One of the main things that graduate students need to cope with in the sciences is giving lectures. For some, they give lectures to undergrads. Others give lectures in their classes. In my case, since I am not fluent in Mandarin, I can’t serve as TA, which is what most of my classmates have to do. However, in both of my classes, we have to give lectures. This is very different from giving a 30 min to 1h presentation. Students have to assimilate new subject matter and present it to the class, while the prof is watching. In both of my classes⁴, there aren’t that many students³.
This can be quite challenging because you need to prepare fully before you give a 3h lecture. While you give the lecture, the prof will ask you questions about the new topics and proofs, to see if you have understood it. He/She will ask to see if the other students have understood as well. In my case, in my Commutative Algebra class, most, if not all, of the explanations are in Mandarin, but I usually get what’s being explained since I tend to prepare the topics even when I don’t have to give the lecture.
In Commutative Algebra, since we are using Atiyah’s Introduction to Commutative Algebra, the proofs are quite sparse and need to be fleshed out. I usually start by reading the assigned paged, then researching papers or coursework based upon those pages on the Internet, then I start to assimilate what’s really going on. It’s a process that can take quite a while, 6 to 12 hours if not more per lecture.
Today, for some reason, probably because it’s the end of term, Dave didn’t prepare his lecture enough. It was somewhat slow and he only managed to do one proof¹. He fleshed out the proof a lot more than I did by myself, and it was was painful to watch. While he was doing this, the prof kept asking him questions and he had trouble responding. She also got frustrated and one point, had her head on the table because Dave had missed an obvious point². This was late in the 3rd hour of his lecture.
It was a long class, but since I had prepared the material, it wasn’t so bad. My last lecture of the term was last week and it wasn’t my best. Still, after the 1st hour, I think I did well. I went over quite a few remarks and presented alternate proofs for Proposition 8.8 to 9.1. Sure, I made a mistake in one of them, but it was fine.
* * * * *
[¹]: Proposition 9.2 in Chapter 9: Discrete Valuation Rings and Dedekind Domains.
[²]: That a discrete valuation needs to be onto, so he had forgotten to verify this in the proof.
[³]: In one class, there are 4, in the other there are 3 but most of the time, we are only 2.
[⁴]: I actually have three classes, but the last one is a colloquium class, so I don’t have to prepare, just be present.