Math 357

Discrete Dynamical Systems

How to get in touch with me

Office: Olin 314
Office Hours: see schedule
Phone: 933-7463
Email: tlofaro@gustavus.edu

Text

A First Course in Chaotic Dynamical Systems: Theory and Experiment, R.L. Devaney, Perseus Books..

Objective

This course provides an introduction to discrete dynamical systems on the real line and in the complex plane._ In particular, we will learn techniques for understanding systems that exhibit chaotic behavior

Chapters Covered

We will be covering parts or all of chapters 1 through 12 concerning dynamics on the real line and chapters 15 through 17 on complex dynamical systems. These chapters will be supplemented with additional material as necessary. Here is the tentative schedule for the semester.

Grading

Homework Assignments	70 points
Challenge Problems	30 points
2 Exams	200 points
5 Projects	100 points
1 Final Exam	150 points

Homework

Homework assignments will be given daily at the beginning of each class period and will be posted on the Math 357 homework page. Explain your work clearly and concisely in complete sentences when appropriate. Each set is worth 10 points. Homework will be collected every Friday in class. No late homework is accepted for any reason. The lowest homework score will be dropped. Staple each homework set separately.

Challenge Problems

Challenge problems are generally more theoretical than the homework problems. There are no due dates for challenge problems. You should turn in challenge problems when you think you have completed it. What you turn in should be well written, legible, etc. At the beginning of each problem you should write the problem number and statement of the problem. Proofs should be complete and examples or counter-examples clearly explained. There is no partial credit for these problems, but you will be able to redo a problem that is not correct. Everyone must complete at least 3 challenge problems during the semester. Each additional challenge problem that you complete can be traded for a final exam problem. For example, if you successfully complete 13 challenge problems then there will be 10 problems (equaling 100 points) that you will not have to complete on the final exam.

Exams

The two midterm exams will be individual take-home exams. You will be allowed a note card and calculator for each exam.

Exam Schedule

Midterm I	10/6
Midterm II	11/14
Final Exam	TBD

Projects

You will be doing three computer projects in this class. The projects will be done in groups of 2 or 3. The final report must be typed and will be graded on both mathematical content and accuracy as well as on style and grammar. I will provide you with guidelines on the project later in the semester. Here is the schedule for the projects.

Project 1 (Section 3.6, Maple Worksheet 1)	9/12
Project 2 (Section 6.4)	9/26
Project 3 (Section 8.3)	10/10
Project 4 (Section 10.4)	10/31
Project 5 (One of 17.3-17.7)	12/??

Helpful Links

· A graphical analysis applet. (from my pal Bob D.)

· A bifurcation diagram applet. (again from big Bob)

· Julia sets and the Mandelbrot set. (same Bob channel)

· The Mandelbrot Set Iterator (same Bob time)

· If you don’t like Bob’s then try these by C.J. Kentler who wrote them for me at WSU.

· There is a ton of this stuff out on the web. If you find any you like better than these (in particular ones that will print) then let me know and I’ll add the links).

Maple Worksheets

In Firefox:_ To download these worksheets right click on the link and choose Save link as …from the drop-down menu._ Save the file as whatever.mw (the browser may add the extension xml._ If so delete this.)_ After you save the file you can then open it in Maple 10.

In Internet Explorer: To download these worksheets right click on the link and choose Save Target as …from the drop-down menu._ Save the file as whatever.mw (the browser may add the extension xml._ If so delete this.)_ After you save the file you can then open it in Maple 10.

· An Introduction to Maple for Discrete Dynamical Systems (Project 1)

· Plotting and Graphical Analysis using Maple (Chap. 4 homework)

· Fixed and Periodic Points (Chap. 5 homework)

Academic Honesty:

As a community of scholars, the faculty and students of Gustavus Adolphus College have formulated an academic honesty policy and honor code system, which is printed in the Academic Bulletin and in the Gustavus Guide. As a student at Gustavus Adolphus College I agree to uphold the honor code. This means that I will abide by the academic honesty policy, and abide by decisions of the joint student/faculty Honor Board.

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