Instructor: Dr. Tom Carter
DBH-287 667-3175
tom@csustan.csustan.edu
http://csustan.csustan.edu/~tom
Texts: The required texts for the class are:
Chaos: Making a New Science, James Gleick
Mathematics and the Unexpected, Ivar Ekeland
The Computational Beauty of Nature, Gary Flake
There are also many other books that are worth looking at -- I will
talk about a variety of them during the semester.
Purpose of Course and Objectives: The world is filled with systems of various degrees of complexity, which behave in various ways. Scientific/mathematical approaches to understanding systems always involve approximations, simplifications and modelling. The primary traditional paradigm has been to assume that systems are linear, but this assumption severely limits the extent to which we can understand systems, and the kinds of systems we can understand. Discarding the assumption of linearity opens new possibilities. In this course, we will develop a general understanding of the traditional linear approach, and then explore various nonlinear approaches and systems. Among the topics we will explore are phase space maps, Poincare sections, basins of attraction, strange attractors, fractals and fractal dimension, catastrophe theory, discrete approaches, and some of what is currently called complexity theory. The course will of necessity have a relatively high mathematical content, but I will work hard to provide the background for the material and to explain things in comprehensible ways. I don't necessarily expect you to understand everything we do, but I do expect you to work hard and apply yourself to understanding what you can. The laboratory component (which we will discuss in class later) will help you develop practical experience with nonlinear systems.
Grading:
The grades for this course
will be based on three components: written homework/in class quizzes, a
midterm (either a test or a paper -- we'll have to discuss this),
and a final project/paper.
Each of the components will be weighted
approximately equally.
Also, at the beginning of each class period, I want you to hand in a brief response to
the readings for the day. The response should contain a two or three point summary of
the important ideas of the section, and two or three points which you found confusing or
weak or deserving of additional coverage.
The work you do for this course will be your own. You are not to submit other people's
work and represent it as your own. However, I do expect and encourage you to work
collaboratively with others during the course.
General Summary of Material to be Covered:: (MU = Mathematics and the Unexpected, C = Chaos, CBN = Computational Beauty of Nature, Notes = other sources)