Math 551 - Advanced Probability I - Fall 2007

Probability theory based on measure theory. Strong law of large numbers, central limit theorem, martingales, more if time permits.

Topics covered:

Review of measure theory;  expectation and independence;  weak and strong laws of large numbers;  zero-one laws;  martingales;  applications of martingales;  characteristic functions;  central limit theorem;  Lindeberg-Feller theorem (if time permits).

Prerequisites: A good course in measure theory, or permission of instructor.
Textbook: Kai Lai Chung, A Course in Probability Theory, 3rd edition.
(Academic Press, paperback, 2001)   ISBN 0-12-174151-6
Class Time and Location:   TTh 2:30-4:00pm -- Earth/Planetary Science 203
Instructor: Prof. Stanley Sawyer -- Cupples I, Room 107
Phone: (314) 935-6703   --   Send an email
Office Hours: MWF 2:00-3:00pm   Office:  Cupples I  Rm 107
(Warn me in advance if you are coming  --  other times are OK by appointment)
Links: Homework Assignments
Ergodic-Theory Handout
Washington University Home Page

Take-home Final due Dec 20, 2007

Exams,  Homework Sets,  Grades,  Last Day of Classes,  and TakeHome Final:

There will be around three homework sets and a takehome final. Grades will be based on on the homework sets (around 60%) and the final (around 40%). Cr means D or better if you elect ``Credit/No Credit''.
The Last Day of Classes for the Arts and Sciences College this Semester is Monday, December 10. That means that the Last Day of Classes for us is Thursday, December 6. The takehome final will be due on or before Thursday, December 20, 2007 at 5:30 PM (WUCRSL Exam Code XXIV).

Collaboration:

Collaboration on homework is allowed and can be helpful (and fun). Collaboration on homework is encouraged. However, you must do all written work by yourself. If you collaborate with someone on a homework, you must list his or her name in a note at the top of the first part of your homework.

Collaboration on Takehome Tests:

There should be NO COLLABORATION on takehome tests.

WARNING:

Make a copy of each homework before you hand it in !!
It may not be returned before you need to refer to it for the next homework (or for the next test).

Some useful references:

S. I. Resnick, A Probability Path, Birkhauser 2001.
Richard Durrett, Probability: Theory and Examples, Wadsworth Brooks/Cole, 1991.
David Williams, Probability with Martingales, Cambridge University Press, 1991.

Click here for Prof. Sawyer's home page:

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    Last modified November 13, 2007