MAT335 - Chaos, Fractals and Dynamics

Department of Mathematics, University of Toronto
Winter, 2002

Instructor: R. Pyke (office: at the back of the math aid centre, SS1071; email: pyke@math.toronto.edu)
Lectures: Wednesday and Friday, 8:45-10:00 a.m., SS 2127.
Office hours: To be announced (check the course web page), but will probably be right after classes (and by appointment).
Text: Chaos and Fractals: New Frontiers of Science, H.-O. Peitgen, H. Jurgens, D. Saupe. Springer-Verlag, 1992.
Course web page: http://www.math.toronto.edu/courses/335

Please check the course web page regularly. You will find comments about the course material, homework problems, resources, and computer programs that we will use during the course.

References (On reserve in the Gerstein Science Information Centre, short term loan section) You may also want to browse through sections Q 172.5, QA 447, and QA 614.8 in the library, which contain books on the topics of fractals and chaos, as well as applications.

Some popular books
For a general discussion about the history behind 'chaos theory', the scientific ideas and the people involved, I would recommend the following books. Videos
The audio visual library at Gerstein (one floor down) has several videos about chaos and fractals (just type the key words 'chaos' or 'fractal' on the on-line catalogue). We will watch one video, Fractals: An Animated Discussion, call #002948, at some point in the course.

Web sites
There are many web sites devoted to chaos and fractals, so there is much to explore here (eg., 'text book' descriptions, pictures, applications in science, fractal music, etc). Note that many universities have web sites describing the research of 'dynamical systems' or 'nonlinear dynamics' groups working in mathematics, physics, chemistry, biology, computer science, and medicine. You can start with the links listed in the resources section of the course web page (the 'Internet Resources' appendix of the Hypertextbook on Chaos website lists many, many links).

Prerequisites
Students should have second year calculus (can be taken concurrently) and a course in linear algebra. Differential equations and complex numbers will come up, but you are not expected to have studied these before.

Marking scheme Students may be able to do a term project in lieu of writing the final exam. Those interested in doing a project should talk to me about possible topics before the end of February and present to me a written outline of the project. If the outline is satisfactory, the student will be allowed to persue the project. The project could be, for example, a topic in the text that we didn't cover in class, an 'experiment' using a computer program, or some topic related to your studies in another course (some possible topics are listed in the "suggestions for term projects" link on the course webpage; see the "student projects" link on the course webpage for previous year's projects). Students doing the term project will also have to make a short (10-15 minutes) presentation to me. The due date for the term project is the last day of exams.

Students will be allowed to work individually or in groups of 2 for the homework, but otherwise students are expected to work independently. Homework problems will be assigned as the course progresses (and posted on the webpage). They will be handed in for marking approximately every two weeks.

Course Outline