## 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.