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 about

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

Homework: There will be weekly homework assignments of both computational and conceptual nature.

Quizzes: There will be weekly quizzes with questions related to recent material.

Exams: There will be two midterm exams.

Technology: Here are some general remarks on the use of calculators, software, and phones:

  • For all homework, quizzes, and exams, you may use a scientific calculator, but it is not necessary or required (I generally write questions that can be done by hand or left unsimplified).
  • Software like MATLAB, Wolfram Alpha, Desmos, and CalcPlot3D can be used on homework or other outside the class work, but its use should be cited unless the problem explicitly requires its use. You’re expected to show your work on problems and be able to do problems without these tools on quizzes and exams.
  • Software like ChatGPT or other AI models should not be used.
  • Online forums, solutions manuals, or similar resources should not be used.
  • It’s ok to take photos of the board for note taking, but please don’t post these online.
  • Please keep your phones on Do Not Disturb mode in class, especially during quizzes and exams so as not to disturb others.
  • If you’re unsure whether something is ok to use, please feel free to ask.

Project: We’ll devote the last couple weeks of the semester to to a short project involving some selection of topics we wouldn’t otherwise have time to cover. The project will involve a presentation or report. Details will be discussed in the middle of the semester. Topics might be taken from a section of the textbook or a scientific paper; I’ll have a list of suggestions.

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 class and engaging in activities consistently, participating on the Q&A forum).

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 1 day extensions if you ask in advance. The only caveat to late submissions is that their grading could be delayed and you’ll get less time to submit redos since redo deadlines are firm. It is very possible you will not have the opportunity to submit redos if you submit too long past the deadline. Quizzes and exams need to be taken as scheduled except in cases of emergency (eg. severe illness) or pre-approved absence (eg. school-related athletic event). We’ll need to meet and make detailed plans if you go through an extended absence or missed deadlines start to pile up, but my goal is to help anyone who falls behind.

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%
  • Quizzes: 10%
  • Exam 1: 25%
  • Exam 2: 25%
  • Project: 10%

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 or work that uses the restricted resources mentioned above. I will have to refer such issues to the Academic Honor Board. 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 Disability Services, to make sure the class is accessible and equitable.