## Math/Stat 235: Probability Theory UC Davis, 2011-2012

This is the web page for the Math 235 (a.k.a. Stat 235) yearly graduate course at the UC Davis math department.

The course comprises three quarter-long classes: 235A (fall), 235B (winter) and 235C (spring).

Below you will find some useful general information about the course. Information specific to each of the three classes will be found by clicking on the appropriate tab in the menu bar to the left.

• Instructor: Dan Romik
• Textbook: Probability: Theory and Examples, 4th Ed., by Rick Durrett. (The textbook may be downloaded as a PDF from the author's website). The 3rd edition may also be used without significant issues.
• Course description: A rigorous mathematical treatment of modern probability theory, including some of the measure-theory foundations, and selected advanced topics. A rough planned outline is as follows:
• 235A: Chapters 1, 2 and 3 (foundations, laws of large numbers and central limit theorems).
• 235B: Chapters 5, 7 (martingales and ergodic theorems) and optionally parts of chapter 4 (random walks) or chapter 6 (Markov chains) as time allows.
• 235C: Chapter 8 (brownian motion), and additional selected topics from the theory of percolation.
• Prerequisites: You need to have taken undergraduate classes in probability and real analysis, equivalent to the UC Davis classes Math 125 and Math 135. In case of doubt please contact instructor.
• Grading: The final grade for each of the three classes will be determined as follows:
• 235A: 50% homework, 50% final (take-home) exam. Homework will be assigned weekly. When computing the homework component of the grade the 2 lowest homework grades will be dropped.
• 235B: The grade will be based on four homework assignments which will be given during the quarter, and weighted equally.
• 235C: A final project, which will take the form of reading a research paper or section of a book and writing about it. Depending on the number of participants, I may require each student to present their project in a short (25-30 minute) lecture.