Course overview
This is a graduate-level course on the theory of probability, covering measure-theoretic foundations and classical results essential for research in information theory, communications, and related mathematical fields.
Topics include: probability spaces and measure theory, random variables and expectation, modes of convergence, laws of large numbers, central limit theorem, conditional expectation, martingales, and an introduction to stochastic processes.
The course is aimed at graduate students in Information Engineering, Mathematics, and related programmes. A solid background in real analysis is recommended.
Course page on Piazza: piazza.com/cuhk.edu.hk/spring2026/ierg5400 (enrolled students only) · Course outline: [pdf]
Key information
Details
| Course code | IERG 5400 |
| Title | Theory of Probability |
| Term | Spring 2026 |
| Instructor | Prof. Chandra Nair, Room 811, Ho Sin Hang Engineering Building |
| Level | Graduate (MPhil / PhD) |
Assessment
| Homework | 4 assignments (dates below) |
| Midterm | February 11, 2026 |
| Final exam | To be announced |
| Discussion | Piazza (enrolled students) |
Lecture notes
| # | Notes | Date posted |
|---|---|---|
| 1 | Probability_MT.pdf posted | Apr 15, 2026 |
Further notes will be posted as the course progresses.
Homework
| # | Assignment | Due date |
|---|---|---|
| 1 | Probability_hw_1.pdf posted | Jan 16, 2026 |
| 2 | Probability_hw_2.pdf posted | Jan 23, 2026 |
| 3 | Probability_hw_3.pdf posted | Feb 6, 2026 |
| 4 | Probability_hw_4.pdf posted | Mar 13, 2026 |
| 5 | Probability_hw_5.pdf posted | Mar 27, 2026 |
| 5 | Probability_hw_6.pdf posted | Apr 20, 2026 |
Homework solutions will be posted after each deadline. Late submissions will not be accepted without prior arrangement.
General resources
| Resource | Description |
|---|---|
| Course outline | Full course outline including topics, schedule, and grading policy. |
Recommended texts
- R. Durrett, Probability: Theory and Examples (5th ed.), Cambridge University Press, 2019.
- P. Billingsley, Probability and Measure (3rd ed.), Wiley, 1995.
- D. Williams, Probability with Martingales, Cambridge University Press, 1991.
These are standard references; the course does not follow any single text exclusively.