MATH 178 Fractals and Chaos
Summer 2007

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Instructor: Dr R. Pyke Office: K10504 (top floor, Schrum Science Centre)
email: rpyke@sfu.ca
Office Hours: Wed, Fri 11:00 - 11:20, 1:30 - 2:30 (or by appointment)
Teaching Assistant : Austin Roche aroche@sfu.ca
Assigment drop box : Near the mathematics workshops (one floor below the math and statistics offices in the Shrum Science Centre)

Lectures: Wed 11:30 - 12:20 WC 3253, Fri 11:30 - 12:20 WC 3253
Seminar: Wed 12:30 - 1:20 WC 3253
Course webpage: http://www.sfu.ca/~rpyke/math178

* * * Supplemental material; http://www.sfu.ca/~rpyke/335/index.html
"Math 335 course material" (link at bottom of Math 178 course webpage)
Applets and programs; http://www.sfu.ca/~rpyke/335/software.html , also linked at bottom of course webpage.

Text: Chaos and Fractals, New Frontiers of Science, 2nd Ed., by H-O Peitgen, H Jurgens, D Saupe. (Two copies are placed on reserve in the library.)

Prerequisites: Principles of Math 12 with a grade of at least C.

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Course Description: Fractals have been referred to as the "new geometry" and chaos as the "new science". This course will describe what these topics are, their historical development, and their use in mathematics and in areas outside mathematics (such as the arts, science, business) with a minimum of mathematics prerequisites. Along the way we will develop mathematical methods to understand and describe these concepts, as well as develop writing and verbal skills in this context.

The subject matter was (and is) greatly influenced by computers. We will often use various computer programs (available on the course webpage) to experiment, explore, and illustrate concepts. Lectures will include the use of computer programs, videos, possible guest speakers, and student presentations.

This course will appeal to those who have heard something about chaos and fractals and who want to know more, regardless of their mathematical background (for example, How do you draw fractals? What is a Julia set?). It will also appeal to those who come from areas outside of mathematics and have seen these concepts used in these areas (eg., life sciences), but have not had any formal mathematical study of these topics.

Course Objectives : This is a designated Q, W, B course (Quantitative, Writing intensive, Breadth). As such, there are learning objectives specific for each of these areas. In general, this course will increase your confidence in writing and reading articles and essays about scientifically technical topics, giving presentations, using quantitative methods to study complex problems, understanding how new scientific ideas arise and become accepted in the scientific community.

This course is designed to help you

• Q
  • Know what fractals are in a precise, mathematical sense
  • Analyze the mathematical properties of fractals
  • Understand various ways to draw fractals
  • Become familiar with the notion of dynamical systems
  • Study the mathematical properties of discrete dynamical systems (and why they appear in applications)
  • Appreciate the differences between deterministic dynamics and random dynamics, and to contrast these with chaotic dynamics (chaos)
  • Understand the mathematical equations that describe the Julia and Mandelbrot sets
  • Become familiar with the basic properties of Julia and Mandelbrot sets
  • Use various computer programs to investigate and help understand fractals, chaos, and the Julia and Mandelbrot sets
  
  
  
• W
  • Write and read articles of various lengths about mathematics
  • Critically analyze articles about fractals and chaos and related subjects
  • Prepare and present visual and oral projects
  
  
  
• B
  • Become knowledgable about the historical development of fractals and chaos
  • Look at how these new paradigms influenced mathematics and areas outside mathematics
  • Look at some some areas outside mathematics (eg., art) where fractals and chaos have appeared

See also the math department posting of the Math 178 outline for more information about the topics covered.

Course Evaluations:

Writing assignments 20% Combination of short (less than a page; approx 6) and long (2 - 4 pages; approx 3). Examples; summary of lectures, critical review of assigned reading material, review of video documentary. Students will also have an opportunity to critically (positively) evaluate other students written work and group presentations (and these evaluations will be marked). Guidance concerning the writing assignments will be provided (eg., marking rubric) as well as opportunity to revise the long assignments
Quantitative assignments 15%
Independent project (term) 15%
Group project, including presentation (term) 10%
Midterm test (Friday, July 6, 2 hours) 15%
Final exam (3 hours) 25%
Midterm and exam will have a writing component.