Math 450 - Topics in Applied Mathematics

Random Processes

Spring 2007

room meeting times
Cupples I - 216 M W F 3:00 - 4:00 PM

instructor phone # office e-mail office hours
Renato Feres 5-6752 Cupples I 17 W 4:00 - 5:00 PM / F 2:00 - 3:00 PM

Note: You can see me outside the set office hours, but contact me in advance to be sure I'm in.

General Information

Topics. This is an introductory course on stochastic processes that takes a computational approach to the subject, with an emphasis on developing operational skills in modelling random phenomena.

Here are some of the topics we plan to cover:

Prerequisites. Math 449 or permission of instructor.

Text. There is no single textbook that covers the above topics in the way we plan to approach them. A large part of the theory can be found in the text: Markov Chains, by J.R. Norris. (Cambridge University Press, 1998.) I haven't placed an order for it with the campus bookstore, but I recommend that you buy it. (The paperback edition should cost around $35.) I plan to assign readings from this text and supplement it with notes to be handed out in class, as well as other reading material given on-line. (A list of web sites will be added to the bottom of this page.)

Homework. There will be (roughly) weekly homework assignments. You are encouraged to collaborate on them. Please return your solutions to the instructor by the end of class. Late homeworks will not be accepted. The homework will be judged for correctness and clarity. When the problem requires a computed solution, it must be accompanied by a correct, well-documented computer program which will be judged for its understandability. The homework problems will be posted on the lesson schedule at least a week in advance of its due date. They will also be announced in class.

Essay. You will also write a 5 to 15 typed pages essay about a topic of your choice in any area of the natural or social sciences, engineering, arts, or pure math, whose method of analysis relies on probabilistic modelling. You should have a preliminary write-up ready by the middle of the semester, and a final draft by the end of the semester. The final version will contain an exposition of the topic, with enough background information to convey the nature and interest of the subject to someone not familiar with it, and a numerical case study. You may choose to work individually or do a joint project with one or more classmates.

Computing. Students are encouraged to use MATLAB. It is available on the computers in the Arts and Sciences Computing Center. It does not take that much time to learn to use and program in Matlab for the needs of this course, if you do not have previous experience. Look for Matlab tutorials on-line. Here are two: tutorial 1 and tutorial 2.

Grades. Your grade will be calculated on the basis of homework assignments, the preliminary draft of your essay, and the final article. Each will contribute to the final score according to the following percentages: HW 70%, Prel. Draft 10%, and Final Art. 20%. Students taking the Cr/NCr or P/F options will need a grade of D or better to pass.

Score Grade is at least (possibly with + or - attached)
90-100% A
80-89.99% B
65-79.99% C
50-64.99% D
Below 50% NCR (F)

Lesson Schedule

The topic of the day, new assignments and solutions, supplementary reading material, as well as occasional news, will be posted below. I will post from time to time lecture notes supplementing the main text. This is a tentative schedule. It will be updated and modified as the course progresses. (For now, most links are inactive.)





References and sources of project topics

This is a list of bibliographical references. You may want to browse some of these books for inspiration as you try to decide which project topic to choose. More references may be added throughout the course. Of course, you do not have to restrict your choice to what is listed here.