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.
235A course description
- The 235A course will cover chapters 1-3 of Durrett's (4th edition) book. In the 3rd edition, this corresponds to chapters 1-2 and Appendix A. See the 235 Home tab for more information on the syllabus and general course policies.
Lecture notes and other useful things
- I will follow these lecture notes (last updated: 12/15/11). The notes make occasional reference to Durrett's book, but are mostly self-contained.
- Here is a summary of important distributions in probability theory.
Organizational details
- Lectures: MWF 2:10-3:00 in Physics 130
- Discussion section: T 2:10-3:00 in Storer 1344
- Office hours: T 10:30-11:30 at my office, MSB 2218, or by appointment
- T.A.: Hao Yan (Office hours: M 3:10-4:00 at MSB 1226)
- Final exam: A take-home exam will be given at the last course lecture (Friday, 12/2/11).
Homework
235B course description
- The 235B course will cover chapters 5 and 7 of Durrett's (4th edition) book. In the 3rd edition, this corresponds to chapters 4 and 6. Parts of chapters 4 and/or 6 (3 and 5 in the 3rd ed.) may be covered as well. See the 235 Home tab for more information on the syllabus and general course policies.
Lecture notes
- I will follow these lecture notes (updated 3/15/12). The notes make occasional reference to Durrett's book, but are mostly self-contained.
- Here is a messy write-up of Markov chains, the last topic we discussed.
Organizational details
- Lectures: TR 3:00-4:30, Physics 140
- Discussion section: there will be no discussion section
- Office hours: by appointment (or just drop by anytime) at my office, MSB 2218
- Final exam: there will be no final exam. The grade will be based on four homework assignments which will be given during the quarter.
Homework
- Assignment #1. Due on 2/7/12.
- Assignment #2. Due on 2/21/12.
- Assignment #3. Due on 3/8/12 (note extended deadline).
- Assignment #4. Due on 3/19/12 at noon.
235C course description
-
The 235C course will be in two parts. In the first part, I will cover selected parts of the last chapter of Durrett's book (i.e., chapter 8 in the 4th ed., chapter 7 in the 3rd).
In the second part, I will give an introduction to the theory of percolation and related discrete planar processes such as the self avoiding random walk. This is an important topic in contemporary probability theory that arose out of statistical physics. I will cover some of the classic theory as well as exciting developments from the last 10 years, which took the mathematical world by surprise and have already been recognized as part of 2 Fields Medal award decisions. This material is covered in Grimmett's book (Chapters 1-2) and Werner's lecture notes (Chapters 1-2) -- see the Resources tab for references and links.
See the 235 Home tab for more information on the syllabus and general course policies.
- Lectures: T 3:00-4:30, R 2:40-4:00, Bainer 1130
- Discussion section: there will be no discussion section
- Office hours: by appointment (or just drop by anytime) at my office, MSB 2218
- Final project: details will be announced later.
Some useful resources for the class:
- Rick Durrett's Probability: Theory and Examples page.
- Additional recommended reading:
- Probability with Martingales, by David Williams. Cambridge University Press, 1991.
- An Introduction to Probability Theory and Its Applications, Vols. 1-2, by William Feller.
- (For 235C) Percolation, 2nd Ed., by Geoffrey Grimmett. Springer, 1999.
- (For 235C) Lectures on two-dimensional critical percolation, lecture notes by Wendelin Werner.