stoutfellow

One of my geometry students is a young Chinese fellow. He has struck me, mostly by his demeanor, as having a good head on his shoulders; today, after presenting a number of theorems, I tossed out a calculation problem that could be solved using them. About half the students got out paper and started scribbling; he just gazed at the blackboard. After a short time, he piped up with the correct answer.

After class, he came up to me with a geometry problem - nothing we'd do in this class, but still, geometry. He wrote an equation on the board and told me the book told him it was true, but he didn't see it. I made a fairly obvious suggestion as to how to proceed; he replied, "Yes, yes, I did that." I made a please-proceed gesture at the board, and he went to work. When he stopped, there were two terms left; one was what he wanted, and the other... wasn't. He said, "This has to be zero, but I don't see why." I pointed out that there was one more term he hadn't worked out. He went to work on that one. I smiled, nodded, made encouraging comments - I could see what was coming. Finally, he said, "That's all I can do." I smiled and nodded at the board, and he looked again. "Oh. Oh! THEY CANCEL!" By this time I was grinning like a monkey. He thanked me profusely, wished me a good evening, and headed out.

There are times when I love my job.

Linear algebra is, for me, an interesting course to teach. One of my fundamental maxims of mathematics is this: "Algebra yields information. Geometry yields understanding." (I sometimes call it "Stoutfellow's First Law".) Linear algebra is a hybrid field, which can be viewed algebraically or geometrically, and I always push my students to be prepared to view it either way.

Today, we discussed systems of linear equations and the method of Gaussian elimination. GE is a procedure for changing a system of equations without changing the solutions, pushing it towards a form where the solutions are easy to compute. To illustrate how it works, I wrote down a pair of equations, say, x + y = 3, -x + 4y = 5. (Those aren't the equations I used, but they'll do.) Then I drew coordinate axes and the lines corresponding to those equations: two lines, intersecting in a single point, and that point's coordinates are the unique solution to the equations. Then I began working the transitions.

"The first operation of GE is to swap the equations - put them in a different order. What does that do to the geometry?"
"Nothing."
"Right - the lines get relabeled, but nothing else changes."
"The second operation is to multiply one of the equations, say equation two, by a nonzero constant. What happens to the geometry?"
(Some fumbling, a student talking to himself): "Nothing."
"Right; if you multiply an equation by a nonzero constant, its solutions don't change."
"The third operation is to add a multiple of one equation to another." (I do an example, and draw the new line.) "Line two rotates around the intersection point. If I add different multiples of equation one, line two rotates to different places. In particular, making the right choice, I can rotate it to be horizontal. What does that mean algebraically?"
(Hem, haw.) "The variable x no longer appears in that equation."
"Yes!" (I then point out the connection between this and the algebraic concept of "row echelon form". With many gestures, I try to display what happens if you're working with equations in three variables instead of two.)

Algebra yields information. Geometry yields understanding. I hope I can drive that through to my students.

I should probably add that I am not blaming the department secretary in any way for the classroom computer problems. I'm sure she's done everything I've asked her to; if anyone is to blame, it's OIT.

I'm not sure I can entirely blame them, either. A few weeks ago, the university network was attacked; no permanent damage was done, but they've been cleaning up the mess ever since. They tell us they should have everything back in order by the beginning of the semester.

It's just *frustrating*. I've been a bit of a Luddite as far as adopting technology for the classroom, but the last few years I've found it to be so useful, and I'm looking forward to applying it to DiffEq in particular. (It'll be a few lectures before the first time I'm hoping to bring it in, fortunately.)

I'm just about done with the grading in DiffEq. (I meant to do it all on Friday, but found myself nodding off, so I took them home - all but one, as it turns out.) I've graded the ones I brought home and posted the raw results on Blackboard, an interface they can access. I've also posted the official letter grades on CougarNet, but they won't be able to access those for a few days. The letter grades are not quite consonant with the raw grades - usually they're a bit higher - and I've already gotten three worried messages, and expect more.

Some of them, I can relieve immediately. Others... I can't.

This is one of the less pleasant parts of the job.

