Rest your weary head

Last night I worked from 10 pm until 1.30 am, completing to my satisfaction every assignment question except 3 and 4. Once they were all written up neatly I slept for four hours, then raced up to university to finish the other assignment I had due today. After it was done I had one free hour remaining, in which I wrote out some scratchings for the two hard questions of the MATH assignment, then stuck it in the box and got on with my life.

All I handed in for question 3 was an incomplete proof with a discussion of why that method couldn't possibly work. For question 4 it was just a list of what I had deduced and what had still to be shown in order to complete the proof. The latter was more extensive than the former - I hadn't got very far at all with question 4, despite my premature confidence about it.

If this was MATH 312 I would have kept the assignment over the weekend in order to perfect it. It would eventually be handed in next Friday [in all probability still imperfect], and then I'd remain one week behind for the rest of the trimester. There were only 12 people in MATH 312 for most of the course; Chris didn't mind when we handed in the assignments, so long as they were handed in. This was very bad for the perfectionist in most of us. With so many people in MATH 301 he's unlikely to settle for such a relaxed approach this time around, which will certainly be good for me. Sometimes you just have to say goodbye to perfection.

The best thing to come out of this assignment - and this is a very good thing indeed - is that I can now construct epsilon-delta proofs if I try hard enough for long enough. I've never been able to do it before, and I just did it three times!

Today's lecture was oddly short on notes. Chris spent quite a long time talking in a general way about polar coordinates, particularly to what extent the polar coordinate function is invertible. This was in aid of introducing the concept of a local inverse; that done, he wrapped up with the inverse function theorem. Something tells me it might be rather wonderful. I'll have to look at it more closely after I've had some sleep.

On Monday I wrote more than two pages of notes in one lecture for the first time this trimester. This occurrence has not yet been repeated, but if memory serves it will soon be standard note-taking procedure. Mathematics is very costly in paper and ink, as well as in time.