Winter 2023 - This review is for 23W 131AH. Biskup's lectures are extremely organized and clearly explain the motivations. He is patient in explaining proof details during lectures and offers an insane amount of office hours. Biskup is a very knowledgeable and interesting person, so you would enjoy his office hour even if you don't have questions prepared beforehand. Additionally, the exams are similar to the homework (even easier), and Biskup's grading is more than very lenient, so the workload will not be too bad compared to other 131AH classes. My only possible complaint about this class is that we spent weeks on the fundamentals, including building the natural and then building the reals, and the pace was probably a bit slow. However, this class is still amazing and provides an excellent, comprehensive foundation for further real analysis. Don't forget to take the BH because the AH doesn't cover much real analysis.
Prof. Brown was one of the best professors I ever had at UCLA. His lectures were crystal clear and explains in details of proofs. Math 131A was almost all about writing rigorous proofs, so he really helps students. Two midterms and a final, no alternating grading schemes like some other professors. Got an A- from him, which, in my opinion, was fair b/c I screwed up 2nd midterm in a very bad way. Recommended for serious learners. If you want easy A, just stay away.
Fall 2020 - Prof. Cameron was decent. Math 131A is known to be one of the toughest math classes, so much of my difficulty was with the topics rather than him as a professor. He is kind, fair in his exams, and really does try his best to be helpful in his lectures, although I always felt a bit confused. He definitely knows his stuff, just has a hard time conveying that knowledge in a way that students can understand. Reading the textbook was helpful to supplement his lectures. I think taking the class online is what saved my grade, so I can’t say what he's like in person. Would I recommend him for 131A? No. However, it won’t be the end of the world. Be prepared to put in the work on your end. Assignments consisted of doable but challenging weekly HW, 2 midterms, and a final exam; as most math class are.
Spring 2020 - I took this class (online) spring 2020. Chernikov is a good lecturer, but not an exceptional one, but IMO the way he sets up his class makes it the best class I have taken so far in this online environment. Firstly, he published all his lectures on youtube (https://www.youtube.com/user/archernikov) beforehand, and then during scheduled lecture hours, he just went over HW problems. Also, he types up all his notes on Latex, and they are really neat, so it's not really needed to even watch the youtube lectures, instead it's possible to just glean enough information from the notes he publishes. However, the lecturers/notes are not very helpful when compared to the homework he gives. He gives 8 homework questions a week, and they are incredibly difficult. Even with online resources and friends, the averages on these homeworks consistently ranged around the 70/80% range (the TA grading was also exceptionally difficult). The saving grace is that Chernikov gives hints on the homework in his scheduled lecture hours (which are just extra OHs), and then he records/posts the videos on CCLE. Most of my friends in this class stopped even trying to do the homework before thursday or friday, since without Chernikov going over the HW problems, they are basically impossible. The textbook is freely available online, but it's not that helpful. Online resources are often more helpful. He takes a lot of HW questions from Rudin Real Analysis, so if you get an answer key for that, it's quite helpful. Exams are easier than HW, but not much easier. Each took me about 6-8 hours to complete (but I was being really careful to complete everything correctly due to the harsh grading by the TA). If I took the tests in person, I would probably get around 15% on the midterms and final. They were that hard! As much as I complained about this class, however, I learned a lot. Chernikov's homeworks are pretty different than his lectures, so it's not necessary to go to lecture, but instead forces you to actually understand the content by doing the homework (learn by doing philosophy). I would say the homework was too hard if he didn't give hints, but with hints, the homeworks were definitely reasonable. I also enjoyed how the homeworks often referenced old material; for example, for homework 6, you would have to refer to week 5, 4, 2, and 1 notes. Ultimately, this class is fairly difficult, but Chernikov is an excellent professor to take it with. He really cares about his students, but also makes sure that you actually learn something in the class. Also, I think Chernikov has adapted best to the online format at UCLA due to COVID-19. So if Chernikov is teaching a class online, I highly recommend you take the class with him!