## 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)

**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.

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.