Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 235B: Probability Theory
Approved: 2010-05-01, Janko Gravner
Units/Lecture:
Winter, every year (alternating years, taught by Dept of Statistics); 4 units; lecture/term paper or discussion
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Prerequisites:
MAT/STA 235A or consent of instructor.
Course Description:
Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory.
Suggested Schedule:
Department Syllabus
MAT 235B: Probability Theory
| When taught: | Winter, every year (alternating years, taught by Dept of Statistics) |
| Suggested text: | Probability: Theory and Examples, by Rick Durrett ($70 ISBN: 0534424414) |
| Units/lectures: | 4 units; lecture/term paper or discussion |
| Prerequisites: | MAT/STA 235A or consent of instructor. |
| Lectures | Sections | Topics/Comments |
|---|---|---|
| 1 week | Conditional expectation | |
| 3 weeks | Martingales | |
| 3 weeks | Markov chains | |
| 2 weeks | Selected applications |
Additional Notes:
The above topics cover chapters 4 and 5 of Durrett.
A good supplementary reading is "Probability with Martingales," by David Williams.
A good supplementary reading is "Probability with Martingales," by David Williams.