My Fridays begin at 9 in the morning at Juisseau. Except, seeing as I don't live right there, and even if I did I'd still need time to get ready in the mornings, this required getting up significantly earlier. Early enough that the sun had not finished rising when I woke up, though it was up by the time I had to leave. With it being late September, and the days only getting shorter from here, I have a feeling I will get to see my share of sunrises this semester.
Proving that I had not learned anything from the topology TD, I did not prepare for Friday's integration TD by reading through the entire polycopie. Since this was analysis and not topology, this was not a problem. The TD introduced himself, confirmed that this was the TD for Monsieur Lévy, and handed us out a single page of exercises. He gave us time to work on them, and then we went over them together. The exercises were drawn from the first week, so they stopped at proving countability.
The questions were pretty much exactly the kinds of questions I would expect to show up for homework. More, they made the already comprehensible class even clearer. We had a chance to work with the concepts that had been defined, but not yet used, like symmetric difference or indicator functions. And the near-instant feedback of the professor going over the exercises we'd just done was incredibly helpful for making sure I was doing the right things.
There were eight exercises, (most of them had multiple parts) and we got through about five of them in the three hour class. The first exercise was on sets and the symmetric difference, the next two were about sets, functions, image and pre-image, the fourth was arithmatic of the indicator function, (I liked those a lot, because they became very easy if you were famliar with mathematical logic and used that as a stepping stone) two on lim sups and lim infs (not my favorite topic, but certainly something that practice helps with), and finally two on countability. None were two difficult, but none were way too easy either.
All in all, it was probably the last frustrating three hours I'd ever spent in a classroom doing math. It would be a lie for me up say the class flew by and I was shocked and disappointed when it was time to leave, but I wasn't constantly sneaking glances at the clock (my phone since no rooms appear to have a real clock) to see if it was time to go, so it must have been a decently pleasant three hours. Certainly, given what the rest of my Friday looks like, I'm glad it's analysis and not another subject.
After that, I had two hours to get lunch before history of mathematics. This was enough time to leave the Latin quarter, but not enough time to go back to my apartment. I settled on L'as du Falafel, which was about half an hour walk away. It didn't make for the most relaxing lunch "hour", but it did give me a change from the surrounding seven hours of class.
Then history of math. We spent more time and detail on the Greeks, talking about the four most important locations we needed to know, who was associated with each location, and what they were known for. The week before he'd mentioned that this class was treating math in its modern conception, but the subjects that fell under the category of "math" had changed over time. For example, astronomy used to be considered part of math. This hit home when, in describing what ancient Greek mathematicians were famous for, pretty much all of them had contributed to arithmetic, geometry, and astronomy. Because at the time, that's what mathematics was.a And then it was time to focus on Euclid. His definitions and what they were really saying, his common notions and why they weren't completely common, and his demands and why they were necessary. Especially the fifth postulate, which raised the question: were these things obvious facts of life, or were they the rules of the game of geometry? The class was split about 50/50 on that. However, change the question to "what are the requirements of groups? Are they obvious facts, or rules of the game of algebra?" And a rather clear consensus arose in favor of the latter. Basically, geometry seems a lot less arbitrary than algebra, even if it isn't necessarily.
During the TD, we started working through his propositions and theorems. My proposition was 31, (given a point and a line not on that point, you can construct a line through that point parallel to the given line) and, while I understood the proof, the thought of getting up and presenting it to the class was nerve-wracking. There are a lot of presentations I haven't wanted to give, but that's the most I've ever not wanted to give a presentation. And I knew it would be good practice, but I couldn't help being relieved when the professor said proposition 29 was the last one we'd do today. It can't permanently get me out of speaking in class, but it can postpone it.
Then an hour break before phonetics. Phonetics also started late, which gave me time to listen to, and finally join, a conversation between a Canadian environmental science undergraduate and a Cambodian/American math graduate student.
The phonetics instructor gave us a quick intro to the course, (we'd be focusing on vowels, don't skip more than twice without an excuse) asked a couple questions about ourselves and our native languages, (like, "how many vowels does it have?" Winners are Arabic ["Umm... It's different"] and Cambodian [upwards of twenty.]) and gave us a quick crash course in the different vowel sounds. Then we spent a lot more time talking about the [i] sound, and then my academic day was finally over.
My actual day lasted a good deal longer, as the Canadian, (Lucy) masters student (Kimsy) and I ended up in an extended conversation outside the building. We talked about our classes, Paris, bureaucracy, and what things had been like at our North American universities.
Lucy was super-resentful of Toronto. Apparently, she thought the people there were rude. Which made me and Kimsy (who had gone to university in New York) burst out laughing. While I can believe Toronto people are rude compared to Canadians from smaller towns, they're still friendly compared to people from the US.
It turned out that Kimsy and I lived really close to each other, so we took the same trains back, and even got out at the same station. We'd both done REUs, (she'd participated in the misleadingly-named SMALL program at Williams College. With 30 people, it is one of the larger programs.) So we were able to talk about that, and also just math in general. After a month of interacting more with humanities people, it was really nice to be able to discuss math again.
