Syllabus: MA 471-671

Chaotic Dynamical Systems

Fall 2017

Robert L. Devaney
Department of Mathematics
Office: Room 274 MCS
Tel. 617-353-4560
Office hours: M Tu W 12-1 and by appointment. But feel free to stop by anytime I'm in my office.

The goal of these two courses is to introduce some of the spectacular new discoveries that have been made over the past thirty years in the field of Mathematics known as Dynamical Systems. MA 471 is an undergraduate level course, designed for students who have completed at least MA 123, 124, and 225. More advanced coursework in the mathematics department is helpful but not absolutely necessary. MA 671 is a graduate course aimed at students who are not graduate students in the Mathematics Department. Mathematics graduate students should enroll in MA 771. Unlike 771, this course does not presuppose acquaintance with ideas from analysis such as found in MA 511-512. MA 471 and 671 will meet concurrently: students enrolled in MA 671 will have to complete all of the requirements of MA 471 plus an extra project.

We will use a number of novel techniques in these courses, including a variety of computer experiments. Students will be expected to carry out a series of experiments using software that is posted on the web at the Dynamical Systems and Technology Project. Or you may use any software that you find to be more convenient.


The textbook for the course is A First Course in Chaotic Dynamical Systems, written by your favorite Math professor and published by Perseus Press (sometimes called Westview Press).


There will be two midterms in this course, the first on Wednesday, October 11 and the second on Wednesday, November 15. These exams will each count for 20% of the final grade. The final exam will count for 35% of the course grade. The final is scheduled for Monday, December 18, 3-5PM. The remaining 25% of the course grade will be derived from computer lab reports and, in the case of MA 671, a special report. Homework will be assigned weekly but not picked up or graded. Solutions have been posted on the web. There is also a solutions manual for all problems in the textbook available here.

I regard this course as a rigorous mathematics course where students are required to understand all of the definitions, theorems, proofs and so forth. You will often be asked to explain mathematical concepts in essay questions on exams, to prove certain facts, and to write concisely and accurately about the mathematical ideas in the course.

MA 671

Graduate students registering for MA 671 are required to hand in a special paper dealing with dynamical systems and chaos in their own specific area of interest. For example, engineering students could discuss the behavior of a chaotic system (like the double pendulum) that arises in mechanics. SED students could produce a module on dynamics that could be used in a secondary school mathematics class. The exact topic will be decided in individual meetings to be scheduled in October.


Grades for both MA471 and MA671 will be posted on the MA471 Blackboard or MA671 Blackboard websites. Please check these listings occasionally to check that all of your grades have been recorded correctly.