Chaos and Complex Systems

Fall 2004

Course Overview


Instructor: Dave Feldman Email: dave@hornacek.coa.edu
Office: Second Floor, Turrets Annex Phone: x249, 276-5284
Mailing List: odes@hornacek.coa.edu Office Hours: By appointment: email, call, or just stop by


Course Overview

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?

Text

Our primary text will be The Computational Beauty of Nature (CBN) by Gary Flake. Note, however, that CBN isn't a textbook in the normal sense. It's much more interesting than many texts, and there aren't problems at the end of each chapter. Although you could get by without buying a copy, I recommend purchasing one. The paperback edition is around $30.00. We will also do readings from a variety of other sources, including several textbooks, web sites, research papers, and articles.

At a bare minimum, I expect we'll cover the material in the following chapters of CBN: 5, 10, 11, 12, 15, 16, 17, 20. Many of these chapters are fairly brief; we'll supplement them with other readings. I also want to spend some time on graphs and networks. These topics aren't covered in CBN. As time permits, we may also discuss symbolic dynamics, incomputability and incompleteness, Mandelbrot and Julia sets, and other things.

Evaluation

Your evaluation will be based loosely on the following: I will assign grades (for those who so opt) by following the guidelines on page 8 of 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 Stuff

  1. The final version of this and related documents can be found on the course web page, http://hornacek.coa.edu/dave/Teaching/Chaos+Complex_Systems.04.
  2. Homework will 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, class tutors, 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. Information on what is expected for your final presentation can be found in a separate document.
  5. Information on what is expected in homework solutions can be found in a separate document.
  6. I will almost always assign reading for each class. You should do the reading before class and come prepared to discuss.
  7. I will have to miss classes on Tuesday September 21 and Tuesday November 16. We will discuss how to make up these classes.
  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. We may use the computer algebra system Maple. If you haven't learned to love Maple yet, you will soon. Here is a page with Maple info.
  12. 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.
  13. A more informal description of the course can be found here.


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Web page maintained by dave@hornacek.coa.edu.