This was an amazing class where I learned a lot but also extremely challenging. We used the textbook Calculus and Analysis in Euclidean Space by Sherman, and as the title implies, this class felt like MATH 131 taught in a way that simultaneously teaches MATH 32A. Homework is light, only about 3-6 problems per week, but sometimes the problems are challenging and you might have to spend a long time thinking about them. Tests are fair and are mostly textbook-based. If you do most of the textbook problems and study, you'll be fine. The instructor's teaching is very clear and follows the textbook, but gives more insight into the intuitions.

MATH 32AH was my first introduction to a proof-based course in mathematics, making it tougher than expected. Many of the material covered in this course is the exact same from the textbook, Calculus and Analysis in Euclidean Space by Shurman. Most of the material taught was essentially basic analysis, topology, and linear algebra to supplement and create a foundation for the important calculus-based theorems in the class such as the inverse function theorem, implicit function theorem, and Lagrange multipliers.

The class is taught at a quick pace, so it was easy to get behind if you didn't keep up with the lectures, notes, and homework. Professor Kwon was quite helpful although some of the lectures tended to be a bit rushed and unclear as he assumed we knew what he was talking about. Nonetheless, I would take this class again.

His lectures are very clear and he rigorously proved nearly everything we learnt, also occassionally giving insights to different concepts. He is definitely making the class much more enriching than the standard 32A.
There are very little homework, but each of them would require a real understanding of the concepts. The tests would require you to prove a number of things, which are a bit challenging but really fun.