Theory I: Probability & Stochastic Processes - Fall 2025

Course information

• 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
• Support and Policies:
  • Course Policies
  • School of Data Science Support and Policies
  • University Support and Politices

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Course materials

• Probability and Random Processes (Grimmett and Stirzaker) (PDF)

• Introduction to Probability for Computing (Harchol-Balter) (PDF)

• Introduction to Probability (Blitzstein and Hwang) (PDF)

• High Dimensional Probability (Vershynin) (PDF)

• Course notes

• Course code snippets

• Course reading quizzes

Additional Resources

• Joe Blitzstein's Statistics 110 course materials

• Applied Stochastic Processes

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Topics

1. Foundations of probability

   • Events and probability spaces
   • Conditional probability
   • Independence

2. Random variables

   • Probability distributions
   • Expectation, variance, and moments
   • Multiple random variables, covariance, and correlation

3. Limit theorems

   • Sums of random variables
   • Law of large numbers
   • Central limit theorem

4. Stochastic processes

   • Markov processes
   • Poisson processes

5. Tail bounds

   • Concentration inequalities
   • Sub-Gaussian and sub-exponential distributions

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Schedule

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)

Oct 13 2025: Fall reading day (no class)

Oct 15 2025: Conditional densities, conditional expectation

• Reading assignment TBD
• No homework assigned

Oct 20 2025: Midterm review

Oct 22 2025: Midterm exam

Nov 26 2025: Thanksgiving recess (no class)

Dec 13 2025: Final exam (2:00 - 5:00 pm Data Science Building 246)

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Grades

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.