Chaos and Complex Systems

Fall 2006
Informal Description

This course is, in some important ways, different than most other courses I offer. Also, I suspect that this class will be very different than math classes you have taken elsewhere. To get the most out of the course, it's important that you know what to expect.

  1. This course is a survey course. My goal is to give you a good introduction to a wide range of really cool, fun, modern topics. Due to time constraints we will not be able to go into enormous depth into any one topic.
  2. My experience has been that some of you may find the survey nature of this course somewhat frustrating. The only alternative is not covering some topics, which would mean we would miss out on some stuff that's too good to miss out on.
  3. Although this is a math course, and although calculus is a prerequisite, most topics we cover will bear little resemblance to things you've done in other math classes. You'll be exposed to many different styles of thought and, hopefully, go through some fun mental gymnastics.
  4. I expect that this course will be fairly interdisciplinary, especially in the final projects you chose to do. We will do readings from math, theoretical physics, and computer sciences books and articles. We will probably also read at least one anthropology article and perhaps some short fiction.
  5. We will also frequently discuss what lessons, if any, a given topic might have for other fields, including biology, ecology, economics, and political science. There will be ample room for lively disagreement.
  6. I hope this course is a beginning and not an end. If you're frustrated that you don't have time to learn all the details about a particular topic or idea, don't worry. You have many years left to learn.
  7. Particularly at first, we'll be jumping from topic to topic. The topics may seem disconnected, but eventually a handful of themes will emerge.
  8. The topics we'll be covering are, to different degrees, all areas of active research. This means that for many topics there are few textbook-style readings appropriate for the level of the class. So on some occasions we'll have to read some current review articles or rely on my lectures or lecture notes. This also means that we will encounter many open questions and some disagreement along the way.

Homework thoughts:
  1. In many traditional math classes the instructor shows you how to do a bunch of problems, you go home and obediently practice the stuff your instructor showed you, and then you take a test. This class will not be like that -- there will be some "plug and chug"-esque problems, but there will be many other exercises too.
  2. There will also be some more open-ended, exploratory problems, often involving some sort of computer exploration. I'll ask you to explore some stuff, make observations, and look for patterns. You will enjoy these assignments more (and do better on them) if you approach them as you would a good laboratory exercise in a science class.
  3. I also anticipate that on some assignments there may be at least one question where you will need to write a prose response. Your response, probably between one and two pages, need not be a polished essay, but it shouldn't be a sloppy journal entry, either.
  4. Homework is important, but it's less important in this class than in most other math classes that I teach. In order to really get a lot out of this class, you need to do the homework, but you also need to do the readings and push yourself to think and discuss.