Chaos and Complex Systems

Fall 2006
Course Overview

Instructor: Dave Feldman Email: daveATh0rnacekDOTcoaDOTedu
Office: Second Floor, Turrets Annex Phone: x249, 276-5284
Mailing List: ccsATh0rnacekDOTc0aDOTedu Office Hours: Wed 6:30-8:00 in TAB, by appointment

I have several goals for this course:
  1. I want to help you gain experience in and appreciation for a variety of different styles and flavors of mathematics. We will do a lot of different things in this course, and almost all of them should be really fun and interesting.
  2. I want you to gain experience working with and critically evaluating different mathematical models.
  3. I want you to do an in-depth, focused study of a particular mathematical model or technique.
  4. I want to help you improve your quantitative literacy, problem solving skills, and mathematical confidence.
  5. I want to have fun while working hard and learning some challenging material.

But what is this course really about? What are some of the central questions to be addressed by the class?
  • Order and randomness, simplicity and complexity. What do these terms mean? What are the relationships between them? How does order (or randomness, simplicity, or complexity) arise?
  • What are different types of mathematical models---spatial, non-spatial, network, differential equations, agent-based, discrete, continuous, deterministic, stochastic, ... ? What are the important differences and distinctions between these types of models?
  • What are the different uses of mathematical and computational models? What assumptions are behind different models?

Your evaluation will be based loosely on the following:
  • Weekly Homework Assignments: 45 percent.
  • Week 5 Presentation: 10 percent.
  • Final Project: 30 percent.
  • Class Participation: 15 percent.
I will assign grades (for those who so opt) by following the guidelines in the COA Course Catalog. I do not have any quota of A's, B's, etc. In general, I strongly recommend against grades; I believe they are more likely than not to interfere with genuine, reflective learning.

Policies and Course Details:
  1. The final version of this and related documents can be found on the course web page,
  2. Homework will usually be due Fridays at the end of the day. More than one unexcused late homework assignment will result in me likely mentioning this in your narrative evaluation and may result in a lowering of your grade.
  3. You are strongly encouraged to work together on homework. You can also consult me, other faculty, friends, and family. However, the homework you hand in should represent your own understanding. This means that if your friends get a homework problem and you don't understand how they did it, you shouldn't photocopy their solution and turn it in.
  4. You will frequently need to consult a variety of books, papers, and websites in order to do the homework. This is encouraged. You should be sure to cite any references you use, however.
  5. Information on what is expected for your final presentation can be found in a separate document.
  6. Information on what is expected for homework solutions can be found in a separate document.
  7. I will almost always assign reading for each class. You should do the reading before class and come prepared to discuss.
  8. In order to make time for final presentations, we'll need to schedule a few extra classes toward the end of the term. I would like to open up our final presentations to the full COA community.
  9. As I plan on sending out homework assignments and other information via email, it is important that you check your email regularly.
  10. I expect you to attend class.
  11. Academic misconduct -- cheating, plagarizing, etc. -- is bad. Any cases of academic misconduct will result in a judicial hearing, as per pp. 14-15 of the COA handbook. Possible consequences range from failure of the assignment to expulsion. For more, see the revised statement on academic integrity passed by the faculty several winters ago.
  12. A more informal description of the course can be found here.