References
- Required Books
- Chaos: Making a New Science,
by James Gleick, Viking, 1987. (required)
The textbook is a popular historical account of the people and ideas involved
in the development of "the science
of chaos." It is more of a (nonfiction) novel than a textbook, but it does
allude to many mathmatical ideas.
- Optional Books
- A Toolkit of Dynamics Activities. A series of four interactive
textbooks for Dynamical Systems published by Key Curriculum Press
- Iteration, by Choate J, Devaney R L and Foster A, 1999
- Fractals, by Choate J, Devaney R L and Foster A, 1999
- Chaos, by Choate J and Devaney R L, 2000
- The Mandelbrot and Julia Sets, by Devaney R L, 2000
- Arcadia, a play by Tom Stoppard, Faber and Faber, 1993. Multiple references
to "chaos" and related mathematical ideas.
- Website: Interactive computer activities designed to accompany the four
Toolkit books above. Designed by R L Devaney. Freely available at
http://math.bu.edu/DYSYS.
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.
More specifically:
Class attendence: 10%
Class preparation/participation/Journal: 25%->18%
HW/Quizzes/Class reports: 40%->52%
Final Project: written : 15%
Final Project: presentation: 10%->5%
-------------------------- ---
Total: 100%
Journal
Each student should keep a journal for the course. The journal
should be a brief summary of ACTIVITIES done in the class and
OBSERVATIONS/QUESTIONS/IDEAS
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 the date of the entry and the date(s) when activities
were performed.
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/proof to another classmate, except to have the classmate read and
evaluate your work with you present.
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:
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/Math1234S2003.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
Monday, 31-Mar-2003 10:57:12 CST.