Materials for my current courses are posted on MYLMUConnect (accessible only to my current students). On this page, I am posting some materials I have written for past courses which may (or may not) be of interest to others. Feel free to use and modify these freely for your own classroom use.

Mathematics of Symmetry

Several times I have taught a general education course on the Mathematics of Symmetry, directed at students majoring in the liberal arts. I have written a set of notes for this class, taking considerable inspiration from David Farmer's Groups and Symmetry. The class, and the notes, are very much a work in progress, but I'm posting the latest version here for anyone who is interested. Comments and feedback are welcome!

Notes on the Mathematics of Symmetry (version: Spring 2013)

The last time I taught this course, I included a unit on fractals, using the notes below.

Fractal Notes (version: Spring 2013)

Here is a picture of the first three stages of a Menger Sponge, which my class built out of folded business cards (with no tape or glue):


In 2012-2013 I experimented with "flipping" my Precalculus class (having students view lectures online before class, and devoting more class time to working on problems). While the experiment was not entirely successful (and I'm happy to discuss it with anyone interested), the lectures may still be of interest. The lectures were written as pencasts using a Livescribe smartpen. The archive below contains all the lectures (it makes a rather large file, about 180 MB). Each lecture is a PDF file with an associated audio track (essentially, lecture notes with narration). The files may be viewed with any PDF viewer, but hearing the narration requires Adobe Reader version 10 or higher. The lectures are numbered by sections corresponding to the textbook I was using: Essentials of Precalculus by Zill and Dewar (5th edition). I did not always follow the order of sections in that book, however (for example, I covered Chapter 5, on Exponentials and Logarithms, before Chapter 4, on Trigonometric Functions).

Precalculus Lectures (.zip file)

Differential Geometry

I wrote a short set of notes on Differential Geometry which I assigned as a semester-long project in a classical Geometry course. Students worked on the project outside of class, though I provided considerable assistance.

Differential Geometry Project

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