One of the best classes I've taken at Columbia and certainly one of the best Economics courses.
If you are interested in graduate school or advanced studies in economics, take this course. It requires some pure math, but at a very reasonable level- there are very few really challenging proofs in HW, nothing like you might have seen in Modern Analysis. The tests are manageable to easy (see below), the problem sets long but not too hard, and you can do them in pairs. The material itself is hard, butâ€¦
Susan Elmes' legendary teaching abilities are even more manifest in this course than in her better known intermediate micro course. She elucidates concepts and performs proofs in such a clear way that you will hardly ever be confused even by very complex material. She's also much more light hearted in the class, so it's a real treat to listen to lectures- I was often on just a couple of hours of sleep in class but never felt even the slightest bit tired or bored.
Note: I found recitations pretty useless, since you learn the math through lectures and especially PSets, but it might be different in a different year.
The material is extremely interesting, because it is an economics course from a pure math point of view- everything is proven, axioms are created and challenged, and the last chapter has mathematical axioms leading to conclusions about social welfare, like Arrow's impossibility theorem and axioms behind Utilitarianism and Rawlesian theory, which to me was really mind-blowing. However, you don't learn that much that is new per se, it's mostly the same material as intermediate micro, just with a completely different methodology (much like advanced metrics). So if you're looking for fascinating new ideas and new directions in economics you hadn't explored before, and aren't really interested in advanced methodologies and thinking- this might not be for you (especially if you're allergic to proofs and higher math).
But otherwise- you owe it to yourself to check this out. It's a sight to see, and legitimately fun and awesome.