Math 551 - Advanced Probability I - Fall 2009

  Topics covered:

Review of measure theory;  expectation and independence;  laws of large numbers;  convergence of random series;  martingales and applications;  characteristic functions and central limit theory;  central limit theorem for large deviations.  More if time permits.

Prerequisites: A good course in measure theory, or permission of instructor.
Textbook: Patrick Billingsley, Probability and Measure, 3rd edn,
(John Wiley & Sons, 1995)   ISBN 0-471-00710-2
Class Time and Location:   TTh 1:00-2:30pm --- Cupples I,  Room 216
Instructor: Prof. Stanley Sawyer --- Office: Cupples I, Room 107
Phone: (314) 935-6703   --   Send me an email
Office Hours: MW 3:00-4:00pm   ---   Cupples I,  Rm 107
(Warn me in advance if you are coming, since I may have a conflict --- )
(Other times are OK by appointment)
Links: Homework Assignments and Take-Home Final
Measures on Semi-Rings (handout)
Notes on Lifting Measures (handout)
Mathematics Department Home Page
Washington University Home Page
Prof. Sawyer's home page (for other syllabi)

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

There will be six homework sets, a midterm, and a final. Grades will be based on on the homework sets (around 60%), the midterm (around 20%), and the final (around 20%). 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 7, 2009, and thus Thursday, December 3, for us.
The take-home final is due on Wednesday, December 16, by 4:30 PM (WUCRSL Exam Code XVIII).

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 the take-home final is not allowed.

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:

Kai Lai Chung, A Course in Probability Theory, 3rd edition.
(Academic Press, paperback, 2001)   ISBN 0-12-174151-6
S. I. Resnick, A Probability Path, Birkhauser 2001.
Andrei Kolmogorov, Foundations of the Theory of Probability, 2nd edn, Chelsea Publishing 1956, translation of Russian original dated 1933.
Richard Durrett, Probability: Theory and Examples, Wadsworth Brooks/Cole, 1991.
David Williams, Probability with Martingales, Cambridge University Press, 1991.

A useful reference for measure theory:

Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edn (John Wiley & Sons, 1999)   ISBN 0-471-31716-0

Click here for Prof. Sawyer's home page:

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    Last modified December 7, 2009