A good professor who explained things carefully. He always emphasized the intuition before writing down the proof. He always posted his handwritten lecture notes, which were legible and easy to follow. The homework questions were taken out of the Rudin book, so though they were on the harder side, you can practically find answers all over the internet (still, definitely recommend doing the questions yourself and use the online answers to check your work; otherwise exams can feel impossible). Exams were overall on the easier side (easier than homework) and it was not impossible to get a perfect score. I did not take any proof-based math classes before but the class did not feel that hard. Now, a couple of things he could've done better. He did not use Piazza; he did not post HW solutions; he did not give any practice exams (exam solutions were given though). He always said that the best way to prepare for exams was just to understand the theorems and the propositions etc. really well, but not knowing what the problems would be like can be a bit stressful. Overall, for a harder math class like this, he's a good professor to have.
He's a nice guy, but a very slow teacher and doesn't cover much material quickly and crams the rest in at the end of the semester. Not good for learning when you have 1.5 weeks to learn measure theory in Modern Analysis 2. His first exam had a mean of 75%, 2nd exam a mean of 50%, and the final's mean was 90% for some reason. I failed the first midterm, did well on the last two exams, and still got a B so he's not out to destroy your GPA. If I hadn't failed that 1st exam I'd probably have gotten a B+ or an A-, if that's the information you want. I didn't find his lectures very enlightening or helpful since he spends most of the time drawing pictures and handwaving the math, so you need to learn the material on your own. His office hours weren't very helpful for learning. When I'd ask why he took off 8/10 points in a proof he'd tell me "your logic was there and it's the right idea but your answer was messy." When you ask some professors how to improve, they'll provide techniques or ways of thinking for attacking problems, or tell you when you were doing something wrong. Hui Yu would never elaborate beyond "see when Theorems break as you get rid of assumptions" or refer to his solution when I asked, so I had to find ways to improve my proof-writing on my own. It's still shoddy, honestly. One time I wrote a "less than or equal to" inequality instead of a strict inequality and he took off 19/20 points for the problem. I asked him why after seeing the solution which was almost identical to my solution, and he said "the rest was correct but the inequality was wrong." I imagine if you're a perfect student or a good student he's a generous grader, but if you're just an average student like me prepare to have a hard time academically even if you love the material. He's much nicer than some of the other professors here.
Dr. Yu is a very solid professor. Analysis is inevitably a hard subject and I think that Dr. Yu makes it as painless as possible. He's a decent lecturer.His lectures are generally regurgitation of the textbook's proofs (baby Rudin) with some pretty helpful commentary and details sprinkled in. Even though he stays very close to the textbook, I would still recommend going to class. Dr.Yu provides the motivation and bigger picture that is notoriously absent in Rudin. One downside (or upside) is that Dr. Yu moves very slowly and he doesn't cover a good chunk of the material in both Analysis I and II. He's also an incredibly nice guy and really helpful during office hours. In terms of exams and grades, he's extremely generous. The tests are very fair. It should be possible to get above a 90+ on each of them without being a math genius if you understand the material. That being said, it is very hard to understand the material, so the averages are probably going to be in the 60-75 range. There are always a few extremely easy questions that are practically reproving a theorem in the book, and then a few trickier ones that require some thought but aren't crazy hard. The curve is very nice and he factors in how much effort you show in the class. For Analysis I, if you go to class, put in the effort, go to office hours, and do around average on the tests you'll get an A minus. In analysis II the class shrunk to around 12 people and I suspect he gave everybody an A/A-. Now a few random notes about Dr.Yu that you should note. First is that the homeworks are completely unrelated to the tests. Dr. Yu pretty much assigns problems from Rudin at random so the homeworks might take anywhere from 10 minutes to 15 hours. Of course you can always look up the solutions online. Second is that Dr. Yu grades tests exceptionally fast. The Analysis II final ended at 4:00, he had them up by 4:58. The downside of this is that he grades so fast that he doesn't read your proofs carefully and your grade is practically a random variable. that being said he's very generous with partial credit. So if you write something half coherent he'll give you half credit on a problem. So no matter how clueless you are on a proof write something and throw some epsilons and deltas in there for good measure. Overall, Dr. Yu is a great professor to have for Analysis. You'll learn alot and your grade won't suffer.