MATH 4310

This is easily one of the hardest classes that I have taken in the mathematics department, but it is also easily one of the best classes that I have taken in the department. I came in feeling somewhat uninspired by real analysis (based on my experience in MATH 3310), but I came out with a strong interest in analysis as a field. I took the graduate real and complex analysis courses (MATH 7310 and MATH 7340) over my next two semesters as a result, and I thoroughly enjoyed the experience. They were all extremely challenging, but I believe they were worth all of the effort I put into them.

There are two main reasons that this class is so difficult. For one, real analysis (particularly a la Baby Rudin, which is much like this course) is notoriously difficult. Second, professor Humphries does not baby his students. He does an excellent job lecturing, he is very friendly and willing to help, and he provides beautifully thorough LaTeX notes, but he covers a ton of material in rigorous detail and assigns very challenging problem sets and exams.

When I took the course, we covered metric space topology, including compactness, completeness, and connectedness; normed and inner product spaces; continuity and uniform continuity; convergence and uniform convergence of sequences of functions; the Arzela-Ascoli and Stone-Weierstrass theorems for metric spaces of functions; and the construction of Lebesgue measure and the Lebesgue integral on R, including the basic results of integration theory (up to Fubini's theorem). Every week, I would spend a couple of hours reading and taking notes on the material we covered in class and upwards of 12 hours completing the homework assignments, which were very fun but very challenging, even in a group setting (which I absolutely recommend for the sake of your sanity). Professor Humphries will assist you if you are struggling on the homework assignments, so definitely ask questions after class and in office hours---it is well worth the time. The exams were take-home, roughly week-long exams, and they were just as difficult as the homework assignments; that may sound frightening, but the class is heavily curved, so you have more leeway than you might expect. Still, don't underestimate the course.

Overall, while I highly recommend this class, I strongly suggest that you only take it if you have enough space in your schedule to expend a *lot* of time and effort doing analysis. You will absolutely learn a ton of fundamental mathematics, but it will not be easy.

I like Peter a lot as a person! Class is hard as fuc* tho. I did most of the homework with a work of 4 other students and managed to be in the 85s on the hws. The class is hard to follow but the has amazing, Latex written notes. Exams were take home but dont don't expect to get A's on them, they are tricky as hell. I would suggest to take it if you're prepared to expend 12+ hours doing the homeworks . Finding people to work with early in the semester would help you a ton. Luck!