Syllabus Detail

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)
Probability: Theory and Examples, by Rick Durrett ($70)
Search by ISBN on Amazon: 0534424414
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.