When I study a new topic, I never feel satisfied until I have spent some time solving a long list of problems.
I am looking for either a problem book or a list of problems on graduate math topics. While there is an abundance of problem books on undergraduate math topics (such as various websites on quals or books like Berkeley Problems in Mathematics), there seems to be fewer books at the graduate level with a lot of problems. There are books like Evan's PDE book or do Carmo's Riemannian Geometry book which has a good number of problems, but again, I feel like they are in the minority.
The closest thing to what I am looking for is the Cambridge Tripos III.
To clarify, the following is what I am looking for:
- A book with ≥ 10 problems for a particular topic.
- By "graduate topic," I mean anything that requires standard undergraduate curriculum (single/multivariate calculus, basic/Fourier analysis, ODEs, linear/basic algebra, point set topology, basic manifold theory, curves and surfaces, say) as a prerequisite. I am particularly interested in problem books for "advanced topics" whose prerequisites are standard graduate topics (algebraic/differential topology/geometry, measure theory, real/complex analysis, commutative algebra, representation theory, say).