fall 2006
section 1
Instructor: Christopher Tuffley
| ::math 25:: fall 2006 section 1 Instructor: Christopher Tuffley |
|
| I'll
be sharing the TA duties with Sonya Berg this
quarter. We will be taking turns leading discussion and grading the
homework. Please come by with any questions. |
|
| +++ | I'll
have normal office hours on the Monday of finals week (4--5 or later). |
| +++ | Thinking
of a proof as a joke, or a story; it's bad form to speak of characters
(like M, epsilon, N, etc.) before you have introduced them. For
example: let M>0; since a_n converges, there exists N such that...;
there exists a K such that |b_n|< K because we know that (b_n) is
bounded. |
| +++ | If a property is true for all M...then given M and k, the property is true for M/k. |
| +++ | I
think a proof should be like a good joke. The reader should be
thinking, "okay...I believe that...umm, yes...then that means (!) Wow,
that last bit came out of nowhere; but it makes sense." That's the beauty and surprise of math---"Ah-hah! I get it!" The reason it's not always like this is the same as for jokes: If the set up takes too long, or the supporting characters have to be explained too much; then the punchline isn't enough payoff for what's been invested. And the audience doesn't feel relief/enlightenment/laughter. |
