Konstantin Aleshkin

Basic ring theory, theory of fields, extensions, finite extensions, Galois extensions, Galois theory, insolvability of the quintic. Towards the end we covered introductory module theory.

Just a handful of psets, usually every other week, or so. 2 midterms and a final, all of a similar format. He gives practice exams, but they are often riddled with mistakes, and it was normal to get the answer key to these not more than a day or two before the exam (the answer keys often had mistakes too). The biggest struggle is that he would test material that he did not teach, and given he did not follow the book much, it was a goose-chase to find what to study and then to find the time on such a short notice. The homework usually wouldn't take more than like 6 hours, but I studied upwards of 20+ hours for each exam, only to end up dead average. He's a cool dude, but the way Aleshkin teaches makes it much harder than it should be. That being said, I feel that I have a decent grasp that will prove useful in high math courses, so pick your poison.

A lot about Matrices and Linear Algebra.

I learned calc 3. Mainly topics surrounding vectors.

IRRELEVANT TO THIS CLASS - This is a huge inconvenience, please stop blocking us from accessing courseworks during finals for evaluations.

Overall, super split. In class, the material that he actually sought to cover, he usually did very well. Like most professors, he is very proof-based, tragically. However, he often comes back to explain why this is true and give a reasonable intuition. The only challenge with Aleshkin is that he simply does not do this with topics that take a while to prove (i.e. actually difficult concepts). Because of this, you get left doing an insane amount of studying to try and catch up on the things you need to know, but he simply did not cover.

Linear Algebra topics (Gauss-Jordan Elimination, eigenvectors, bases, matrix transformations, etc)

Chapters 12 to 14 of Stewart's Calculus book.

Learned how to work with matrices and gained a solid understanding of topics in linear algebra

We learned about calculus involving 3-dimensional shapes.