Northeastern University
Mathematics Department


MATH 1240: Chaos and Fractals

Summer 2001

Hours: Mon, Wed, Thurs, 10:30-11:35
Location: 424 Hayden; Key# 80534

Instructor: Stephen Lovett
Office: 535 Nightingale Hall (NI)
Office Hours:
Phone: 373-2080
Email: slovett@lynx.neu.edu

Your computer's date must be accurate.
   

Required Text: A First Course in Chaotic Dynamical Systems
by Robert L. Devaney


Course Description

This course is designed to introduce the student to a rigorous study of chaos and fractals. We will cover many of the central examples and common techniques in the study of dynamical systems.

This course is about discovery. Though we will emphasize the accurate mathematical aspects of these fields, chaotic systems continue to provide stunning and beautiful phenomenon. There will be two assigned "research" projects that will make use of computers. I will provide ideas for the projects but I strongly encourage extra work beyond the questions I ask, thereby hopefully motivating a more interactive discovery of these fields.

Chap.TopicHomeworkUseful Tools
3Dynamical Systems; Function Iteration1, 2, 7, 8, 15-17 P.26  
4Graphical Analysis1a-e, 2, 7 p.34Graphical Analysis in Maple
5Fixed Points; Attraction and Repulsion1a-d,j; 2a-d,f; 4a,c,e p.50Calculus Rules (pdf file)
6Bifurcations1a-d, 4, 5, 15 p.67Answer Sheet: p1, p2, p3, p4
 Metric Spaces, Open SetsHandout 
 Cantor Set  
7Quadratic Family1, 2, 9-14 p.80 
8Orbit Diagrams4, 5, 6, 8 p.94Orbit Diagram Java Applet
9Symbolic Dynamics1-4, 11-14 p.111 
10Chaos8, 9, 21 p.131 
14Fractals; Fractal Dimension1, 2, 4, 11, 15 p.199 
15Complex Functions1, 2, 3, 5, 9-11 p.218 
16Julia Sets1, 3, 5 p.243 
17Mandelbrot Set  


Course Policies

  1. This syllabus is intended as a template. We will cover other topics and other problems as time or context permit.
  2. The student is responsible for keeping up with any changes announced in class, whether or not he or she is present.
  3. Tools: Many of the programs that I will use will be on the Maple tutorial on my website. Please see the section on Examples from Dynamical Systems.
  4. There will be weekly quizzes (no matter how much material is covered), a one-hour midterm and a two-hour cumulative departmental final. I will drop the lowest quiz grade. Otherwise, the final course grade will be calculated as follows:

     
    Homeworks and Projects       30%
    Weekly Quizzes15%
    Midterm Exam20%
    Final Exam35%
  5. If you have any questions, please feel free to talk to me. If my office hours are not convenient for you, please contact me and we can find some other time to meet.