Instructor: Tim Chumley
Office: Clapp 423
Phone: 413-538-2525
e-mail: tchumley

Course: Math 241, Dynamical Systems

Prerequisites: Math 102 (Calculus II), or equivalent

Textbook: A First Course in Chaotic Dynamical Systems by Robert L. Devaney, ISBN: 9780429280665

Learning goals: During the semester you will be learning how to

  • understand the basics of deterministic systems that evolve in discrete time steps, including notions of iteration, orbits, fixed points, and periodicity
  • analyze long-term behavior of dynamical systems using tools from calculus, cobweb diagrams, phase portraits, and bifurcation diagrams
  • study the notion of chaos through examples, symbolic dynamics, and Sharkovsky’s theorem
  • study complex dynamics and fractals, time permitting
  • use numerical tools to gain intuition for and analyze complicated systems

Homework: There will be weekly homework assignments comprising both computational and theoretical, writing oriented problems.

Exams: There will be two midterm exams.

Project: We’ll devote the last week of the semester to a mini-symposium of short group presentations. Since the field of stochastic processes 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/application that we might otherwise not have time for in class. Topics might be taken from a section of the textbook or a scientific paper; I’ll have a list of suggestions. Presentations might be a blackboard chalk talk, or with slides; a simulation demonstration could very useful in a lot of the presentations. 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 in the second half of the semester.

Participation: Part of your grade will depend on participation and there will be a number of opportunities to participate (eg. asking and answering questions, coming to office hours, responding to feedback surveys, and doing informal presentations).

Attendance: You are expected to come to every class ready to do mathematics. This means that you should bring paper, pens, pencils, and other equipment that you may need. Before each class please prepare by doing any assigned reading and suggested problems. Please expect to talk about math in small groups as well as in class discussions. Other classroom activities may involve worksheets, computer explorations, and informal presentations at the board.

Late work, makeups: In general, I ask you to turn homework in by the deadlines and take exams on time because it helps you keep up with the class and it helps me to stay organized. However, I nearly universally say yes to short extensions if you ask. Please just get in touch as soon as possible and suggest how long you think you’ll need. We’ll need to have a longer conversation if deadlines start to pile up.

Getting help: Here are some of the resources that will be available:

  • Office hours: These times (which will be posted near the top of the class web page) are open drop in sessions where there may be multiple students getting help. It’s expected that you come with specific questions about notes, homework problems, or the text that you have thought about already. If you need to schedule a time to meet with me one-on-one, either to discuss something private or because you can’t make my office hours, please send me an email with times that you are available to meet, and I will find a time that works for both of us.
  • Study groups: Other students in the class are a wonderful resource. I want our class to feel like a community of people working together. Even though our class won’t have a TA or evening help, I will work to find ways for you to feel supported both by me and each other.

Grades: Grades will be assigned according to the following weighting:

  • Participation: 5%
  • Homework: 25%
  • Exam 1: 25%
  • Exam 2: 25%
  • Project: 20%

Overall letter grades will be based on a scale no stricter than the usual:

  • 93-100: A
  • 90-93: A-
  • 88-90 B+
  • 83-88: B
  • 80-83: B-
  • 78-80: C+
  • 73-78: C
  • 70-73: C-
  • 68-70: D+
  • 63-67: D
  • 60-63: D-
  • 0-60: F

Academic integrity: It is very important for you to follow the Honor Code in all of your work for this course. Collaboration on homework assignments is encouraged. However, it is important that you only write what you understand, and that it is in your own words. My first instinct is always to trust you, but I cannot give credit for plagiarized work and might have to refer such issues to the deans. If you have any questions about whether something is an Honor Code violation, please ask me.

Students with disabilities: If you have a disability and would like to request accommodations, please get in touch with me. We’ll work together, along with AccessAbility Services, to make sure the class is accessible and equitable.