As I've mentioned, I will be teaching a compressed five-week class in differential equations this summer, beginning tomorrow. The class meets five days a week, for 2:20 each day. We're looking at a 3-1 compression here.

I just received a message from one of my students, who will be out of town Monday through Thursday of next week, and who would appreciate it if I would pass on the material to be covered during that time.

I will be grimly amused to inform him that there will be a quiz on that Friday, covering the week's material. (There will be a quiz every Friday except the last, when I will give the final.)

My Master's student gave her presentation today, and passed easily. Afterward, she thanked me for taking her on as a student. Child, that's *what I do*!

That takes care of one of the three obligations carrying over from the last semester. One of the other two will be simple, if I can just noodge myself into doing it. The other... well, I said I'd do it, so I'll do it. Pro crastinus...

This is the last week of classes; I will give lectures in my three classes tomorrow, and that's it for that. I'll be posting a take-home final for Abstract Algebra tomorrow evening; the finals for the others will be in-class, and next week. I still have a stack of term papers from History of Math to grade, and a Senior Project paper to evaluate. Also, a philosophy professor has asked me to beta-read a paper he's written on set theory; he plans to submit it to a math journal, and wants a mathematician's eye. Also also, I'm waiting for the next draft of my Master's student's thesis.

After that, I'll buckle down on Taxonomy III. I'm dissatisfied with the current iteration, but I'm not sure what needs changing. (I should probably quit trying to write the introduction until I've finished the body of the paper - and I'm barely an unsatisfactory third of the way into that.)

It's a dreary day outside, which matches my energy level. (I got caught by the rain on the way home, and had to use my canvas shoulder bag as a makeshift rain-hat. No, I did not stick my head in it; I just laid it flat on top.) So much to do...

I wasn't planning on teaching this summer - I'm still not - but there is a possibility that I will be doing so. Yesterday the Assistant Chair, who handles scheduling and teaching assignments for the department, sent out a message: three courses needed instructors, thanks to some scheduling changes. One of them is Combinatorics and Graph Theory, which I haven't taught in a while but enjoy. It's a compressed course, five days a week for five weeks, which dampens my enthusiasm a bit, but still, I told him that I'd be willing to teach it if he couldn't find anyone else.

We shall see.

"Spring" Semester classes begin on the 14th. I will go onto campus a few times this week, to write the syllabi and handle other pre-semester duties.

This semester, I will be teaching: history of math in Science East, 3:00-4:15 MW; abstract algebra (theory of rings and fields) in Peck Hall, 4:30-5:45 MW; and Linear Algebra I in Science East, 6:00-7:15 MW. This presents a few problems.

1. Transit. It's about a five to ten minute walk between the two buildings, so of course the one in Peck is sandwiched between the other two. I note in passing that the bus stop is next to Peck Hall. Not a big problem, deserving only a rueful smile. Fortunately, my office is in Science East, so I'll be able to switch textbooks in between, rather than carrying all three with me.

2. Hunger. Somewhere in that time period I'm going to need sustenance, and I won't have much time to deal with it. I'm thinking I'll pack a couple of sandwiches and eat one in each break period. I suspect there will be days when I'll fall back on the vending machines in Peck.

3. Office Hours. This is the biggie. Normally, I schedule my OH for each class the hour before or after, but that's out of the question this semester. I'm planning on coming in five days a week anyway, to work on the Taxonomy papers if nothing else, and I'll probably have to schedule some office hours TTh. I don't know how that will fit my students' schedules; I suspect there'll be some appointments made (and probably broken) as well.

Ah, well. I haven't taught the abstract algebra class in a while, and I'm looking forward to it. History of math is always a pleasure, and linear is, if nothing else, familiar turf. I hope for a good semester.

The finals are all in; the last of them dropped into my mailbox yesterday afternoon. Twenty-one group theory tests, eighteen foundations of geometry, five real analysis. (None of the later geometry tests was anywhere near as big as the first. Thank heaven for that!) Final grades have to be submitted by noon Monday.

I know what *I'll* be doing this weekend...