Instructor: Tim Chumley
Office: Clapp 423
Phone: 413-538-2525
e-mail: tchumley
Office Hours: Mondays & Wednesdays 1:00-2:00; Tuesdays & Thursdays 2:00-3:00; additional availability by appointment

Textbook: A First Course in Chaotic Dynamical Systems by Robert L. Devaney, ISBN: 9780429280665;
available as a free e-text


Announcements

Announcements will be posted on the Course Announcements Moodle forum throughout the semester, but essentially all other materials will be posted on this page.

Syllabus

Check the syllabus for all the important class policies (grades, attendance, etc.).

Homework

There will be weekly homework assignments throughout the semester to be turned in. Please read these guidelines for writing in our class.

  • General information. A selection of problems will be assigned to be written up individually and turned in each week.
    • These problems will be due Wednesdays at 5 pm.
    • You may work with others but the writing should be done on your own.
  • Gradescope. Homework will be turned in through Gradescope.
    • You should be enrolled automatically. Please let me know if you have any issues logging in.
    • Gradescope has made a short tutorial on submitting homework.
  • Collaboration. I want you to work together on the homework! The process of explaining your ideas to one another really helps in learning math. However, you must write up the assignments on your own and avoid copying others’ work directly. Also, please only write what you understand so that I know where to help, and please avoid using online forums like Math StackExchange, solutions manuals, or similar resources. A huge part of learning in this class comes from figuring out how to get unstuck by spending time thinking on your own or talking to me and classmates; these other resources can end up being counter-productive in the long term.
  • Rewrites. Homework is for practice, and you are not expected to write perfect answers from the start!
    • You will be allowed to submit revisions of most problems for full credit each week.
    • Your revisions will be due on Fridays at 5 pm.
    • Please resubmit (only the problems you’re revising) on Gradescope.
Assignment Due
Homework 0 Jan 28
Homework 1 Feb 2
Homework 2 Feb 9
Homework 3 Feb 16
Homework 4 Feb 23
Homework 5 Mar 9
Homework 6 Mar 23
Homework 7 Mar 30
Homework 8 Apr 6
Homework 9 Apr 20
Homework 10 Apr 27

Exams

There will be two midterm exams. The dates for the exams are subject to change slightly.

Exam Date Format Material
Exam 1 Mar 3 TBA TBA
Exam 2 Apr 14 TBA TBA

Project

In lieu of a final exam, we’ll devote the last week of the semester to a mini-symposium of short group presentations. Since the field of dynamical systems is rich with interesting examples and topics, more than we could cover in a single semester, each group of 2-3 students will choose a topic that we might otherwise not have time for in class.
We’ll also plan to have a writing component to the project and some preliminary deliverables in the lead up to the final week. More details will be discussed in class later in the semester.

Course plan

Our plan is to cover parts of the first 11 chapters of the textbook, as well as parts of later chapters, time permitting. Below is a rough outline of what is to be covered week by week through the semester. Please check back regularly for precise details on what is covered, as well as postings of class materials like lecture notes.

Introduction


Tuesday
Thursday
  • Topic: Sections 3.1, 3.2: Iteration and Orbits.
  • Class materials: Lecture notes
  • After class:

Chapters 3, 4


Tuesday
  • Topic: Sections 3.3-3.5: More on orbits.
  • Class materials:
  • After class:
Thursday
  • Topic: Chapter 4: Graphical Analysis.
  • Class materials:
  • After class:

Chapters 4, 5


Tuesday
  • Topic: Sections 5.1-5.3: Attraction and repulsion.
  • Class materials:
  • After class:
Thursday
  • Topic: Section 5.4: More on attraction and repulsion.
  • Class materials:
  • After class:

Chapter 5


Tuesday
  • Topic: TBA
  • Class materials:
  • After class:
Thursday
  • Topic: TBA
  • Class materials:
  • After class:

Chapter 6


Tuesday
  • Topic: Chapter 6: Bifurcations.
  • Class materials:
  • After class:
Thursday
  • Topic: Chapter 6: More on bifurcations.
  • Class materials:
  • After class:

TBA


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

Chapter 7


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

Spring Break


Tuesday
  • Topic: Spring break, no class.
Thursday
  • Topic: Spring break, no class.

Chapter 8


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

Chapter 9


Tuesday
  • Topic: Community day, no class.
Thursday
  • Topic:
  • Class materials:
  • After class:

Chapter 10


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

Chapter 11


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

TBA


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

Presentations


Tuesday
  • Topic:
  • Class materials:
  • After class:
Thursday
  • Topic:
  • Class materials:
  • After class:

Wrap up


Tuesday
  • Topic: Wrap up.
  • Class materials:
  • After class: Enjoy your summer! Keep in touch!

Getting help

Here are a few ways to get help:

  • Office Hours: Mondays & Wednesdays 1:00-2:00; Tuesdays & Thursdays 2:00-3:00; additional availability by appointment
  • Study groups: Other students in the class are a wonderful resource. I want our class to feel like a community of people working together. Please get in touch if you’d like me to help you find study partners, and please reach out if you’d like others to join your group. You may work together on homework, explain and check answers, but make sure you write what you know on homework in order to get good feedback.

Resources

  • We will be using MATLAB, a programming language and piece of software, to experiment with some of the theoretical ideas we learn. LITS has a short installation guide and MathWorks, the creators of MATLAB, have an onramp guide for learning the basics.
  • Our textbook’s author has written a number of Java Applets to aid in our understanding. Unfortunately they seem to be out of date and it might not be possible to run them without some work but I’ve put a link here in case they can be used.
  • Over the course of the semester, I’ll be posting MATLAB scripts that we will use as we learn new concepts. I’ll be posting them here: