Professor Burke was pretty nervous the first two weeks of class, but he did get a lot better the following weeks. Sometimes he got nervous when students asked him questions in class, but he always did follow up with an email of the correct answer when he wasn't sure. He went too fast most of the time, so I didn't learn much from lecture. I just mostly showed up to see what was being taught so I could learn it on my own with patrickjmt videos on youtube. I did some of my learning from TA office hours and review sessions also. Burke did sincerely cared that students understood the concepts in class and he wanted to help also. I never went to his office hours because of schedule conflicts, but I heard he was more helpful there with a small group rather than a 200 people lecture hall. Quizzes were given in discussion, which were exactly the same as problems from the hw, but he gave out a lot of hw problems every day. I thought his midterms and final were pretty reasonable. The average was always around 65% for midterms and around 70% for the final. I would recommend this class with Burke to those who don't mind putting extra effort out to understand concepts taught but also want the benefit of taking reasonable tests.
Course: Math31B I personally find his class VERY stressful. He is a nice guy and I guess he can be helpful one-on-one during office hours, but during lecture I understand absolutely nothing. I basically depend on discussion and teaching myself everything from the book. Which would be okay if his tests weren't so tricky. Plus he's super nervous in front of a big class. And just makes everything more confusing and trickier than it needs to be. I wouldn't recommend him if you're the kind of student who needs things explained to you clearly and, like me, whose brain shuts down during a midterm when given super tricky questions and ends up doing poorly even after countless days of studying.
I haven't really been to the lectures, but I think what I disliked most of him is his curve. Unlike the previous math courses I've taken, Prof Burke's 33A does not give As to all in the top 25%. I lost 2points for the first midterm, ranked 6th in class for the second midterm, was in the top 25% for the final and yet I got a B+. Well I don't regret taking him since I had to choose between Dearricott and him. At least Burke's midterms and finals are reasonable and simple. The only issue in addition to the harsh curve is that he deducts tons of points for calculation mistakes even if the method is right. Anyway, just my two cents worth.
I took this class with him in Spring of 2013. He's a great guy and is really intelligent, but I did not like his class at all. The class material was already very difficult, especially for first timers in proofs, and this professor just rushed through the material day after day. I don't think I learnt anything from him. To be fair, I heard he was new to UCLA then, and I pretty much gave up on this class by Week 4, so it was a pretty horrible experience. Still, I never felt so lost and discouraged by a class before. I really wish I took this class with a more experienced professor.
I just took professor Burke's Math 115A and absolutely loved it. He very much cares about the learning of his students and is willing to take the time and consideration to help them learn the material. At times he assumes that a student may know a concept, but if you are willing visit his office hours (which were beyond helpful) or just raise your hand in class he will take the time to give more details until it is better understood. Being Dr. Burke is a new professor at UCLA there is no doubt he will continue improving ( after reading these comments here I can without a doubt say he has already taken leaps and bounds in improving his teaching style). If you are actually interested in learning mathematics and want a teacher that is willing to put the time into helping you develop your foundation, then you should really consider taking one of Dr. Burke's courses.