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What Are You Working On? May 16, 2022

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Figuring out how to organize my research without a dissertation to stick it into, since I finished my PhD this semester :) so far I’ve just got a “misc. results” overleaf file.
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I am currently "interleaving" between Harvard's online course in abstract algebra (Currently lecture 11) and Abbott's Understanding analysis (Chapter 7, the last of core material).

When I finish Abbott's book, I will probably replace it with Axler's LADR, as it is a good companion to the Harvard course.  The Harvard course uses Artin, and it is quite LA oriented.

I am super excited about what I have learned this year of self-study, and I am looking forward to learning more and more. My reading list has grown so much in the last year that I am not even sure I will finish it!
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I'm revising for my numerical methods exam in two weeks' time. It's going to be difficult; I've got hours and hours of lectures to catch up on, plus reading notes for the differential equations bit because there was another *pissing* strike. Good news is threefold: (1) that's the hump and then it should be relatively easy to make the cheat sheet and practise, (2) I'm going clubbing with a friend this week (which is notable because I'm not really a clubbing kind of girl, and the last time I went I didn't like it, but I also wasn't with people I knew very well), and (3) the Champions League final is the Saturday before the exam and LIVERPOOL ARE GONNA WIN (or at least I fucking hope they do; not only are they my PL team, but if Real win *another* fucking CL it's going to be a right downer for my exam).
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Studying for exam fm (financial math) by doing practice tests
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I’m bored of geometry so when I have free time I’m teaching myself higher level things, like solving integrals
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I've finished up the exposition to abelian categories and I feel slightly more comfortable with the Freyd-Mitchell embedding theorem, at least to the extent that I can work with elements with a clear conscience. Moving on, we've defined the category (co)chain complexes in an abelian category and proved it's abelian. We've also extended the snake lemma to the long exact sequence in cohomology. I'll have to work through it again to internalize it, but it's certainly a neat result.

Aluffi ends the section with a brief aside on viewing a short exact sequence of complexes as a triangle with zero as a connecting morphism and then taking the cohomology of that. I'll have to reread that part a few more times but there are some aesthetically pleasing diagrams involved.
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I've been working on writing a book focused on an algebraic approach to computability theory. As a wee undergrad, I thoroughly enjoyed algebra and wanted a comp sci minor so I took all of the computability theory courses available from my uni. First and second year computability theory courses from the CS dept glossed over all the very beautiful and intrinsic algebra in computability theory and I accidentally derailed tutorials regularly asking algebra questions.

The CS courses focused on how to use and abuse computability to solve problems, and the maths focused on doing broken shit with recursive sets. I've never run across an algebra or computability course that showed how deeply the two are related.
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I've been prepping for dual enrollment at a college by reviewing all of my mathematics books, and putting the notes into a latex file on my computer.
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I'm looking into the no-wandering-domain theorem in complex dynamics. Trying to solve it with möbius-transformations for circles
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I taking a test to evaluate everything I’ve done throughout the years

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