Integration and Infinite Series
Professor is really nice, she answers every question people have in the lecture even ifit takes 30 minutes to go through a problem (which many people may already know). Lectures are short so you might actually have to read the textbook for more comprehensive understanding. Midterm consists of 8 problems, 5 points each. Final has 12 problems. For both midterm and final she added one or two specific problems that you probably won't get by reading the book but were went through in the lecture. Generally the exams are a little harder comparing to the materials she covers in lectures.
Professor Castella has a very heavy accent, so most of the time I have no idea what he is saying (but since the things he write on board make sense, it's fine). Most of the examples he use in class comes from the textbook, so if you don't understand just go read the book. His homework questions are a little bit more challenging than the textbook questions, but those questions really do increase your understanding of the concepts. I had Brown for Math 31A and I got a B because Brown is very conceptual (his tests are very challenging for me, and they look nothing like the textbook questions), however professor Castella's tests are very fair, there are no surprises and he doesn't really try to trick you. I got A on both midterms (the class average for both is around 90).
Actually I took his 31B Scary grading system but a nice guy. Professor De Sapio is definitely not bad as a lecturer. Make sure you go to his classes and take good notes. Do previews and try to catch the thing he is talking about. He usually says the name of a theory once and then rushes to the proof. If you don' t get the topic, you are probably done with the lecture of the day. Also ask him questions. Though he might trick you, he will give a fair explanation. 40 years experience guarantees his knowledge. Unfortunately he never uses technology. Even for subjects like math technologies are not that important, you will still encounter troubles handwritten tests and syllabus, and no email response. Midterm is easy(100points). 50 out of 240 got above 90. But the final worth 200 is hard. The first three questions( out of 4), as he claimed, were written by TAs and they were doable. But the last one is kind of crazy except extensive review for a small topic. He tested Taylor polynomials, Taylor series expansion, and radius of convergence FOR ARCTANGENT for the last 2 questions. Take him if you are confident to be the top 10% of the class, and the median is C
while kucherkenko is a good lecturer and knows what she is talking about, the problems on the midterms/final were nothing like the homework problems. I practiced even the hardest problems that the book offered and still was totally lost on the exams. this is a good class if you plan on going further in math, but if not, i would take a professor that is more straightforward in their testing.
I had Sargsyan for two quarters, both Math 31A and 31B. I didn't particularly think that his class was hard per say, but it was annoying to have to memorize all of the proofs, which is the easiest way to get an A in his class. Out of the Math professors I've had at UCLA, he was actually one of the better ones. The reason being that during lecture, if you did manage to muster up the courage to ask a question, he did try to explain his answer so that you would get it. And if he found that the class was struggling on a particular topic, he went over it again, which is more than I can say for the other math professors I've had. He does have an accent, but its not terrible. Like the other reviewers said, he is obviously a really smart guy, he's just not the best professor. The best thing to do if you have him is to go to his office hours and ask him to do any of the problems on the homeworks (especially the further insights) questions that you might not have gotten. Those further insight questions usually pop up on his midterms and finals. Even if you don't actually get how to do the problem, just memorize it -- thats the easiest way to get an A. That's why I didn't really understand why people often failed his midterms and finals -- usually the problems were ones that you did before on your homework. He's definitely an interesting character -- but he's not a total douche. He actually tries to interact with the class (he makes weird jokes and then he asks the everyone why they aren't laughing) and he seems care at least somewhat cares about teaching, which, once again, is more than I can say for other professors. The bottom line is that if there is an easy professor (ie Brown) then don't take him, but if the other professor doesn't have great reviews then take Sargsyan, he's not a terrible choice. No one actually failed his class in the end (although I think he did give out Ds).