Spring 2015 - Math 115A is the UCLA introductory course in proof-based mathematics. This class is a very well thought out introduction of a simple topic, with rigorous proofs of mathematical theorems. Professor Heilman is an organized and engaging teacher, as far as math professors go at UCLA. All of the lecture notes will be provided before the first day of class, so students can keep up with where lecture material is going. The homework is also posted well in advance of its due date. All lecture material is carefully explained and paced during the quarter. In office-hours, Professor Heilman is always willing to walk through class notes and homework problems. He'll even give advice outside of lecture material about further study in mathematics, such as graduate school and research opportunities. It's very clear that Professor Heilman is concerned with his student and a phenomenal teacher. I would highly recommend taking any upper division math class with him.
Spring 2016 - I took this class after already taking 115a with Heilman. The course by itself is amazing and I would recommend it to anyone who wants to learn about analyzing games and situations. Heilman is a very straightforward lecturer. He provides typed up LaTeX notes ahead of time which make it very easy to follow along and review something later if you're having trouble. He has a bit of a dry wit and will crack a small joke every once in a while but it's mostly just straight lecture. I think he explains everything very clearly and all of his proofs are very in depth. He makes sure that everyone is following along and will answer questions but there usually weren't any because he is so clear. The midterm had a very difficult question on it that no one got right so he went over it in class and gave the solution then asked it again on the final. Overall, I think Heilman is a great professor and would definitely recommend him for this class.
Winter 2016 - Professor Heilman is a very organized and engaging instructor. All lecture notes are posted online before the first day of class. All relevant topics are carefully discussed, and practice problems are well designed to help students master the material. Lecture notes and homework problems are very helpful when preparing for exams. In office hours, Professor Heilman is very willing to clarify concepts and answer questions regarding homework problems. Even though the exams are a little challenging, Professor Heilman will provide a very generous curve for the class. I would highly recommend taking any math class with him!