Instructor: Jim Wiseman
Office: Buttrick 331
Phone: x6202
Email: jwiseman@agnesscott.edu (I check email much more frequently than voicemail.)
Office hours: Mon 11-11:30, Tues 2-3, Wed 2-3.
Course information: Available on Blackboard and the course website, http://ecademy.agnesscott.edu/~jwiseman/mat311 .
Required material: None. There is no textbook for the class; I'll give you handouts throughout the semester. We'll be using Maple extensively - it's installed on most of the computers in Buttrick and the Science Center. A good supplemental text is Chaos: An Introduction to Dynamical Systems, by Aligood, Sauer, and Yorke, available electronically through SOPHIA.
Plan: Our ultimate goal is to sketch the proof of the existence of chaotic dynamics in the Lorenz equations. To get there, we need to learn a lot about the properties of dynamical systems and ways of describing them (one-dimensional dynamics, attractors, fixed points, periodic points, chaos, sensitive dependence on initial conditions, fractals....). There's a detailed schedule at http://ecademy.agnesscott.edu/~jwiseman/mat311/schedule.html, but it's subject to change. On exploration days, I'll give you a list of questions, and you'll work in groups to try to answer them, mostly using Maple. On exercise days, you'll present your solutions to the homework. On mini-project days, you'll present your mini-project.
Homework: I'll hand out the homework assignments and projects in class. Due dates will also be posted at http://ecademy.agnesscott.edu/~jwiseman/mat311/assignments.html .
Final project: The final project consists of an 8-10 page paper and a 30 minute in-class presentation. Here's a list of some possible topics (I encourage you to think of your own): cellular automata, symbolic dynamics, notions of recurrence, complex dynamics, Julia/Mandelbrot sets, the Poincare-Bendixson Theorem, fixed-point theorems, n-body problem, tiling spaces, applications....
Honor code and group work: All students are expected to follow the honor code throughout the semester; all work should be pledged.
Getting help: My office hours are above - these are times when I'm guaranteed to be in my office and willing to talk. If you want to see me at other times, the best thing to do is to set up an appointment with me by email or after class. Of course, you're welcome to just drop by my office, as long as you don't mind if I'm not there or don't have time to talk.
Finally, I can't emphasize enough that your classmates are your best source of help.
Course goals: Learn to
- Define, describe, and apply the concepts of dynamical systems
- Communicate mathematics effectively, both orally and in writing
Dates and deadlines:
- Proposal for final project due: Thursday 3/20
- Final project outline and bibliography due: Thursday 4/10
- Final presentations begin: Thursday 4/17
- Final paper due: Monday 4/28
- No final exam.
Late work: Late work won't be accepted, and you won't be allowed to make up missed exams, except under very exceptional circumstances (e.g., the sasquatch attacks - and even then you should get a note from the sasquatch).
Attendance: Attendance is required at every class meeting.