Wednesday, January 06, 2010

choosing words carefully.

tomorrow i teach my first analysis class. already i see the need to be careful.
just earlier i was writing a lecture and decided to include one theorem. i read the proof in the book and immediately thought: wait, this is silly. can't you just pick the right subsεquence?

i was halfway done with writing my own proof, when it occurred to me: sh-t. they might not know what subsequencεs are.

i looked at the book again. sure enough, the discussion about subsequεnces appears 2-3 sections later.

argh ..

.. oh well; i have a page left, anyway
[1]. so i wrote down a definition for subsεquences and an example of even numbers from the whole numbers.

i'm reviewing material from last semester, anyway. q-:
i'm excited about teaching a course where, for once, "proοf" is not supposed to be a scary word. then again, i wonder how many times i'll slip up and forget that something isn't obvious.

on a lighter note, for this lecture i have planned, among other things:
a proof by induction,
a proof by contradiction,
a direct proof (of a concrete case),
and a diagram!

[1] it doesn't matter if it's a lecture for a class i'm teaching or a talk i'm giving at a conference; somehow 50 minutes ~ 5 pages.

this post was reformatted to fit the layout (as of 2 feb 2013).


Anonymous said...

Good luck with the new class! Upper level courses are fun. You'll be quickly reminded of what it was like to learn how to write good proofs. Don't be surprised when you see 2 page proofs that would now take you 4 lines. You're about to be reminded of the difference between a correct proof and an elegant correct proof. Have fun! Your students are in good hands.

Leonid said...
This comment has been removed by the author.
Leonid said...

You may also be reminded of the difference between proofs that are wrong and proofs that are not even wrong

Leonid said...

Apropos of proofs