Introduction to Chaos and Fractals
Office: Second Floor, Turrets Annex
Phone: x249, 276-5284
Office Hours: By appointment. Feel free to call or stop by
Mailing List: chaosAThornacekDOTcoaDOTedu
Help Session: Wednesdays, 6:30-8:00pm TAB
I would...urge that people be introduced to [chaos] early in their
mathematical education. [Chaos] can be studied phenomenologically by
iterating it on a calculator, or even by hand. Its study does not
involve as much conceptual sophistication as does elementary
calculus. Such study would greatly enrich the student's intuition.
Not only in research, but also in the everyday world of politics and
economics, we would all be better off if more people realised that
simple nonlinear systems do not necessarily possess simple dynamical
Sir Robert May, 1976
I have several goals for this course:
- I want you to gain a solid understanding of the basic mathematical
ideas behind chaos and fractals. As part of this, I hope you'll leave
this course thinking somewhat differently about order and disorder,
simplicity and complexity.
- I want to help you improve your quantitative literacy, problem
solving skills, and mathematical confidence.
- I want you to gain a sense of how math and physics is done, and
gain an awareness that these are not static, "dead" disciplines. I
want you to gain a greater understanding of science as an institution
and science as a culture.
- We will read Chaos: Making a New
Science by James Gleick. This is a "popular science" book and is
not a traditional text.
- We will also use draft zero ofIntroduction to Chaos and
Fractals. This is the first draft of a book that I am writing to be
used with this course. I will hand this out chapter by chapter. I
will be working frantically this term to stay one or two chapters
ahead of the class.
- Toward the end of the term we'll read a number of short papers,
and quite likely a short story and some poetry. The exact assignments
will depend on the interests of the class.
Your evaluation will be loosely based on the following:
I recommend against grades; I believe they are more likely than not to
interfere with genuine, reflective learning. However, I will assign
grades (for those who so opt) by following the guidelines in the COA
Course Catalog. I do not have any quota of A's, B's, etc.
- Weekly Homework Assignments: 45 percent.
- Final Project: 25 percent.
- Class and Lab Participation: 15 percent.
- Short Papers: 15 percent.
Class Structure and Policies
- The final version of this and related documents can be found on
the course web page, http://hornacek.coa.edu/dave/Teaching/Chaos+Fractals.S06.
- This class meets both the ES and the QR
requirements. Previous versions of the class only met the QR
- Homework will usually be due Fridays at the end of the day. More
than one unexcused late homework assignment will likely result in me
mentioning this in your narrative evaluation and may result in a
lowering of your grade.
- You are strongly encouraged to work together on homework. You
can also consult me, class tutors, other faculty, friends,
and family. However, the homework you hand in should represent
your own understanding. This means that if your friends get a
homework problem and you don't understand how they did it,
you shouldn't photocopy their solution and turn it in.
- Guidelines for writing up homework problems can be found here.
- There will be no exams. However, there may be a large-ish,
synthetic assignment toward the end of the term.
- You will do a final project for this class. If you wish, you can
collaborate with other students. Although projects can take varying
forms, most will end up giving presentation
of around 15 minutes
towards the end of the term. For
more info, see the project
- There will frequently be reading assigned for class. When this
is the case, you should prepare several questions or comments on the
reading, and get them to me by 9pm the evening before class. Email or
paper is fine.
- You will write three short (2 page) papers exploring ideas from
the book by Gleick and/or our discussions. Information about
what's expected for the short papers can be found here.
- We will probably need to schedule an extra class or two during
weeks 9 or 10 so we have enough time for the presentations.
- As I plan on sending out homework assignments and other
information via email, it is important that you check your email
regularly. Also, you will need to use the www for some of your
- Labs will meet Friday afternoons. There will be very little, if
any work associated with the labs outside of the labtime itself. Labs
will take one to two hours; we will arrange to stagger lab groups'
arrival time, as there is only one set of apparatus for most
experiments. It is important that you attend lab and arrive on time.
It will not be possible to make up missed labs.
- The labs for this class were developed with the support of the
Maine Space Grant Consortium, via grant # SG-05-31.
- I expect you to attend class.
- Academic misconduct -- cheating, plagarizing, etc. -- is bad. Any
cases of academic misconduct will result in a judicial hearing, as
per pp. 14-15 of the COA handbook. Possible consequences range
from failure of the assignment to expulsion. For more, see the revised statement on academic
integrity passed by the faculty several years ago..
- For a more informal description of this course, see a list of
what to expect.
[ Dave ]
[ Chaos and Fractals ]
[ COA ]