DS6300

Theory I: Probability & Stochastic Processes - Fall 2025

Course information

• Instructor: Jordan Bryan (jbryan@virginia.edu)
  • Lecture: Mon, Wed 9:30 - 10:45 am Data Science Building 246
  • Office hours: Tu 12:30 - 1:30 pm, Data Science Building 347
• Teaching Assistant: Marco Gutierrez Chavez (sgw3fy@virginia.edu)
  • Office hours: Th 6:30 - 7:30 pm, Data Science Building 246
• Canvas site
• Support and Policies:
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Course materials

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

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

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

• Reading assignment TBD
• HW 03 assigned

Oct 13 2025: Fall reading day (no class)

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.

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