stoutfellow

I'm really short on energy, thanks to this muscle strain thingy. I grab for a couple of hours of sleep, courtesy of Icy Hot (but only once or twice a day), or for an hour or so of rest (tucked into the right-hand corner of my couch, one of the few places of minimal pain); I eat a bit, or drink a bit more (water, milk, OJ. coffee, tea, cocoa). Once in a while I have the energy to post something for my classes.

Today, I put up something on the Bernoulli brothers (took longer than I expected, straightening out their work on the brachistochrone problem); I've mapped out a post on Nicolaus and Daniel, focusing on the work on the fringes of mathematical expectation (a concept in statistics).

For my other history of math clase, I've mapped out a couple of posts on the solution of cubic and quartic equations - one on the people, with some discussion of Renaissance Italian politics and economics, and one on the methods: how they solved those equations, the problematic aspects of their techniques, the first evidence of the necessity of complex numbers even for the solution of real problems, and why their techniques, though quite ingenious, were ultimately a dead end.

And in differential geometry, the stretch drive: the concept of parallel transport, which leads to geodesics, which finally leads to the brilliant and beautiful Local and Global Gauss-Bonnet Theorems.

I think I can, I think I can...

I have now begun posting online material for my students in all three classes.

All of the material will be asynchronous; my students can view it at their leisure, but there will be no immediate feedback. This is primarily because some of my students have limited access - spotty internet, phone access only, and so on. Partly it's due to technical and supply difficulties; I haven't worked out how to do audio yet (but should get that cleared up soon) and I still don't have a webcam (Amazon says it'll arrive in another few days).

The two history of math classes, I'm so far handling via PowerPoint slide shows. Differential geometry doesn't fit that motif well, so I'm posting Word documents expanding on the text and offering exercises. I'm not sure how I'm going to handle the humongous calculations that pop up a few times in the next sections; I planned to use my Wacom tablet, but I still have to get it registered, which means I have to get some ID numbers off the back, which I can't make out. I've ordered another magnifying glass from Amazon, but it'll be a couple of weeks before it gets here.

I'm trying, folks. I really am...

We held our emergency department meeting this morning. Tomorrow, I will wander over to Best Buy, in hopes of purchasing a Wacom tablet, a webcam, and a mike and headset. (I could get the latter three items on loan from the university, but they seem useful enough to warrant private purchase.)

After that, I may head to Dierbergs, to see if they have any of the items I wasn't able to get from Schnucks: cereal, dog treats, instant cocoa.

Goshen Coffee has informed me that my order of coffee has been shipped; unusually, it had not yet arrived when they sent me the message. Tomorrow, I expect.

After these events, things will begin to happen.

My university has joined with a number of others in the area: spring break is being extended by one week, during which time we will be working on - possibly, it's not settled yet - transitioning to entirely on-line instruction for the remainder of the semester.

This is going to be a bitch.

I've graded the finals for Linear Algebra, and submitted the grades. That was my largest class. DiffEq is up next. (My friend and colleague V drove me over to the university to pick up the tests I'd left in the office.)

This past week was finals week; all that remains for me is to grade the finals and post the overall grades. That will occupy a good bit of the weekend. Twenty-some tests in Linear Algebra, eighteen or so in DiffEq, and ten in E/NE Geometry.

There's a bit of a hitch. Some special-needs students - two each in Linear and DiffEq - took their tests separately, and the relevant office was supposed to send their papers to me. Three of the four had arrived by mail time today, but one is still outstanding. Grades have to be submitted by noon on Monday; I'll have to go in early, in the hope that the fourth paper was sent late today.

Other than that, I'm done for the year. Next semester, I'll be teaching the two history of math classes and differential geometry. That last class is probably a last hurrah; we've had such trouble getting enough students to take the course that we've decided (unhappily, in my case) to remove it from the regular schedule. The industrious Chinese student I mentioned a while back wanted to take it, but another mandatory class (he's actually a graduate student in engineering) conflicts. He decided to take it second-hand; he talked two of his fellow engineering students into taking it, and he will study their notes. Clever fellow.

A couple of weeks ago, at the end of one lecture, after most of the students had left, one student burst out, "How can I take notes in this class? You talk fast, and by the time I've written down what you wrote on the board, you're off on something else!" Two other students were still there and sort of gravitated toward us. I made the usual suggestions - sharing notes with another student, putting together a study group (although sometime before week thirteen of a fifteen-week class might have been better), and so forth. He was still upset ("I'm already in study groups in three other classes!"), but the other students offered to help. I had to leave, but they were still talking.

This afternoon, I got an e-mail from one of them. They have, indeed, formed a study group, and wanted suggestions for practice exercises. I can't give them that until Monday - I don't bring the book home - but will do so ASAP.

It heartens me that they followed my advice. I have to admit that going too fast is one of my perennial faults, and I'd gotten signals from that first student that he was having trouble; I should have thought about how to help him earlier in the semester. But maybe all will be well that ends well.

Today I returned the second (and last) midterm to my Linear Algebra class. I wasn't pleased with the scores, and I guess quite a few students were even more displeased. I hate when this happens - I feel as though I've failed them somehow.

At any rate, I went over the problems for them. One of the problems had several different lines of attack, and I went over two of the most direct methods. One student - one who'd done well - raised his hand: "Could you do :this:?" It was a good idea, and I quickly described what he'd find if he took that route.

Finishing the review, I continued with the current material, involving coordinates with respect to a basis. I showed them a few examples, pointing out the geometric content and showing how this allowed a shift from abstract vector spaces to things that look very much like R^n. I got just to the verge of discussing the mechanics of change-of-basis when time ran out.

The student with the good idea came up to me then, and said, "I see what I did wrong. I stopped too soon; I should have gone and :done this and this: Then I'd wind up with :this:" I agreed, and pointed out that he was doing precisely what I'd been talking about moments before, and that the result was precisely change-of-basis - the subject of the next class session. "Yes, you're on the right track!"

As he walked away, he was laughing softly, in tones of joy.

I may not have connected with quite a few students, but this kid's got it.

One of the things I enjoy most in a class is to ask, "Questions?" - and get them. My Linear Algebra class this term is good that way. There are five to ten students who can be relied on to raise questions, including one who wants every detail nailed down firmly. This, I approve of.

DiffEq is less active in this respect, and in the geometry class I'm more apt to ask *them* questions on the fly. They often answer, which is another good way for a class to go.

(My student evaluations from this summer's DiffEq course were pretty bad, but the evals from the courses I taught in spring were good to very good. I'm hoping the same will be true this semester, especially in DiffEq; that will greatly mitigate this summer's flop.)

Today in Linear Algebra, we began discussing matrix operations. Matrix addition is simple enough, even obvious, but matrix multiplication is an altogether different beast, and making it digestible to students is a perennial problem.

About half an hour before class, an idea struck me. When the time came to introduce multiplication, I asked if anyone in the class had ever played Skyrim. Only a few hands went up - perhaps half a dozen, out of a nominal thirty students - but I forged ahead, talking about the problem of building and furnishing a homestead, and the levels of complication - finding or buying the basic components, assembling them into furnishings, and installing the furnishings into rooms of the house. Representing these as matrices ("You need so many nails, so much lumber, and so many hinges to build a chest/desk/cabinet" and "A fully stocked storeroom includes this many chests, this many desks, this many cabinets", leading to "How many nails/boards/hinges do you need to furnish a storeroom?"), I showed that matrix multiplication arises naturally. I provided a couple of more mundane examples as well, but I hope the first one will stick in their minds and get them comfortable with the operation.