Tuesday, January 23, 2007

Monday, Monday


Yesterday felt a little...off. Not that any class went particularly poorly, but I don't feel that any of them "zinged" either.

In 280 we put a stopper in negation, spending the hour negating all sorts of statements with quantifiers. I think order of quantifiers and scope of variables is still confusing to enough people that I spent an hour or so last night and wrote up a handout with 17 more examples of quantifier statements, organized by "Statement/Negation/Reordered quantifiers." I hope that'll help folks to get a better handle on such statements as we go into tomorrow's class on compound statements. We start things off with presentations of the solutions to two of the first set of homework problems.

In 368 yesterday we pounded away at Pythagorean triples. It took us about 30 minutes to prove the characterization of all primitive integral triples. There was call to use our characterization to come up with a massive primitive triple, so we took s = 625 and t = 729 and generated

(st, (s2-t2)/2, (s2+t2)/2),

just to look at it. They're working on a different Diophantine equation for next week's homework. Tomorrow will start off with presentations on the second homework set, and we'll go from there to work on basic divisibility.

In Calc I we finished up with exponential functions and various perturbations thereof that can be used as more realistic population models. After working with Mathematica on the logistic equation, several of the students expressed interest in obtaining the free version of the software they've got coming to them under our site license. Score.

Today's a bit laid back, I've got a few student meetings and some prep work to do, but nothing crushing...there is an all-campus faculty/staff meeting in a few hours, but nothing else to keep me away from the office until class. Calc I today: shiftin' and scalin' and other nonsense with functions.

1 comment:

eliz said...

I'm glad we will be going over quantifiers more tomorrow because they are confusing.