stoutfellow

There's a winter storm a-coming; NWS is predicting snow, beginning imminently and tapering off around 4PM tomorrow, with accumulation up to 7". Probably as a result, only about a third of my geometry students showed up for class tonight. There was only one theorem left in the current section, so I went over that proof, answered a few questions, and sent them home. (Normal class is 75 minutes; we went for about half of that.) To be honest, I wasn't looking forward to the possibility of trudging through snow myself. (As it happened, I didn't have to.)

On Wednesday, I posted the second take-home midterm for my geometry class. I told them, as I had said before, that I would accept electronic or dead-tree versions of their work. The word "dead-tree" amused some of them, and I found myself explaining that "'dead-tree' is perfectly standard... slang". This amused them even more.

Oh, well. In a week's time, I will have my revenge for their laughter, just you wait.

My student and I had a productive session today. She's gotten hold of a whiteboard at home; she writes her calculations on it, photographs them, wipe and repeat; she then e-mails me the photos.

While we were discussing her work, I saw a few things she wasn't quite clear on, and tried to clarify them. But her work... She's using the techniques I've taught her, but she's using them in directions I hadn't anticipated, and as a result she's discovered a few things I did not know. (I told her so, which pleased her immensely.)

Her attacks are a bit crude, but she carries them through. I suggested a few things which might add some polish; we'll see how that comes out. In any event, I'm very pleased with her.

My student's assignment for today involved some rather tedious calculations. She handed me the write-up, and I scanned it - one of those situations where it's easier to verify that an answer is correct than to actually get the answer. No problems.

Then we went on to the topic of the day, The Care and Feeding of Involutions. I showed her a bunch of tricks for dealing with involutions (transformations whose square is the identity transformation): projecting to eigenspaces, computing the dimensions of eigenspaces without computing the spaces themselves, tricks with commuting involutions, stuff like that. In passing, I pointed out how they could be used to simplify those tedious calculations. Her response was pleased - "Yeah, that's much better" - but there was a hint of asperity in it. (Unspoken: "Why didn't you show me this before assigning me that problem?" "So you'd appreciate it!")

There is a psychological element to the business....

My new Masters' student is an assiduous worker - but I knew that already.

After our talk on Tuesday, I sent her a .pdf of Taxonomy I, telling her to read Sections 1 and 2. On Wednesday, she e-mailed me about an unfamiliar term, asking for its definition. (It's most commonly used in another branch of mathematics, and its definition there is complicated. I use it in an idiosyncratic but natural way, and I don't think any experienced mathematician would have had any trouble, but of course she isn't one. She did due diligence by looking it up, was confused, and asked for explanation.) When we met again on Friday, she had printed out Sections 1 and 2 and copiously annotated them. We spent half an hour going over her questions about the material, and then another half talking about group representation theory. (That's a humongous topic, but it provides some tools that I've found useful, so I'm just going to teach her that much.)

At the end of the Friday talk, I gave her some simple exercises to work; they're designed to help her gain some feel for the machinery I've developed. She should have no trouble with them. I'm very pleased so far.

This fall I'm scheduled to teach three courses, one from each of the great branches of mathematics: algebra (Introduction to Algebraic Structures), geometry (Foundations for Euclidean and Non-Euclidean Geometry), and analysis (Real Analysis I). This is the first time, I think, that I've been assigned that range.

I just looked up the enrollments for those courses. The first two are safe: they have fifteen and thirteen students signed up, respectively. Most of the students are in my history of math course this semester; the sequence of courses for the Math Ed track, which most of them are on, is fairly rigid. The third one may be in trouble. Only four students have signed up so far, and we'll need ten. It's still early in the undergraduate registration cycle, though, and the course is also taken by some graduate students, who tend to register late. Still, it makes me a little nervous.

We shall see.

Almost all of the grading's done; one class, four students, remains. I've had messages from one student concerned about a low grade, and one from a student dubious of a high grade. Both seem to have accepted my explanations.

