Part III during Lockdown III

Hi! My name is Alice, and I’m doing the Part III Master’s in pure math(s) here in Cambridge this year. It’s split into three 8-week terms (Michaelmas, Lent, and Easter), and during the first two terms, we take math classes. The third term, as far as I can tell, is preparing for the year-end exams which are in early June. These exams are the only measures of our performance the whole year—no homework or midterms or anything! It’s definitely a new structure for me, and it’s been a real test of my planning skills.

I’m lucky to live in a house with several other Churchill College students, so I still get to have social interactions during this third UK lockdown, like watching TV or making food together. Here’s a picture of a recent Sunday dinner, where Carmen and I made nachos with all the toppings, as well as a kimchi cabbage slaw.

By total coincidence, my childhood friend Connie is working in a lab in Cambridge this year, and I’ve loved being able to spend time with her as best as lockdown restrictions allow. Last Saturday, we biked to the “big” Waitrose (an analogue of Whole Foods) just south of Cambridge. Spring is in the air, and the day was sunny and beautiful. Snowdrops are blooming everywhere, and daffodils are starting to emerge. The only stain, so to speak, on that day was that a wood pigeon managed to unload on my arm while I was biking home. :/

The Saturday before that, we biked to a hill called Gog Magog a bit south of Cambridge, where we bought mini ham/chicken pies and walked by beautiful fields and along a Roman road in nearby Wandlebury Country Park. Here are some photos of our journeys!

Academically, this year has been a trial run for learning how to learn without the rigid structure of weekly problem sets and midterms and finals, even more so because of the total lack of in-person learning. Having regular study group meetings for my classes this term has made Lent a huge improvement over Michaelmas: I reap a lot of my enthusiasm for math by talking about it with other people. Last term, I felt a bit deprived of mathematical discussions because I mainly studied in isolation. It doesn’t work for me! I’ll definitely keep that in mind in grad school.

This term, I’m taking three “modules”: Profinite Groups and Group Cohomology, Algebraic Number Theory, and Modular Forms. I branched out last term by taking Differential Geometry, Algebraic Geometry, Local Fields, and some of Algebraic Topology. The pace of the lectures is not too different from the more difficult undergraduate courses I’ve taken, but the fact that the classes are condensed into 24 lectures over 8 weeks instead of the 12 weeks at Princeton makes it feel much faster (not to mention that we have lectures on Saturdays, too).

In addition to classes, I’m writing an essay about abelian varieties over finite fields. The essay is a way to practice reading difficult math on your own and writing good expository math. It counts as 3 units, which you can use in lieu of a final exam. An unavoidable task for me was to translate a foundational paper for the topic from French into English, so that was an interesting and niche crash course in French (i.e. a crash course in using Google Translate efficiently, since je ne sais any French).

My translation process while working on my essay. It was faster than I expected!

I spent most of my day, every day, at my desk in my room—quite a shift from my library-centric work habits in undergrad. Instead of beautiful views of the Moore library or the rest of the mathematics center, I attach a snapshot of the current state of my workspace.

This year is strange, but I think I am happy anyways. I am slowly filling in my understanding of concepts I’d only glimpsed in previous years, like schemes, topological groups, and class field theory. Lockdown restrictions are easing up. I was gifted a guidebook to England for Christmas, and I leaf through it at the dinner table sometimes, looking for places to go visit once travel is allowed again. Fingers crossed for mid-April!

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