# Class Day Three, Spring 2012

Originally Posted 01-13-2012

Today’s classes were fun!

In dynamics we had a good discussion about a dynamical system for approximating the square root of 5. Basically, any orbit of a positive real number under iteration of $f(x) = (x + 5/x)/2$ will converge quite rapidly to the desired result. The class has a broad range of backgrounds: a few graduate students who really should have gone somewhere else to get a PhD instead of UNI for an MA to a freshman who is concurrently taking linear algebra. But they are very enthusiastic, and working together well for now.

Linear Algebra was mostly me talking today. This makes me feel weird. I very rapidly introduced several very computational ideas, we spent time looking at pictures on the computer (Sage in action) and discussing the possibilities of intersecting hyperplanes, and then I connected several equivalent versions of the fundamental problem of linear algebra: solving equations. I still feel like I am getting my feet under me for this course, and it will take some more planning this weekend.

Mathematics in Decision Making started with what I hoped would be a quick discussion about the concepts of “set” and “element” in the context of one of our size comparison problems. It turns out that they are starting to come around on the idea of matching the elements of two different sets as a sufficient condition for those sets having the same size. But the problem is that they are uncomfortable deciding when a certain object is in a certain set. In particular, task 6 in my activity sequence really threw them. A half hour of discussion got everyone on the same page. Then we tried to discuss task 8, and the same thing came up, and I don’t think they recognized it as being the same issue. So…we’ll have to work on that more.

This weekend promises lots of diversions. One of my daughters is having a birthday on Saturday, and many grandparents are “descending upon us.” My wife likened it to the doorbell ringing in “Christmas Vacation.” (Where’s the Tylenol?!?!?!)

Also, Jean and I are going to enjoy the free babysitting and go to the theater with some friends. There is nothing like some high art to soothe the soul.

I’ll be glad for the extra day without class meetings on Monday. Maybe I can even do some math.