Expect to work hard. Between week 1 and finals week, almost half the class had dropped. Attendance is not graded but is still critical to doing well in this class since the professor does not post any lecture notes or recordings. The four mandatory homework assignments are very challenging. They are graded on accuracy and can hurt your grade.

That being said, the midterm and final exams were both very fair (though far from easy), and I felt well-prepared for both. The provided practice exams were great indicators of what to expect on the actual exams. The TA's review sessions were also very helpful and insightful. As Gangbo himself said, the exams are specifically meant to NOT trick you and are merely meant to see how much you've been paying attention.

The lectures were information-dense, but Gangbo still left a lot of room for interactivity. He leveraged pictures and intuition when it mattered, and his examples often doubled as valuable lessons in proof-writing.

If you are fine with a challenge and want a taste of graduate-level material, I definitely recommend this class.

I did badly in this class, and that was not the professors fault. However, Gangbo's lectures were dry and at times confusing to follow. The exams were difficult, as to be expected in an honors class. The homework was exceedingly difficult at times and graded for accuracy, probably more than to be expected in an honors class. There were multiple occasions when I emailed him and never received a response back.

A tough class, but anyone looking to get real rigorous might enjoy it. Prof. Gangbo's lecturing style isn't the most animated, but he was always clear and his lectures are by far the most meticulous I've had at UCLA. I can't say to what extent this is simply due to the nature of the class vs Prof. Gangbo himself, but speaking as someone who had little exposure to either real analysis or proof-based mathematics (beyond Math 61), I learned a *lot* about both just from listening to Prof. Gangbo's proofs.

About the homework - four homework assignments, each ~12 questions (2/3 proof-based, 1/3 computational). We had 2 weeks for each assignment, but they are looong - as someone who is not the greatest at real analysis, a single assignment could easily take me 10+ hours to complete. The kicker is that of the 12 questions, the TA would pick 3 to grade for correctness. The questions aren't easy either; our averages were generally in the 70s/80s. That being said, if you take this class, you will 100% walk out of this class a better proof writer as a result.

Two tests - a midterm and a final. The midterm was a bit strange - there were 5 questions, but you only had to do four of them, but depending on your choice of questions your max score would be 80/100, but we didn't know this going into the exam (though everyone got a 5-point bump as partial compensation). The questions weren't easy per se, but the TA gave a fair amount of partial credit (median 64%, despite the capped score shenanigans). For the final, I believe the sentiment after the exam was that the final was fairly okay. Anyway, Prof. Gangbo graded it himself, and presumably did not agree; average 34%.

W.r.t. grading: I was essentially the class median (rank 9/22 on both the midterm & final; above the median on 3/4 homeworks) and received a B-.