Mount Holyoke College

Math 125: Seminar on Fractals and Chaos

The course was established by Prof. Alan Durfee. See his Home Page.

Instructor: Sergei Chmutov

Lectures: Tuesday, Thursday 10:50-12:05 in Cleveland L1.
There are weekly homework assignments.

Basic book: Ian Stewart, Does God Play Dice? (Blackwell 1989).
Other books cited can be found in the bibliography.

Technology: You will need a calculator for this course, one that does logarithms. We will also be using a computer program called "Chaotic dynamical systems software". This program runs on the Mac and is available in the computer labs.

Quizzes, Tests: There will be two tests, a self-scheduled final examination, and perhaps some quizzes (which will be announced in advance).

Grading: Each test will count 20%, the final examination will count 25%, and the homework will count 35%.

List of students

Useful web site: Dynamical Systems and Fractals Lecture Notes by David J. Wright (Oklahoma State University).

(General) Syllabus

Lecture 1

Lectures 2 and 3

Lectures 4, 5 and 6

Lectures 7 and 8: The Feigenbaum diagram

Lecture 9: Dectecting whether iteration is regular or chaotic:

Video "Chaos, fractals and dynamics"

Lectures 10 and 11: Coastlines and the ruler dimension

Lecture 12: Box dimension. (Mathematical reference: FFC I: p.240)

Introductory computer laboratory

Lecture 13: More on fractals

Lectures 14: Continuous dynamical systems and strange attractors

Lecture 15 and 16: Complex numbers.

Lecture 17: Iteration of functions in complex variable.