Math 388: Chaos and Fractals
2005
Chaos: Introduction
to Dynamical Systems, Alligood, Sauer and Yorke, Chapters 1-6, 9, 11-12
Chaos: Making
a New Science by Gleick; and Sync by Strogatz
Dr.
Roland Minton, Trexler 270-G, 375-2358,
office
hours 7-9M, 1-2T, 10-11W, 2-3Th
minton@roanoke.edu www.roanoke.edu/staff/minton/ccourse.html
Course Objectives: The principles of chaos
theory burst upon the scientific world in the 1970’s and 1980’s. With roots in
intractable “random” scientific problems and specialized mathematics, chaos
(more properly called nonlinear dynamical systems) has made a remarkable impact
on modern research. Although much of the mathematics of nonlinear dynamical
systems remains outside of the mathematical mainstream, the ideas and
techniques of chaos have become familiar to researchers in a variety of
disciplines. In this course, the basics of dynamical systems and the fractals
they generate are covered. Through reading and discussion, many of the
applications and innovations and the philosophy of life of chaos theory will be
touched upon.
Attendance Policy: This class meets only two
days per week. Regular attendance is essential. You are responsible for
everything done in class, through your attendance and sharing class notes with
classmates. If you miss a class, e-mail me before class is over and find out
what you missed.
Equipment: We will use the TI-89
calculator in class and on tests and Mathematica on homework assignments.
Academic Integrity: The college policy is
fully supported. Tests are closed notes, closed book. No electronic devices
other than calculators are allowed in a test situation.
Homework: Problems from each section
of the book will be assigned, chosen from in-chapter exercises, the
end-of-chapter exercises and computer explorations. Additional non-textbook
homework problems will frequently be handed out. Assignments will be posted on
the course web site and stated at the end of class. Unless otherwise stated,
your work on these problems is due at the beginning of the next class. Also,
homework assignments will sometimes relate to the reading of the two popular
books.
Co-Curricular: During the course of the
semester, you must attend at least three approved co-curricular events offered
by the math department. For each, write a one- or two-paragraph description of
the event. Each one will count as a homework grade.
Tests: There will be two tests
and a final exam. Each test will cover all material discussed since the
previous test. Anticipated test dates are (Th) 10/6 and (Th) 11/17. The exam is
Friday, December 16, 8:30-11:30.
Make-ups: In case of sickness or
scheduling conflicts, get in touch with me ASAP.
Grading: The homework counts 2
tests, the exam counts one test, each test counts 20% of the final average.
Grades may be curved up based on participation, one unusually low test score or
other extenuating circumstance.
A:
93-100 A-: 90-92 B+: 87-89
B : 83-86 B-: 80-82 C+: 77-79
C: 73-76 C-: 70-72
D+:
67-69 D: 63-67 D-: 60-62
F: 59 and below