The First Day of Classes, and other tales of Survival

Originally Posted 01-09-2012

Well, that went smoothly enough. I managed to make it through the day without any major troubles, despite my incomplete preparation for linear algebra.

Highlights

My new toys were waiting in my office on Saturday night when I arrived back in Cedar Falls. I got to use the iPad in all three classes to take notes and pictures of my students, and I used the MacBookPro to show off the Sage notebook server for matrix computations in linear algebra. I was very pleased. I am still working on set-up, but I have new browsers and LaTeX is up and running.

So how did classes go?

Dynamical Systems

We had good success getting through several of the modeling problems, and we had a nice discussion about the difference between a “time-parametrized model” where exponential growth is determined by an exponential population function, and the dynamical system approach where the same model is determined by a linear function as dynamics. They have new problems for Wednesday, which emphasize the idea of a fixed point.

Linear Algebra

We spent our time talking about linear combinations of matrices. I asked the students to get a copy of the first few chapters of the Woodruff-Grout text. I showed them how to do some very simple stuff in Sage. We will talk a bit about vectors and geometry some on Wednesday.

I still need to set up my WeBWork course, get my Sage intro up and running, and update my personal web page’s linear algebra section. I think this will be my day tomorrow.

Mathematics in Decision Making

This went really well. We had time for the student to work on all five problems from today’s activity and we discussed the first four. I think the concept of checking that two sets are the same size comes from a “matching” between the two sets. Kyle was a good help, too. I am very pleased to have a TA to deal with a slightly larger class.

Research Students

Well, it seems like I have a lot to do on this front this semester. I spoke with all four potential students today about scheduling.

• One graduate student with a non-thesis option will be studying making fractal limit sets on the sphere at infinity for Fuchsian groups and their friends. He is inspired by the book Indra’s Pearls by Mumford, Series and Wright.

• One graduate student starting his thesis work by studying how to think of closed orbits of the geodesic flow of the modular surface as knots in the 3-sphere minus a trefoil knot. (Basically following Ghys’ ICM address from 2006.)

• One undergraduate continuing a project on the divisibility of m-ary parition numbers. Really, this is about some strange structural polynomials that appear when studying this problem. We have experimental results, and we need to find a proof.

• Possibly a new student to study some discretized version of curve shortening flow. We could start with the Monthly Paper by Chow and Glickenstein (2007).

What Else?

I didn’t take any time to work on committee work. I have to schedule some meetings to get rolling on our search for funding to support undergraduate research efforts.