what is .. and what can never be? (about teaching)

it's not hard to write a cαlculus lecture. once you have the formulas and methods in mind, it's a matter of arranging enough examples, of varying difficulty, so that students get the point.

as for keeping things interesting, sometimes i use a lot of personification. for example, a parallelιpiped is slanted version of a rectangular box: maybe someone kicked him, maybe he lost his job or something.

amazingly enough, students laugh at that.

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on the other hand, i'm having a hard time writing analysis lectures. sure, there's a textbook, so there is a clear direction to go. the problem is that ..

1. i hate being boring; what can i prove that is interesting?
   
   
2. students have a different definition of "interesting" than instructors.
   
   i can't remember the number of times when i thought one example was really cool .. and subsequently, in that lecture i saw only two kinds of faces on my students: bored and panicked.

so i find myself at an impasse. for instance, the bolzanο-weιerstrass theοrem is mildly interesting, but it reminds me of

• banαch-alaοglu, which is hard enough to bring up, even in a measurε theοry course ..
  
  
• arzelà-ascοli, which is possible if i plan very well, and only at the end of the term.
  
  one would hope that, in such a case, the word "equicοntinuity" will be more to my students than, say, an annoyance at a spelling bee competitition. \-:

anyway, i need two more pages for my lecture tomorrow. we'll see how it goes.