Math 1234 Chaos, Fractals, and Dynamics

Prof. Peckham

Spring 2005 Syllabus

Syllabus

Course description

Dynamical Systems is a fascinating area of mathematics which is especially attractive to nonexperts because of the combination of wonderful pictures which arise in its study (fractals) and because of the amazing complexity of "behaviors" which arise from very simple "rules." In addition, although dynamical systems can include very deep mathematical analysis, much can be investigated and understood with only a background in high school algebra.

Through hands on exercises, computer experiments, visuals, readings, and discussions, students will be introduced to the concepts of iteration, fractals and chaos and to the people involved in this intriguing field. The course will begin by looking at the basic concept of iteration: repeatedly applying some specified operation. Mathematically, iteration involves defining and investigating a "dynamical system." This will be done through a combination of student exercises (see A Toolkit of Dynamics Activities in the reference list), prepared computer experiments (see website in the reference list), and instructor explanation. A primary goal will be to understand the "eventual state" of an iterative process. Iteration leads naturally to, among other things, the geometric notion of a "fractal," and the notion of mathematical "chaos." These concepts are also introduced and explored via the Toolkit activities.

The mathematics will be complemented by reading Chaos: The Making of a New Science, by James Gleick. This is a (slightly romanticized) historical account of the people and the ideas behind the creation of the science of chaos. It refers frequently to many of the mathematical ideas we will cover in the course.

Course Objectives/Outcomes

Students should learn concepts from mathematics and ways in which these concepts can be applied to model and explain real world scenarios. They should develop an appreciation for mathematics as a current, active, useful and exciting field of study. Students will develop their own research skills, as well as enhancing their abillities to cooperate and communicate.

Grading (Tentative)

Students will be evaluated on a combination of written homework assignments, computer experiments, projects, class preparation and participation, oral presentations, and tests. The following percentages are subject to slight modification by the instructor. Students will be notified of any changes.

More specifically: 

Class prep/participation/journal: ............	25%
  (attendance: 7%, class prep/participation/presentation(s): 10%, Jounal:8%)
Homework Sets (approx. 7):	..............	30%
Quizzes (approx. 4):		..............	25%
Final Problem Set:		..............	10%
Final Paper:			..............	10%
-------------------------		       ---
Total:					       100%

Journal

Each student should keep a Journal Notebook for the course. The Journal should be a brief summary of ACTIVITIES done in the class and OBSERVATIONS/QUESTIONS/IDEAS/EXTENSIONS which have arisen either individually or from the group. There should be an entry for each class, and an entry for each time period between classes. Each entry should have an entry number, entry title, including date(s) covered, and date recorded.

General policy statement

Seminar meetings, material in the readings, homework, Web exercises, presentations and tests are all intended to complement each other. No one is a replacement for any of the others. You are, in general, expected to learn material which is covered via any of these sources.

Reading Assignments

For readings assigned in Gleick's CHAOS: Making a New Science, students should read the first time through for general comprehension, and a second time through for specifics. Make notes about any material on which you have questions, ideas that you think are especially interesting or new, and ideas that extend beyond what is presented in the book. The notes should help you to make contributions to the class discussions about the book.

Homework Sets and Ground Rules

All work should be neatly written, well-organized, and complete.

For Homework turned in individually: You are encouraged to exchange ideas with each other, but each person should write up his/her solutions completely in his/her own words. It is never appropriate to give a written version of a problem solution to another classmate. It is OK to verbally explain your ideas to another classmate, as long as the classmate then writes up his/her work on his/her own. One person copying a classmate’s solutions is expressly forbidden and will result in both students receiving zeroes for that complete homework set and facing academic disciplinary action.

For Homework turned in in groups: Students are encouraged to work in groups of 2 or 3. All people listed in the group should have made contributions to the work or they should not be listed in the group. Everyone in the group should completely understand the work handed in, even if someone else in the group did the original work. As for work turned in individually, work should never be copied from another group's work. Discussion of problems and solutions between members of different groups is acceptable.

Assignments will be confirmed by email, and all past and current assignments will be posted on the web at `www.d.umn.edu/~bpeckham/Math1234S2005.html'

Missed Exams or Quizzes

Missed quizzes or exams will be assigned a zero score unless you provide a valid written, signed (by a Doctor, for example) excuse for your absence; unless it is not possible to do so, you must provide verbal notice ahead of time to your instructor for an absence. Arrangements for a makeup should be made as soon as you know you will miss. Do not wait for the next class. You can leave the instructor a message 24 hours a day by phone or email. Oversleeping, poor preparation, slight colds, and cold weather are not valid excuses.

Liberal Education Justification

This course satisfies Category 2: Math, Logic, and Critical Thinking, of the Liberal Education Program. It introduces students to mathematical techniques and applications and critical thinking skills essential for their functioning in contemporary society.

Disabilities

Please inform me of any disabilities of which I should be aware in order to provide for equitable participation.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by Bruce Peckham (bpeckham@d.umn.edu) and was last modified on Tuesday, 18-Jan-2005 15:30:33 CST.