Thursday, February 08, 2007

It's been a long time...

...since I rapped at y'all. What's up?

We've been chugging away in all three classes, and things are running well all around. The folks who spent last semester with me in Linear who stuck things out to find themselves in 280 agreed with me when I mentioned it yesterday before class: 280's going a lot more smoothly than did 365.

This is large due, I think, to the fact that I've discovered the means of class preparation that works best for me: engage in thorough medium-range planning, punctilious day-to-day planning, and don't sweat the long term. I think mapping out 365 in advance was ultimately a mistake, as it created the illusion of an artificial schedule, a framework which didn't really exist. It existed on paper because it was "supposed" to exist there, but I never really brought it to the classroom.

This semester, both 280 and 365 are being constructed more or less one week at a time, and hours of careful planning goes into each worksheet and homework set, but I'm not worrying about where we'll be in six, seven, eight weeks. I suspect we'll finish the first 20 or so chapters of Silverman in 368, before veering off into primality testing and Fermat's Last Theorem in the context of Gaussian integers...I suspect that after proof methods and propositional logic I'll lead the 280 folks into the wonderful world of axiomatic set theory, and then do some theory of relations...I suspect these things, but I'm hardly going to commit them to paper until we get there. Trust, though, that once we get there, the treatment will be careful, meticulously crafted, and exact.

So what are we doing just now?

This week's Induction Week in 280, and yesterday's struggles reminded me how hard it is for even the most intelligent student to grasp induction when it's first introduced. (To say nothing about the difference between limits and indices in sigma notation...) We'll do a few more examples tomorrow, introduce Strong Induction, and use it to prove the well-orderability of the naturals.

In 368 we're doing congruence computations left and right. Fermat's Little Theorem is our main course tomorrow, when we'll learn how to find the last digit in 4200018 without a calculator.

In Calc I? We're getting nitty-gritty tomorrow with the epsilon/delta definition of a limit. Since they've already seen and drawn a good number of "banded graphs," I'm hoping it's not going to be too much of a stretch.

But it always is.

Anyhow, that's where we are right now. Humdrum, ho dee hum.

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