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Clover May's lectures are usually pretty clear and helpful -- she does a good job explaining why certain concepts or ideas are useful and is always happy to take questions. Homework is pretty reasonable in length.
She is very particular about how she wants you to write proofs, which can be frustrating because it will cost you points on exams if you don't follow her instructions (for instance, you have to explicitly cite theorems and you have to write in full sentences).
Her check-ins (which were 2x per week) took so. long. She did start grading them solely on completion though after enough people complained (she does a mid-quarter feedback form), so that was nice! She also dropped like, 3 or 4 of them out of ~18, which also helped.
Honestly, as long as you remember to follow her specific rules on proof-writing (which will probably honestly make you better at writing proofs, since her rules are designed to make your proofs as clear as possible), go to lectures, do homework, and ask questions, you'll probably be fine.
I am not a fan of Professor May. On one hand, she emphasizes how we are doing so well in the class and how she's happy we are learning, despite the COVID conditions and even extended all deadlines by one day. However, her explanations were pretty subpar. I asked her a question about how I would approach some type of question before the second midterm and her response was super generic along the lines of "I don't know just do it". Unfortunately, that question came up on the second midterm and absolutely rocked me. She is also super anal about how we write in complete sentences for everything. I can understand why she wants this but giving so many penalties for it really irked me. Also, every week, we had one homework assignment and two check ins due. I would maybe appreciate these checkins but I didn't learn anything from them and were a chore to complete. On a more positive note, our TA Zach was super chill and was very open to help us. I think this may be her last quarter at UCLA but I would personally avoid her class in the future.
I appreciate Dr. May, as they are trying to be very understanding during the pandemic. I won't lie the workload is intense; but content-wise, the class is a good combination of theory and computations. The computations help me further understand what I'm doing so I appreciate the computations. Without it, I wouldn't understand this material at all.
Note: this review is being posted from the middle of the quarter.
It feels like Prof. May has confused 120A for a lower division course. When I take an upper division pure mathematics course, I expect a proof-based course that teaches the theory of a subject, not a course that skips the details of important, accessible proofs just because they depend on a little linear algebra (115A is an enforced prereq!). I expect to have my time respected with interesting proof results on homework that extend on the lecture material, not pointless computational exercises that take painfully long on 3 (!) assignments per week.
To recall the course description from the department: "There are some beautiful theorems that if a curve in 3-space forms a closed loop, it has to bend at least a certain amount, and if it forms a knot, it has to bend at least a larger certain amount. Another beautiful theorem is the celebrated isoperimetric theorem, that among all closed curves of a fixed length, the circle encloses the largest area." Well, we moved on to surfaces already and covered none of these beautiful theorems.
If the goal of the course is to allow students to develop an interest in differential geometry so that they may choose to study it more in the future, to put things lightly, Prof. May is not helping.