Chaos and Complex Systems

Course Overview

Instructor: Dave Feldman	Email: dave@hornacek.coa.edu
Office: Third Floor Arts and Sciences	Phone: x249, 276-5284
Mailing List: ccs@hornacek.coa.edu	Office Hours: 6:30 -- 8:00, TBA
Tutors: None.	Web page: http://hornacek.coa.edu/dave

Course Overview

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?

1. Several themes will run through all of what we do: order and randomness, simplicity and complexity. What do these terms mean? What are the relationships between them?
2. American society ... operates under the delusion that we are each a kind of ``solitary knower'' --- that we exist as rootless intelligences without layers of localized contexts. Just a ``self'' and the ``world.'' In this there is no real recognition that grandparents, place, grammar, pets, friends, lovers, children, tools, the poems and songs we remember, are what we think with. (Gary Snyder, Tawny Grammar.) I hope that the topics we explore in this course will give you some new things to think with.

Text(s)

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

• Weekly Homework Assignments: 45 percent.
• Week 5 Presentation: 10 percent.
• Final Project: 35 percent.
• Class Participation: 10 percent.

Final Project

• Can take many forms -- need not be a paper. We will discuss as a class whether or not we want to have a set of presentations open to the coa community, or if we just want to present to the class.
• Should be on some topic that's interesting to you.
• Must be more than a "book report"; you should do something: some analysis, programming, problems, etc.
• You and I share responsibility for the project. I will try to meet with you all individually and discuss possible projects. But you also need to take some initiative; if you're feeling lost or confused, be assertive and find me sooner rather than later.
• I strongly encourage you to work on projects in groups. Perhaps you'll end up doing separate projects, but maybe a few of you have broadly similar interests. If this is the case, I suggest doing some common background readings and meeting to discuss as a group.
• I will give you more information about project expectations sometime during week two.

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.
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. In order to make time for final presentations, we'll need to schedule a few extra classes toward the end of the term.
8. As I plan on sending out homework assignments and other information via email, it is important that you check your email regularly.
9. I expect you to attend class.
10. For the assignments and/or your final project, you may wish to 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. There are also a few Maple books on reserve in our library.
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.

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