Which is more fun,
a) Filling in for a colleague with sick kids, getting to teach her Abstract Algebra Class,
b) Filling in for a colleague with jury duty, getting to teach her College Algebra Class,
c) Typing up the committee minutes for last weeks Executive Committee Meeting, or
d) Designing and implenting a random knot search algorithm in paralleel for the Free-Knot problem?
Answer: Close between (a) and (d), but I have to go with (a) today.
I didn’t realize it until today, but it has been a good while since I have had the oppportunity to teach a theory class in mathematics. The closest was Differential Equations last semester, but in our undergraduate DE we rarely get to prove any good theorems. The most recent “proof” class was when I filled in for the same instructor last semester in Discrete Structures.
After getting my palate wet, I am ready for Analysis next semester. I have the opportunity to trade off with a colleague so that every time Intermediate Analysis comes around, we alternate who gets to teach it. Very few of my classes overlap other’s areas of specialty. At a small school like Wayland, there are only four math faculty, one of which is actually a physicist. We have a pure math person, an applied math guy (me), and a statistician. For only four faculty, we cover a pretty good spread. Also, the majority of our upper level courses are taught on a two year rotation, so that my favorite courses, such as Diff. Eq. or Math Models, only come around every couple of years. With the alternating of Analysis, I only get to teach it every 4 years. Early in my time at Wayland, I did get to teach it twice in a row, but now I’m being good and sharing my “toys”.
Don’t get me wrong, I don’t pray for my colleagues kids to get sick, but when I do get to fill in, I have a great time, even with the simple basic definitions of function/maps, image, 1-1, onto, composition, etc. Yes, I even had fun proving the composition of 1-1 (or onto) functions is 1-1 (or onto).