Classes Review
Welcome to my class evaluations. I try to give my honest opinion in the classes I have taken. By the end of every evaluation I like to add a little reflection, so make sure to read each of them in entirety.
Winter 2024
Math 32BH Multivariable Calculus, Instructor: Prof. R. Wong
Overall rating: 7/10
Topics covered: Multivariable integral calculus, including an introduction to manifolds (A k-dimensional differentiable manifold is locally diffeomorphic to R^k).
First I should stress that this is probably the most interesting class in math lower division, and a student interested in math should take it. I personally find it not too much time commitment (5h/week), but for a person without any exposure to analysis before it will probably take 10-15h/week. The curve is very generous (automatic A if you put in the effort), and Prof. Wong is very approachable and tries his best to help us succeed. He has an hour of office hours every time after class, and the class is small enough for everyone to participate. In terms of class material this class is excellent, in that it prepares one in future classes like real analysis (131), linear algebra (115), differential topology (225A), algebraic topology (225C), to name a few.
Overall, however, I think this class is ruined by the intensive quarter system. Beginner students will struggle quite hard in the mathematical maturity required to succeed, as the class is their first exposure to proofs. I would say they learn a lot about the concepts used in the mathematics universe, but 1) in such a improvished interval of time they wouldn’t be able to absorb it thoroughly, 2) concepts such as manifolds or measures will probably be too much for students majoring in say biochemistry or computer science (I know a lot of friends inside the class who are CS majors). On the other hand, for an advanced student, they will feel that the pace of the class is too fast for any meaningful venture into the big theorems/constructions. For example, all the big theorems (Green’s theorem, Stokes Theorem, Divergence Theorem) are introduced in the very last two weeks, but their proofs are just briefly mentioned and we barely got time to focus on computations. I feel like the class would be just much better if we could slow down and actually proof things, but alas, 10 weeks is not enough. Maybe I had too high expectations on a lower division class, but I feel quite awkward in this class, wanting to learn more but unable to.
I suggest two alternative solutions: 1) Cut away relatively advanced concepts like manifolds and focus on a more rigorous treatment of the rest (a good reference might be MIT’s 18.02 on MITOpencourseware), or 2) Extend the 32 series into 3 quarters, so there are more time to discuss deeper into the topics and potientially more fancy jargons could be thrown in (such as differential forms and lebesgue integrals). Suggestion 2 might be unrealistic because there would be a lot of logistics, but it will literally make the 32 series the best class of all time.
32ABH are the only two lower division math classes I need to take in my entire life because I bypassed 31AB and 33AB using upper division classes. When taking this class, I come to the realization that universities as places to learn are not much more effective than, Youtube or other platform online. I think a lot of real learning is spent by the student outside of class through exploring topics they are interested in and engaging in self-studying. A good university just provides one an academic environment to learn with bright-minded people and find opportunities easily like research or reading programs, but a strong student should not be restricted by the standard curriculum. It pains me to see some very talented students in my honors abstract algebra class (110BH) actually tolerated through the entire math lower division series in their first year, which they claimed to be extremely boring. There should be an explicit path (I am a special case of this system) that allows advanced math majors to reach graduate classes as quick as possible, or else many talents are wasted.
Fall 2023
Summer 2023
(Summer classes are usually more compact than regular quarter classes as there are only 6 weeks to cover 10 weeks of material, so especially for math, only take them in summer when you prepare enough.)
Math 131A Real Analysis, Instructor: Prof. F. Scavia
Overall rating: 8/10
Topics covered: Roughly what a standard analysis course covers, without point-set topology and modes of convergence.
Prof. Scavia is a solid teacher. He has a very clear direction for where the class is going and handle the class pace quite well, covering all the materials by the end of the second week, so we can have one week of time to revise for the final. This is extremely important and helpful for the smooth running of a class, especially in the summer session with such a tight paced interval. He also has good teaching skills, as he explains the concept fairly concisely and in detail with visible handwriting. The difficulty of the midterm exam is quite reasonable, so those who prepare enough can really get a high score, and he does curve generously.
I should have taken 131AH, the honors version of the class, but it isn’t offered over the summer, so I take the non-honors version instead. The motive of taking the class is to demonstrate my ability in math, so I can skip calculus (I don’t have any credits because HKDSE isn’t recognized in the UC system) and take advanced upper divs.