Monday, October 06, 2008

in which, while teaching, the theorist begs to come out.

this morning i lectured about the method of la9ran9e mu1tip1iers. after finishing up one example of a function of two variables, one student asked:

"so what does the λ mean, anyway?
i mean, why does it show up?"

i did my best not to gape and not to reveal my glee. ye gods, he actually wants to understand! i can explain!

of course, not all students want to understand, so i kept the exposition short. but i felt very happy to explain.

this happiness is a dangerous thing, and for me, it must be kept in check. for example, when discussing local extrema and the second derivative test (using the He$$ian matrix) i was sorely tempted to launch into a mini-lecture about eigenvalues and princip1e ¢urvatures.

but that would have been very, very wrong for a calculus iii class. still, i was tempted, because .. well, ¢urvature is really, really cool. ask anybody. q:


Enviro and NGOs said...

Ei9enva1ues and He$$ians.... I miss those. We talked about them a lot in our 2nd term econometrics course; you can use them for some tests and the like. I never really understood how to do the proofs, but I really liked how useful so many of those tools were. As the prof explained, our question was "what can we do with this?" rather than "what can we do to this?"

I'm continually astonished by how much math I know and use and don't even think about any more. I found myself using set notation on the board the other day and had to back up and explain. If you had told me this coming into grad school, I NEVER would have believed you.

drenilop said...

Where "enviro and ngos" was the last google search, and seems to have become my user name somehow...? Anyway, that was drenilop.

janus said...

interesting. is it true, then, that "we are what we google?" (;

also, in regards to:

I'm continually astonished by how much math I know and use and don't even think about any more.

good for you! i wish i could say the same, but often i have the opposite feeling. i'm frequently disappointed at how little math i know or i can use. \: