While I am not currently in the rotation to teach 131, and probably will not be for some time, I still sometimes think about it. Frankly, it is nice to be able to just think without the pressure of having to teach it as the lack of pressure allows my mind to wander on the big-picture parts of courses in fun and surprising ways.
Last night my mind was wandering on 131 and I realized that there is another theme running through the course that I had not really made explicit to myself before: a new way to look at math. As you can see from the description of 131, the course braids several different threads. One of these is my general interest in the difference between math-in-physics and math-in-math (see the right column of the poster!). Another is the integration of computation. The insight from last night is that these, along with graphical analysis, are all aspects of the same goal: learning to use math differently than students are accustomed from their math classes.
- Writing equations corresponding to models of nature.
- Reading an equation to predict how systems will behave with changes of variables.
- Using equations (particularly differential equations) as “stepping rules.”
- Graphs as a mathematical representation.
While this is a neat insight, I am now concerned if there is too much in the class.
These are thoughts to keep pondering!