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, one-dimensional maps, period-doubling, 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 rapidly-growing area, and to strike a balance between theoretical analysis, concepts, computer-aided exploration, and applications. The impact of nonlinear dynamical systems on science has been far-reaching, 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
X-hour: Th 1:00-1:50
Lecture location: 004 Kemeny Hall
Office: 210 Kemeny Hall
Office hours: MF  3:00-4:00,  T 1:00-2:00
                      and by appointment

Note that you do not need an appointment to attend regularly-scheduled 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 one-on-one 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 fast-paced 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 2-3 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) write-up.  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 1-2 page description of your project along with references is due Tuesday, October 29. In-class presentations will take place Friday, November 15 and Monday, November 18. Final write-up are due Friday, November 22.  All write-ups 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 disability-related 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.


There are two scheduled exams held outside of class time.

Midterm 1 Midterm 2
  Tuesday, October 8
  5:00-7:00 pm
  Thursday, November 7
  5:00-7:00 pm
 201 Kemeny
  201 Kemeny

If you have a conflict with a scheduled exam contact your instructor as soon as possible.


Grades will be assigned based on homework and exams as follows.

Component Percentage
Midterm 1 20
Midterm 2 20
Homework 20
Project 35
Total 100
Last modified 30 Oct 2013 by AG.