Professor Zhao is a great professor and I'd highly recommend taking 131A with him if you get the chance. This is a very difficult class, but Professor Zhao taught it very effectively and was helpful outside of class as well. He's incredibly smart and his lectures can be very fast-paced, to the point where I stopped trying to keep up with his notes a couple of weeks in and just started taking photos of the board to copy down later so I could follow along better. That said, he is a very clear lecturer and at times is very funny too. He also makes sure to take time for questions if people are confused.

The topics in this class are largely the same as the topics in introductory pre-calc and calc classes: sequences, limits, derivatives, functions, integrals, and key theorems related to each topic. However, instead of simply giving you a definition and asking you to solve computational problems, this class focuses largely on the theory behind each definition and on learning rigorous proofs of all the theorems. On the exams, you are asked to give proofs of various statements using the theorems and definitions from class. This is what makes the class so challenging, especially if you have limited experience in math upper-divs, and the exam scores reflected that.

The average for the midterm was around 50%, and although he didn't release the average for the final, my guess is that it was similar. Both the midterm grade and the class grade as a whole was curved up heavily, so don't panic if you feel like you bombed a test (I barely answered 2 of the 5 questions on the midterm and got an A). The best thing you can do to prepare is go over all of the practice problems Professor Zhao recommends from the book and make sure you know the solutions thoroughly, because multiple questions on the exams were from the book. Aside from the exams, the homework was manageable enough and you should be able to get 100% on everything if you give a decent effort and turn it in on time.

Overall I ended up really enjoying this class because of the way it gets into the "why" of everything you've learned in calculus, and I feel like I walked away with a much deeper understanding of most of the math I'd learned up until this class. Professor Zhao was a big part of that and I'd certainly recommend him to anyone who needs to take this class, with the understanding that it will be challenging for most people.

I took Math 132 with Professor Zhao in Winter 2025. He spends lots of time going through proofs in lecture, and the homeworks are designed to be more proof-based based which goes very well with his teaching style. The midterm and final were very similar to the content we covered in class, and he gave plenty of time in class to review for each of the tests. Overall, would recommend this professor if you are interested in a more proof-based course.

The tests were quite difficult, but he gave a generous curve in the end. He went through proofs at a fairly good pace and took his time to prove some of the more difficult theorems in class, which was very useful for both the midterm and final. The homework was manageable and not too difficult.