week 01

Class 01 (January 3, 2022): Logistics, Introductions

Pre-class:

In-class content

Discussion 01 (January 4, 2022): Introduction to Iteration

In-class content:

Class 02 (January 6, 2022): More Iteration

In-class content

Homework 01 (Due Friday, January 7, 2022)

Week 02

Class 03 (January 10, 2022): More Iteration

In-class content

Discussion Section 02 (January 11, 2022): Chaos! The Butterfly Effect!!

Before Class

  • Do these explorations
  • Read Chapter 1, "The Butterfly Effect", from Gleick's book. Among other things, we'll discuss questions of forecasting and prediction. Here are some things to think about as you're reading:
    • What's something that is currently unpredictable but which you think science will eventually be able to predict or forecast?
    • What's something that is currently unpredictable but which you think science will eventually be not able to predict or forecast?
    • What is something you wish was able to be forecast better?
    • Is prediction synonymous with understanding? Are there types of understanding (scientific, or otherwise) that do not result in greater predictability?
  • Optional

In-class content

Class 04 (January 13, 2022): Bifurcation Diagram

Before Class

  • Watch this video and this one. In these videos I show how the logistic equation arises as a simple model for the growth of a population that has some constraint to its growth. Alternatively, read sections 7.1 and 7.2 from the textbook.

In-class content

Homework 02 (Due Friday, January 14, 2022)

Week 03

Class 05 (January 17, 2022): The Butterfly Effect, SDIC, Randomness

In-class content

Discussion Section 03 (January 18, 2022): Logistic Equation, Möbius Strips and Topology

Before Class

In-class content

After class content

Class 06 (January 21, 2022): Universality

Before Class

  • First, do these explorations
  • Then, read "Universality", from Gleick's book. Please note that this is not the next chapter in his book. We're going out of order.

In-class content

Videos that cover what we covered in class

Homework 03 (Due Friday, January 21, 2022)

Week 04

Class 07 (January 24, 2022): Statistical Stability of Chaos, Mixing and Ergodicity

In-class content

Discussion Section 04 (January 25, 2022): The Nature of Scientific Change

Before Class

Class 08 (January 27, 2022): Introduction to Fractals and the Self-Similarity Dimension

In-class content

Optional Videos. These videos from one of my online courses cover material very similar to what we did in class. (These videos have captions in English, Serbian, Spanish, and Portugese.)

Homework 04 (Due Friday, January 28, 2022)

Week 05

Reflection 01 (Due Monday, January 31, 2022)
Class 09 (January 31, 2022): More Fractals, Infinities, and the Cantor Set

In-class content

Optional Videos. These videos from one of my online courses cover material very similar to what we did in class. (These videos have captions in English, Arabic, and Portugese.)

Discussion Section 05 (Feb 1, 2022): Fractals

Before Class

  • Bring scissors, if you have some. I now have a bunch of high-quality scissors to use, but if you have some scissors that you like, perhaps bring them with you.
  • Read "Geometry of Nature", from Gleick's book. Please note that this is not the next chapter in his book. We're going out of order.
  • Optionally, Read "Father of Fractals", a review by Brian Hayes in American Scientist of Mandlebrot's memoir.

In Class

After class: Here are some videos that cover what we did in class.

Class 10 (February 3, 2022): Power Laws

In-class content

Optional Videos. These videos from one of my online courses cover material very similar to what we did in class.

Homework 05 (Due Friday, February 4, 2022)

Week 06

Class 11 (February 7, 2022): Fractal Show and Tell, the Chaos Game

In-class content

Optional Videos. These videos from one of my online courses cover material very similar to what we did in class.

Discussion Section 06 (Feb 8, 2022): Fractals

Before Class

In Class

  • Handout: None
Class 12 (February 10, 2022): Cardinality, Infinite Sets, and Fractals

In-class content

Optional Videos. Coming soon.

Homework 06 (Due Friday, February 11, 2022)

Week 07

Class 13 (February 14, 2022): MT Check-in, Complex Numbers, Phase Space

In-class content

Optional Videos. These videos from one of my online courses cover material very similar to what we did in class.

Discussion Section 07 (Feb 15, 2022): Models, CAs, etc.

Before Class

In Class

Class 14 (February 17, 2022): CAs, Julia Sets

In-class content

Optional Videos.

Homework 07 (Due Friday, February 18, 2022)

Week 08

Class 15 (Feb 21, 2022): Julia Sets and the Mandelbrot Set

Before Class

  • Bring: a Julia set to class. Instructions are here

In Class

Optional Videos.

Discussion Section 08 (Feb 22, 2022): Misogyny and sexism in math and physics

Before Class

In Class

  • Handout: None
Class 16 (Feb 24, 2022): The Morning after the War Began: Hitomezashi Patterns, More about the Mandelbrot Set

In Class

Optional Videos.

Homework 08 (Due Friday, February 25, 2022)

Week 09

Class 17 (Feb 28, 2022): Finally, Strange Attractors!

In Class

Optional Videos.

Class 18 (March 3, 2022): More Strange Attractors, Poincare-Bendixson Theorem, More Fractal Drawing

In Class

Optional Videos.

Week 10

Class 19 (March 7, 2022): A Few Presentations, Concept Mapping

In Class

Class 20 (March 10, 2022): Presentations and Exhibition, Conclusion

In Class