The Life of a Mathematician

Today was my birthday, which makes me think of last year when I ended up helping Mike with algebra homework on that day, then later played Star Wars: Epic Duels with Abe, Greg and Kyle after Mike told them it was my birthday and I was by myself. And, this line of thinking is going to make me homesick so we'll move on to another.

Class this morning was talking about the final for the first few minutes, then the rest of the lecture was a biographical sketch of Euler. Quite interesting. I didn't remember that he was contemporary to Goldbach and mentored by Gauss. Then again, I have a poor memory for historical details in general. Next Tuesday he plans to answer any study questions they have, then prove that e^(i*pi) + 1 = 0.

After class we did the last round of placement testing (until this fall) with the homeschoolers. Just two students this time, a Level 2 and a Level 3. The boy taking the Level 2 test also had a birthday today. He turned 14. It also looks like he did well on the test, based on a quick look-over. I'll actually grade them in the morning.

While they were taking the test I started writing up more formally some thoughts I'd had about a problem some of us attempted when we were taking combinatorics. The problem itself comes from point-set topology. Given a finite set of n points, how many topologies are there on the set (assuming the points are distinguishable)? I realized it had been a while since I'd written up a technical proof, but it came back pretty quickly. I haven't gotten as far as trying to do any counting yet, but I've got what might be a good system for describing the topologies.