- Lecture: Mon, Wed 9:30 - 10:45 am Data Science Building 246
- Office hours: Mon 1:00 - 2:00 pm, Data Science Building 347
- Teaching Assistant: Marco Gutierrez Chavez ([email protected])
- Office hours: Th 6:30 - 7:30 pm, Data Science Building 246
- Canvas site
-
Probability and Random Processes (Grimmett and Stirzaker) (PDF)
-
Introduction to Probability for Computing (Harchol-Balter) (PDF)
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Introduction to Probability (Blitzstein and Hwang) (PDF)
-
High Dimensional Probability (Vershynin) (PDF)
Additional Resources
-
Foundations of probability
- Events and probability spaces
- Conditional probability
- Independence
-
Random variables
- Probability distributions
- Expectation, variance, and moments
- Multiple random variables, covariance, and correlation
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Limit theorems
- Sums of random variables
- Law of large numbers
- Central limit theorem
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Stochastic processes
- Markov processes
- Poisson processes
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Tail bounds
- Concentration inequalities
- Sub-Gaussian and sub-exponential distributions
Aug 27 2025: Course overview
- Read G&S 1.1 - 1.4
Sep 01 2025: Probability spaces
- Read G&S 1.5 and 1.7
Sep 03 2025: Probabilistic reasoning
- Read G&S 2.1 - 2.3
- HW 01 assigned (due 09/10/2025 at 9:30 am) [Solutions]
Sep 08 2025: Random variables
- No reading assignment. Finish HW 01.
Sep 10 2025: Distribution functions
- Read G&S 2.5 and 2.6
- HW 02 assigned (due 09/17/2025 at 9:30 am) [Solutions]
Sep 15 2025: Multiple random variables, Buffon's needle
- Read G&S 3.1 - 3.2 and 4.1 - 4.2
- Finish HW 02
Sep 17 2025: Independence and common random variables
- Read G&S 3.3
- HW 03 assigned (due 09/24/2025 at 9:30 am) [Solutions]
Sep 22 2025: Practice problems, mean and variance
- No reading assignment
- Finish HW 03
Sep 24 2025: Mean, variance, and moment derivations
- Read G&S 4.4
- HW 04 assigned (due 10/01/2025 at 9:30 am) [Solutions]
Sep 29 2025: Moments of random variables
- Read Blitzstein and Hwang 6.4
- Finish HW 04
Oct 01 2025: Moment generating functions
- No reading assignment
- HW 05 assigned (due 10/08/2025 at 9:30 am) [Solutions]
Oct 06 2025: Weak law of large numbers
- Read Blitzstein and Hwang 10.3
- Finish HW 05
Oct 08 2025: Central Limit Theorem
- No reading assignment
- HW 06 assigned (due 10/15/2025 at 9:30 am) [Solutions]
Oct 13 2025: Fall reading day (no class)
Oct 15 2025: Conditional densities, conditional expectation
- No reading assignment
- No homework assigned
Oct 20 2025: Midterm review
Oct 22 2025: Midterm exam [Solutions]
- No reading assignment
- HW 07 assigned (due 10/29/2025 at 5:00 pm) [Solutions]
Oct 27 2025: Conditional probability, simulation
- Read Harchol-Balter Chapter 24, 24.1 - 24.3
- Finish HW 07
Oct 29 2025: Markov chains
- Read Harchol-Balter Chapter 24, 24.4 - 24.6
- HW 08 assigned (due 11/05/2025 at 9:30 am) [Solutions]
Nov 03 2025: Markov chain examples, autocorrelation
- No reading assignment
- Finish HW 08
Nov 05 2025: Aperiodicity, irreducibility, and the Ergodic Theorem
- No reading assignment
- HW 09 assigned (due 11/12/2025 at 9:30 am) [Solutions]
Nov 10 2025: MCMC and Metropolis Hastings
- Read A History of the Metropolis-Hastings Algorithm
- Finish HW 09
Nov 12 2025: Metropolis Hastings examples
- Finish reading A History of the Metropolis-Hastings Algorithm
Nov 17 2025: Discussion and conclusion of Markov processes
- HW 10 assigned (due 11/25/2025 at 11:59 pm)
Nov 19 2025: Introduction to concentration inequalities
- No reading assignment
- Finish HW 10
Nov 24 2025: Hoeffding and Chernoff inequality
Nov 26 2025: Thanksgiving recess (no class)
Dec 03 2025: Sub-Gaussian and sub-exponential random variables
Dec 05 2025: Optional makeup lecture (SDS 246 1:00 pm)
Dec 08 2025: Final exam review
Dec 13 2025: Final exam (2:00 - 5:00 pm Data Science Building 246)
Final grades will be computed using the following weighting of assignments and exams:
- Homework (40%)
- Reading quizzes (10%)
- Midterm exam (20%)
- Final exam (30%)
Grading scale:
- 93-100 A
- 90-92 A-
- 87-89 B+
- 83-86 B
- 80-82 B-
- 77-79 C+
- 73-76 C
- 70-72 C-
- <70 F
Note that a B- is the lowest satisfactory grade for graduate credit.
Submitting Homework
Homework will be accepted through the Assignments page on Canvas. Submissions will be in PDF format. You may hand-write and scan problem solutions, or you may use a typesetting software like LaTeX, Markdown, etc. Some homework assignments will involve using code to produce graphical or numerical outputs and will require the use of software. Please compile all materials in a single PDF for submission and make sure that whatever you have written can be clearly read by the grader.
Grades for (on-time) homework will be made visible to students no later than one week after the assignment due date. Grades for late work (see below) will become available as time permits.
Late Work Policy
The expectation in this course is that all assignments will be submitted on time. Submitting your work on time respects the efforts of your instructor and teaching assistant, and it ensures that you are prepared to learn subsequent material.
Assignments turned in after the due date incur a 10% penalty per late day. For example, an assignment due at 9:30 am on Wednesday that is submitted to Canvas at 3:00 pm on Friday will incur a 30% penalty. If the assignment would have received a 95% had it been returned on time, then the late grade is 65%. Note that weekend days count towards the late penalty.
I will not accept work that is late by more than one week past its due date.
To provide flexibility for weeks in which life circumstances do not permit the completion of your coursework, your lowest homework grade will be dropped. Additionally, your two lowest reading quiz 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. You are responsible for keeping up with the lecture material, but I am happy to work with you during office hours or by appointment to brush up on things you may have missed.
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 assignment submissions, may be affected by them.