I've also finished arrangements for B&G while I'm gone - a pet sitter, who aims at becoming a pro, and the necessary 20 lb bag of Dog Chow. I need to run over to Best Buy tomorrow morning to pick up a cheap phone, in case something goes wrong with my flights; I also need to try to shrink the pile of bills and receipts on my desk. (I really am going to have to revamp my financial database.)

I'm going to download some more books for my holiday reading. I'm two stories behind on Penric; I haven't gotten hold of "The Stone Sky" yet; and I should also pick up at least one more Peter Grant novel, one or two Mercy Thompson books and maybe a Kitty Norville story. (I read the first one earlier this year.) There are several other series I ought to dig further into... Where does the time go?

Ah well. Let the tension go, and r-e-l-a-x, willya?

We had a bit of fun in yesterday's geometry class. We were finishing up the section on triangle geometry, with the capstone being the proof of the existence of the Nine Point Circle. That done, I began showing them some odds and ends about the various points we'd been discussing - the circumcenter O, the orthocenter H, and the nine-point center N. Using Sketchpad, I'd set up a dynamic sketch displaying all of those points, and how they behaved as the triangle ABC changed shape.

One of the students then asked if it was possible for the vertex A to coincide with N. I said, "I don't know. Let's find out!". I grabbed A with the mouse and pulled it towards N. The latter point also moved, of course, but more slowly, and I was able to catch up. I couldn't get them to coincide exactly, but that was a matter of human clumsiness - clearly they could be made to match. I had a doodad off to the side keeping track of the angle BAC; one of the students pointed out that the angle was almost exactly 120 degrees. 120 degrees being a Significant Angle, I decided this couldn't be a coincidence. Then, the student who had suggested the problem pointed out that the triangle was demonstrably (not just apparently) isosceles, and we saw that that meant the triangle HBC was equilateral! I realized that this tied in to another interesting set of ideas, which I pointed out as time ran out.

Understanding may not be teachable, but it is learnable!

Week three of the semester is complete. I'm teaching three courses: Math 320, "Introduction to Algebraic Structures"; Math 421, "Linear Algebra II"; and Math 435, "Foundations for Euclidean and Non-Euclidean Geometry".

Math 320 is a tough course for our students. The problem is that the mathematical objects we study in that class, "groups", are totally unlike anything else they've ever encountered. I mean, calculus is tough, but going in the students know what functions are and they can visualize things like tangent lines. Linear algebra is hard, but they've at least seen vectors in 2- and 3-space. Groups? Nothing like them. I have thirteen students in the class; four of them have had classes with me before. (I think all four have had multiple classes with me, in fact.) When I ask questions in class, ("Okay, what's the next step?" "Why did I just do that?") it is almost always one of those four who answers. I have to directly choose one of the others to get them to speak up.

Math 421... On Thursday, I asked my students for input on the time and content of the first midterm - two weeks hence, including the extensive review material, or a week later and concentrating on the new material. The discussion was lively, one student in particular pushing hard for the latter, but the consensus favored the former option. After class, she apologized to me for the, um, vigor of her opinions... She teaches high school math, and mentioned that her students were complaining about the amount and difficulty of their homework, saying, "Kids, if you only knew!" - the latter a reference to the homework I was giving her. I told her the story of Janis Ian and Connie Willis (subtitle, "In which the famous singer learns about fangirling from the other side"); she laughed, then caught my point. "Ok, that gives me a different perspective on my students...." That may have been the best thing I did that day.

Math 435 only has four students. It probably would have been cancelled, but V, who heads our Math Ed program, vigorously defended it before the Dean as an essential component of that program - cancel it, and the students wind up delayed a full year. I enjoy that class. The first couple of weeks dealt with familiar, high school geometry, results, but this last week we got to more advanced topics like the Star Trek and Bow Tie Lemmas, and the Cyclic Quadrilaterals Theorem. Next week we fall back to similar triangles, but then roar ahead into circle geometry - radical axes, coaxal systems, and so forth.

So that's where we stand at the end of week three.

Oof! :creak:

One stack of finals done; two to go. (One only has five tests in it.)

I have to post grades by noon tomorrow.

:creak: