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Thursday, September 27, 2007

And we light up the sky

Following a session with Rebecca the assignment is done, TeXed, beautiful [apart from the ugliness of the derivatives in question 4] and ready to hand in as of 11.30 this morning, which does set a new record for this course. I won't hand it in today though; if changes suggested themselves overnight and it was already in the box then I would be really annoyed. It can go in at deadline tomorrow like usual.

There seems to be less intellectual challenge and a bit more mechanical procedure in this part of the course - at least so far. The derivations go on for pages and pages, but in the end we're only expected to know the end results. Presumably it would be a good idea to at least know the gist of said derivations, though, just in case they turn up in the exam.

Today's lecture was on the Heat Equation. Peter introduced it with the intention of using it to demonstrate a new technique for solving second-order PDEs, but then he spent the rest of the lecture trying to show how the equation is derived from physical reality, so we never got to the technique itself. This was after we'd already lost about five minutes of lecture time to lateness, disorganisation and a quick trip back to Peter's office to collect some missing notes. Dare I suggest that this wouldn't have happened if he wasn't relying on slides?

The tutorial was slow but ultimately enlightening, including a rather nice [if simple] proof that a linear combination of solutions is also a solution under special conditions. Peter went through the technique he hadn't got to in the lecture, and then we did an example straight off. We didn't quite finish it though - after reducing the PDE to a system of ODEs, we stood around gazing at them and trying to remember stuff from MATH 206 before concluding with "it can be done, so there's no need for us to do it". See earlier comment about not being used to getting my hands dirty.

That been-done-before mentality is one of the things I love most about maths. It means that the only truly interesting problems are unsolved ones, which leaves apparently endless scope for creating new material by accident. It also puts me in mind of one of my favourite mathematical jokes:

An engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard. After some observations and rough calculations, the engineer realizes the situation and starts laughing. A few minutes later, the physicist understands too and chuckles to himself happily as he now has enough experimental evidence to publish a paper. This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.


lorne said...

It's often quite amazing that lecturers writing things on the board (or equivalent) never seem to leave their minds in their office. (Or if they do, we can't tell). Then you only have to worry about things like permanent markers (or writing directly on the projector).


Gael said...

I presume that's because no-slides lecturers must necessarily come to class extremely well prepared.

I-E-A-I-A-I-O it is. What shall I bet that you had to look up the spelling before typing it? ;)

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