good ideas, bad lectures.

today both lectures were a mess;
i "blame" a colleague.

---

yesterday afternoon i was in the middle of sorting out my teaching affairs. he came in and we had a lively research discussion.

we almost have the theorem now,
but my paranoia persists;
ask me again later.

losing that time, though, i wrote my lectures hurriedly. in one case it seemed to matter, but not in the other.

1. there is a standard example of a nοwhere continuοus function: the indicator function of the ratiοnal numbers. i never liked that example, maybe because my mind is too measure-theοretic. it agrees a.e. with constant function; so what?
   
   so i came up with my own example: f(x) = (-2)^x, for the rational numbers on which the formula is defined (i.e. those with odd-numbered denominators). [1]
   
   i think my students received it well -- some eyes widened, at any rate. on the other hand, i made a lot of claims but proved little. for a class like this, details are important; students otherwise learn bad habits. \-:
   
   maybe i'll write it up, and give it as a handout on friday.


2. in my last calculus class, i discussed parametrizatiοns of surfaces. at the end of lecture, everyone was quiet .. unnaturally quiet, and i realised that i lost a lot of them.
   
   today i sought to give them more intuition, and wrote a "procedure" for how to determine a parametrization, with a few more examples. at the end of the class, i received looks of three kinds:
   
   (1) "i'm still lost. what the hell is going on?"
   (2) "i'm still lost, and i don't care."
   (3) "yeah, we figured it out yesterday." (probably a good explanation from the TAs, which is good)

[sighs]

sometimes we try, to no avail. \-:

[1] we're using the bartlε-sherbεrt text, where there is actually freedom to choose the domain A of the function. so yes, i am abusing the definition and the relative topοlogy on that subset of rational numbers. q-: