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 235C: Probability Theory
Approved: 2010-05-01, Janko Gravner

Units/Lecture:

Spring, every year (alternating years, supposed to be 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 235B 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 235C: Probability Theory

When taught: Spring, every year (alternating years, supposed to be 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 235B or consent of instructor.
Lectures Sections Topics/Comments
2 weeks
Weak convergence of measures on metric spaces
3 weeks
Brownian motion
5 weeks
Selected topics

Additional Notes:

The above topics cover chapter 7 of Durrett.

For weak convergence of measures, some supplemental text is probably necessary (such as Billingsley's "Convergence of Probability Measures").

Recent selected topics include: Hausdorff measures, mixing times for Markov chains, random walks and electrical networks.