MAT335 - Chaos, Fractals and Dynamics

Department of Mathematics, University of Toronto
Winter, 2003

Instructor: R. Pyke (office: at the back of the math aid centre, SS1071B; email:
Lectures: Monday and Wednesday, 8:45-10:00 a.m. in SS 2127.
Office hours: Monday and Wednesday; 10:10-11:30 a.m. in SS1071 (and by appointment).
Text: Chaos and Fractals: New Frontiers of Science, H.-O. Peitgen, H. Jurgens, D. Saupe. Springer-Verlag, 1992.
Course web page:

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 (The following books are 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 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).

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 by March 14. I will then discuss the project with the student and once we have reached a satisfactory outline of the content and goal of the project, the student may proceed with the project. The project should consist of a written report of 10-15 pages. Students doing the term project will also have to make a short (10-15 minutes) presentation to myself. The project could also contain a computer program demonstrating the topic - the computer program is not a necessary component of the project, however. 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). The due date for the term project is the same date as the final exam for the course.

Homework Homework questions will be posted incrementally on the web page (new questions will be added to the homework as the course progresses; check for updates regularly). They will be handed in for marking approximately every two weeks. Students will be allowed to work individually or in groups of 2 for the homework, but otherwise students are expected to work independently. Students who are working on the homework together will submit one solution set with the names of the group members written on it. Due to limits on the marker's time, only some of the homework questions will be marked (the ones to be marked will not be announced). Students will, however, receive credit for attempting the questions that were not marked.

Course Outline