Math/Stat 831 Theory of Probability

Fall 2007

In-Class Exam:
Friday, December 7. Begins at 4 PM. Do arrive on time because once somebody has left no one can be admitted into the exam. The room is Van Vleck B139 and we have it until 6:30. Please bring your pencil and paper and your 3 sheets of notes. No calculators or other electronic gadgets. The exam asks you to hand in 4 problems out of 7. Short, basic exercises from the material up to and including martingales: types of convergence, 0-1 laws, law of large numbers, normal and Poisson limits, conditional expectations.

Here is the syllabus for the course.

Homework

1. Homework 1 due September 13.
2. Homework 2 due October 4.
3. Homework 3 due October 16.
4. Homework 4 due November 8.
5. Homework 5 due November 27.

Bonus Problems. Bonus problems are for those who would like to work on problems that require further reading, or are open-ended, interesting or hard. If there is interest in this I will add to the list during the semester. There is no due date for these problems.

The Midwest Probability Colloquium runs from Thursday October 18 to Saturday October 20. I recommend that those who are interested and able to make the trip participate in this meeting in lieu of the class on October 18. (I intend to go to the meeting.) It is held at Northwestern University, a 2.5 hour drive away. Usually the organizers have some funds to assist junior participants. The earlier you ask the better your chances to get some, see the website. Students and faculty from around the region and even farther away come to this conference. It is usually a very enjoyable occasion. The scientific program is not very heavy and there is plenty of time for socializing.

Check out the Probability Seminar for talks on topics that might interest you.

Instructions for Homework

• Homework must be handed in by the due date, either in class or by 3 PM in the instructor's office or mailbox. Late submissions cannot be accepted in a course this large.
• Neatness and clarity are essential. Write one problem per page except in cases of very short problems.
• It is not trivial to learn to write solutions. You have to write enough to show that you understand the flow of ideas and that you are not jumping to unjustified conclusions, but not too much to get lost in details. If you are unsure of the appropriate level of detail to include, you can separate some of the technical details as "Lemmas" and put them at the end of the solution. A good rule of thumb is if the grader needs to pick up a pencil to check your assertion, you should have proved it. The grader can deduct points in such cases.
• You can use basic facts from analysis and measure theory in your homework, and the theorems we cover in class without reproving them. If you find a helpful theorem or passage in another book, do not copy the passage but use the idea to write up your own solution. If you do use other literature for help, cite your sources properly. However, it is better to attack the problems with your own resources instead of searching the literature or the internet. The purpose of the homework is to strengthen your problem solving skills, not literature search skills.
• It is valuable to discuss ideas for homework problems with other students. But it is not acceptable to write solutions together or to copy another person's solution. In the end you have to hand in your own personal work.