Intégration was dedicated to proving the Monotone Convergence Theorem. The previous week, he’d given us a statement of the theorem, but said we didn’t have the time to prove it just then. But, with the entirety of a two hour class dedicated just to one proof, we did. Barely.
The Monotone Convergence Theorem say that, under certain conditions, if you have a sequence of functions, the limit of the integral of the sequence equals the integral of the limit. Which is allegedly supposed to be pretty powerful, though we didn’t have much time or examples that we could look at to see why. The seven steps (often with non-trivial substeps included within) took up most of the time.
During the harp lesson, I started to get really, really sick of “Trop penser de mes amours.” The variations might make it slightly more interesting to listen to, but when I’m playing they just require me to pay more attention to the piece and where I am and the fact that it’s the same freaking notes, even if they’re played up an octave or at the same time. At least I enjoy “The Foggy Dew.” (Enough to even find Youtube videos and listen to it there.)
The first part of topology was going over the exam. I’d already looked at the solutions online (they’d been posted within twenty-four hours of taking the exam) so I knew which parts I might have gotten right and which I’d definitely gotten wrong. And, when I was able to see the solutions with their full description there, the questions and answers made a lot of sense, and made a thorough review of the tests not exactly necessary.
The best part came at the end. The professor was talking about how he didn’t think the quiz was that hard (student sitting next to me: is he kidding?) and then he went to the board and drew a grid with a line of slope one. To the left of it, he drew a curve that had points at the origin and the end of the line. And then he explained that the curve is what grades currently looked like, and that the line is what ideally the grades should look like. So if you got a zero or a twenty, your grade would still be the same, but if you got something in between that, it would be raised by a certain number of points. The closer to the average you were, the more points it would be raised by.
I’m used to calling that a curve, and I missed whatever the French name for it is (if there is a French name. The amount of explanation he was giving made it seem like this was a very unusual thing) but I got the general idea. I’d never before been so happy to have a grade raised to a 60%, though I’m pretty sure that’s only vacuously true.
Later on in the class, the fire alarm rang. I would not have figured this out if it hadn’t been for the reaction of my classmates and professor, since it was pretty quiet. I mean, I could hear it, but I’m pretty sure the sirens on passing police cars was louder. Also, point of clarification: “reaction of my classmates and professor” doesn’t mean “oh no! Fire!” It was more of a “Sigh. I guess we need to leave the building” reaction.
The professor told us that although, theoretically, we were supposed to leave our belongings in the case of a fire, this wasn’t a real fire and there were real thieves, so we should bring everything with us. So everyone took their time putting their stuff away and exiting the room to join the long line trailing down the stairs.
Once outside, we kind of clumped right outside the building. Which is obviously not a good thing to do if there is a fire, since burning buildings aren’t exactly structurally sound. Plus, I’m pretty sure there’s a phrase about not standing too close to the fire.
Eventually, we were told to move away, and we did, though I think all this did was make room for other people to go stand where we had been. Someone came over on a megaphone to tell us things, but I’m not sure what. I was not alone in this- one of my classmates even asked if I understood him. Said classmate was a native French speaker.
Other than getting the tests back and having the fire alarm go off, topology was kind of dull.
Russian was more work on the genitive. A lot of work on the genitive, actually. Also, the professor seemed surprised everyone seemed to think French bread was the best bread. I’m not sure who would debate that claim, honestly.
During the Topology CM we had time to actually get into compactness, instead of merely getting the definition. Compactness was something that had come up over the summer. Very briefly, because I’m pretty sure our project didn’t need that at all. It hadn’t made much sense at the time, so I’ll give credit to UPMC and my Topology professor, because this time around, it did. Rather than jumping straight in to talk about covers and open covers, we by working a bit with the definition that a space is compact if every sequence has a convergent subsequence. I’d worked with that property a bit in my semester of real analysis (Bolzano-Weierstrass, when you’re looking at a bounded sequence of real numbers) so that made sense. The arguably more helpful definition that a space is compact if and only if you from every open covering of the space, you can extract a finite sub-covering is less intuitive, but at least I now had something that I understood to fall back on.
And then it was Friday, and time for even more tests.
Our normal professor wasn’t there during the Integration TD. Instead, we had another of the professors step in, and I understood why Mina (other American) switched classes. Possibly he was from the north of France, but I’m not good enough at identifying accents in French to be able to say. All I can say is that I don’t understand him when he speaks. Like, at all. For all that leaving my apartment while it was still dark out that morning had sucked, at least I normally understand Tardif.
We took the quiz first thing, which was nice. It meant that I was working on the problems when my brain was still reasonably fresh. The quiz had one easy question and two more difficult ones, weighted at 8/6/6. The first question literally came out of what we’d done in class, and the other two required more creativity and application. I felt a lot better while taking it than I’d felt about topology, though that probably meant no curve.
Once the quiz was over, our interim professor gave us a break and disappeared for a while. He came back with the answer key. So immediately we could see everything that we’d messed up. Yay!
There wasn’t much time after that to work on problems, but we tried. I continued to not understand anything that the professor was saying, which made things difficult. I tried the problems on my own and waited for the class to end.
Then I had a break, during which I got lunch and tried to mentally prepare myself for the next exam.
Our normal professor wasn’t there for this one either. The test professor sat reading until it was time for the class to begin, at which point she realized that the tests were in several different parts that needed to be combined (answer booklet, more official answer booklet, blank sheet of colored paper for some reason, and the questions themselves.) She started putting them together and handing them to me to pass back (I was sitting directly behind her) and we did about six this way before people started making comments to the effect of “there has to be a more efficient way.” So she stopped worrying about neatly combining them and started circulating large stacks of each of papers and let people grab the papers themselves. And then we were ready for the test.
I have in the past complained about Isabel’s tests. I take all of that back. Yes, hour long French exams with a heavy focus on essays are brutal. But believe me, two hour long exclusively essay exams asking you to do things like analyze the difference between four different versions of one of Euclid’s proofs are so much worse. And when one of the readings that we’re supposed to incorporate is a scan of a 17th century document, complete with fs that look just like an s? It was great fun.
The only good thing was that the TD was cancelled, so I had time to grab dinner before my French test. Have I mentioned how easy a French-language class seems in comparison to a lot of non-language classes taught in French? Because it’s still true.
