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Excellent professor, very open to questions and concerns and cares a lot about student learning. I recommend going to office hours because he really goes out of his way to answer student questions.
Also, I thought his lectures were organized and easy to follow.
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.