Welcome to Math 8
This is Math 53: Chaos!
Chaotic dynamical systems are everywhere: weather patterns, swinging
pendula, population dynamics, even human heart rhythms. With a balance
of theory and applications, this course will introduce: flows, fixed
points, bifurcations, Lorenz equations, Lyapunov exponent,
onedimensional maps, perioddoubling, Julia sets, fractal dimension.
Optional topics may include: Hamiltonian systems, symbolic dynamics.
Numerical explorations will form an integral part of the course; I
recommend (and will be using and demonstrating) Matlab (or its free
cousin Octave). In the final 3 weeks you will research and present a
final project investigating a topic beyond the taught material.
The goal is to introduce you to the recent, exciting, and
rapidlygrowing area, and to strike a balance between theoretical
analysis, concepts, computeraided exploration, and applications. The
impact of nonlinear dynamical systems on science has been farreaching,
including the physical, life and social sciences, engineering, finance
and mathematics, and therefore we expect this course to be of interest
to all such students with a mathematical background in linear algebra
and differential equations.
Instructor and General Information
Adrianna
Gillman
(2 hour) 
Lectures: MWF 1:45  2:50
Xhour: Th 1:001:50 
Lecture location: 004 Kemeny Hall

Office: 210 Kemeny Hall 
Office hours: MF 3:004:00, T 1:002:00
and by appointment 
email 
Note that you do not need an appointment to attend
regularlyscheduled
office hours. If you have a conflict you may make an appointment to
meet outside those times.
Textbook: Chaos: An Introduction to Dynamical Systems,
First Edition, by Kathleen Alligood, Tim Sauer and James Yorke
(Published by Springer, 1996).
Private tutoring: Tutor Clearinghouse
may have
private
oneonone tutors available for Math 46 (although this is rare in
advanced courses, so come and talk to me if you feel lost and no tutors
are available).
If a student receives financial aid, the
College will pay for three hours of tutoring per week. If you would
like to have a tutor, please go to 301 Collis and apply as early as
possible.
Homework: There will be about 7 weekly homeworks due Wednesdays
at start of lecture.
I strongly encourage you to
collaborate, and to
try at least some of the
relevant homework problems
before the next lecture
(leaving it all for Wednesday night
risks you getting left behind in this fastpaced course.)
Please make your working/reasoning as clear as you can, write clearly,
don't be scared of using lots of space on the page, and staple your
work.
Late homework will not be accepted
(unless by prior arrangement for a valid, and exceptional, reason).
Your lowest HW score will be dropped.
Project: Mainly, in the last 23 weeks of the term, you will
work in groups of 2 (or less) researching a topic in detail.
Typically, this will include a mix of background reading and
computer experimentation. Your group will present what you have
learned in class and hand in a short (~5 page) writeup. As this
is a sizable fraction of your class grade, take it seriously. A
preliminary list of topics are provided here:
topics.
Project topics should be chosen by Monday, October 15. A 12 page
description of your project along with
references is due Tuesday, October 29. Inclass presentations will take
place Friday, November 15 and Monday, November 18. Final writeup are
due Friday, November 22. All writeups should be handed in
electronically. (This means you need to type it. Fair
warning!)
Students with disabilities who will be taking this course and
may need
disabilityrelated classroom accommodations are encouraged to make an
appointment to see
their instructor as soon as possible. Also, they should stop by the
Academic Skills
Center in Collis Center to register for support services.
For your convenience, here is the term
calendar as set by the registrar, with deadlines for schedule
adjustment and other significant dates.
The Honor Principle
On Exams: No assistance may be given or received except that
you may ask the instructor for clarification of a problem. In
particular, no calculators or computing devices may be used.
On Homework: You are permitted and encouraged to collaborate
with other students on the
homework. However, after discussing the problems, you should each write
up the final
solutions in your own words and acknowledge your collaborators. You may
use calculators and approved
software. Additionally, you may consult your class notes
and text. It is a violation of the honor code for someone to provide
the answers for you.
Exams
There are two scheduled exams held outside of class
time.
Midterm 1 
Midterm 2 
Tuesday, October 8 5:007:00 pm 
Thursday, November 7 5:007:00 pm 
201 Kemeny

201 Kemeny

If you have a conflict with
a scheduled exam contact your
instructor as soon as possible.
Grading
Grades will be assigned based on homework and exams as follows.
Component 
Percentage 
Midterm 1 
20

Midterm 2 
20

Homework 
20

Participation

5

Project 
35

Total 
100

Last modified 30 Oct 2013
by AG.