Introduction to Chaos and Fractals

Course Overview

Winter 2008

I would...urge that people be introduced to [chaos] early in their mathematical education. [Chaos] can be studied phenomenologically by iterating it on a calculator, or even by hand. Its study does not involve as much conceptual sophistication as does elementary calculus. Such study would greatly enrich the student's intuition. Not only in research, but also in the everyday world of politics and economics, we would all be better off if more people realised that simple nonlinear systems do not necessarily possess simple dynamical properties.

Sir Robert May, 1976

Goals

• I want you to gain a solid understanding of the basic mathematical ideas behind chaos and fractals. As part of this, I hope you'll leave this course thinking somewhat differently about order and disorder, simplicity and complexity.
• I want to help you improve your basic facility with algebra and functions, your problem solving skills, your ability to create and interpret different types of graphs, and your overall mathematical confidence.
• I want you to gain a sense of how math and physics is done, and gain an awareness that these are not static, "dead" disciplines. I want you to gain a greater understanding of science as an institution and science as a culture.

Texts

1. We will read Chaos: Making a New Science by James Gleick. This is a "popular science" book and is not a traditional text.
2. We will also use a draft of Introduction to Chaos and Fractals, a textbook that I am writing. I will hand this out in several installments.
3. Toward the end of the term we'll read a number of short papers, and quite likely a short story and some poetry. The exact assignments will depend on the interests of the class.

Evaluation

• Weekly Homework Assignments: 45 percent.
• Final Project: 25 percent.
• Class and Lab Participation: 15 percent.
• Short Papers: 15 percent.

Class Structure and Policies

1. The final version of this and related documents can be found on the course web page, http://hornacek.coa.edu/dave/Teaching/Chaos+Fractals.W08.
2. This class meets both the ES and the QR requirements. Versions of the class prior to Spring 2006 only met the QR requirement.
3. Homework will usually be due Fridays at the end of the day. More than one unexcused late homework assignment will likely result in me mentioning this in your narrative evaluation and may result in a lowering of your grade.
4. 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 copy their solution and turn it in.
5. Guidelines for writing up homework problems can be found here.
6. There will be no exams. However, there may be a large-ish, synthetic assignment toward the end of the term.
7. You will do a final project for this class. If you wish, you can collaborate with other students. Although projects can take varying forms, most will end up giving a presentation of around 15 minutes towards the end of the term. For more info, see the project guidelines.
8. There will frequently be reading assigned for class. When this is the case, you should prepare several questions or comments on the reading, and get them to me by 9pm the evening before class. Email or paper is fine.
9. You will write three short (2-3 page) papers exploring ideas from the book by Gleick and/or our discussions. Information about what's expected for the short papers can be found here.
10. We may need to schedule an extra class or two during weeks 9 or 10 so we have enough time for the presentations.
11. As I plan on sending out homework assignments and other information via email, it is important that you check your email regularly. Also, you will need to use the www for some of your assignments.
12. Labs will meet Tuesday afternoons. There will be very little, if any work associated with the labs outside of the labtime itself. Labs will take one to two hours; we will arrange to stagger lab groups' arrival time, as there is only one set of apparatus for most experiments. It is important that you attend lab and arrive on time. It will not be possible to make up missed labs.
13. The labs for this class were developed with the support of the Maine Space Grant Consortium, via grant # SG-05-31.
14. I expect you to attend class.
15. 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 years ago..
16. For a more informal description of this course, see a list of what to expect.