Mathematics 439: The Mathematics of Fractals and Chaos

Graduate credit:

This course is also available for graduate credit for mathematics students as Math 590, Section SW. Graduate students not in mathematics can get nonmajor graduate credit by taking Math 439.

Fractals are intricate shapes like the one above, often exhibiting "self-similarity," so that if one zooms in on a region, the magnified region still may have just as complicated and rich an appearance as before. The name "fractal" indicates that the "dimension" of the shape could be a fraction, not necessarily a whole number. Fractals can be used to model complicated situations where objects like circles and parallelograms are inadequate. Fractals also yield very interesting computer pictures. Such concepts will be explored in the course.

Spring 2008, 3 credits

Instructor:

Stephen J. Willson
Office: Carver 411
Telephone: 294-7671
Email: swillson@iastate.edu
FAX: (515)-294-5454

Class meetings:

T Th 9:30 - 10:50 am in Carver 294.
The first class is Tuesday, January 15, 2008. There are no classes on Martin Luther King Day (January 21) and Spring Break (the week of March 17 - 21).

Office hours:

Tentatively these will be MTWThF 2:10-3:00 in 411 Carver. Please also feel free to make an appointment if the office hours are inconvenient for you.

Current homework assignments:

To obtain recent assignments and current information about course requirements, click here.

Selected lecture notes:

Current course grades

Current course grades and all recorded scores are available on the web by clicking grades. Scores are listed by the first 6 digits of the second part of the student identification number. If a score has been incorrectly recorded, you should contact the instructor.

Prerequisites:

Math 265.

Catalog description:

Topology of metric spaces; iterated function systems; algorithms for generation of fractals; fractal dimension; Julia sets and the Mandelbrot set; applications to chaotic systems. Nonmajor graduate credit.

Textbook:

Chaos: An Introduction to Dynamical Systems, by Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke (Springer).

Tentative syllabus (subject to change):

Grading

Grades will be based on points accumulated. There will be graded problem sets approximately each week in addition to ungraded practice problems. There will be one or two hour exams. Students will either take a final exam or turn in an individual project. Course grades may include a plus or a minus.

Graduate students registered for Math 590 will do all the work for undergraduates in Math 439. They will be required to do an individual project with higher expectations. They may also have some additional homework problems, when appropriate.

Computer usage:

Occasional classes will take place in the computer lab. During these classes, students will use Macintoshes to draw and analyze some fractals by a variety of methods.

Computer links about fractals:

There are a huge number of web sites associated with fractals, and a search on Google for fractals will have a huge number of hits. Here are a few URLs to get started:

Disabilities:

Please address any special needs or special accommodations with me at the beginning of the semester or as soon as you become aware of your needs. Those seeking accommodations based on disabilities should obtain a Student Academic Accommodation Request (SAAR) form from the Disability Resources (DR) office (515-294-6624). DR is located on the main floor of the Student Services Building, Room 1076.

Information about the instructor:

For more information about the instructor, click here.

Last updated January 11, 2008.