Dynamics Procedure: Write Problems, Iterate

Originally Posted 12-31-2011

More on Dynamical Systems

I have been working hard on my dynamical systems course notes today. I made good progress, and now I think I have enough material to get me through the first three or four class meetings. Go check it out if you like.

So far, the point of the sequence is to get things rolling by introducing several systems as examples. The notes explicitly introduce basic language including the notions of fixed and periodic orbits.

The next part I wish to write will have to do with the doubling map \$x \mapsto 2x \pmod{1}\$ on the unit interval. This will provide a good place to see some shadows of chaotic behavior already, and point out some of the difficulties in using a computer to do exact computations.

Thanks to Ed Burger

I went to an IBL workshop where Ed Burger of Williams College asked the participants not to name the items on a theorem sequence “problems.” To paraphrase Ed, he said we shouldn’t be giving them problems because of the negative connotation. “Call them anything else, but not problems.”

At first, I thought this was a bit silly, but I take his point:

Mathematicians love problems. Students aren’t there, yet.

It took a while to think of a replacement, but now I have an idea. In my dynamics sequence I’m trying to stick to calling everything either a task to be completed, a question to be answered, or a conjecture to be resolved.

A tougher transition will be shifting away from a “problem sequence” as a catch-all term to something else. The traditional Moore Method practitioners always say “Theorem sequence”, but not all classes are all theorem, all the time. Maybe “activity sequence” is better?

Waiting by the mailbox, modern edition

I got a little bit of grant money, and with some haggling, I managed get UNI to let me turn it all into equipment. Since I am moving to a stage where I will be using Sage a lot more for the purposes behind the money, and Sage runs natively on Mac architecture but not a PC, I bought some expensive Apple equipment. The order was placed a while ago, but with the end of the semester, the holiday shopping rush, and holiday office closures, I don’t have any of it, yet.

Next week when UNI reopens, I will be in Boston for the Joint Mathematics Meetings, so I had resigned myself to having to wait until I get back, the Sunday before classes begin, to get my hands on the equipment I am planning on using in class on Monday. The UNI IT staff has its own set up routines to run on new computing equipment, so even after the stuff arrives it takes another day to get in in service. BUT! I did order an iPad, which needs no such set up. I really want to take it to Boston with me. I think it would be much more convenient for the workshop and conference stuff I will be doing.

I noticed earlier this week that deliveries were still being made to departments. Apparently, the University is officially open, but most departments are not because the administrative staff is taking their hard-earned vacation days this week. This gave me a shady way around my problem.

So, today, I went in to the office to see if there was a package with my name on it that I could run away with. To my delight, there was a package from Apple! But it was the laptop. No luck.