I am taking modern algebra and I'm not having an easy time. The problem, I think, is the symbolic manipulations. I like discrete/graph theory/algorithms/computing type math because the arguments tend to be high level, conceptual, and mostly in English. However, when a proof depends on a bunch of symbolic twiddling, I can verify every step and finish reading it with zero understanding. It doesn't sink in. Maybe it is a problem of visualizing; I can think, OK, a coset, but I don't have a clear way of thinking about a coset other than a couple of symbols on paper. The only actual mental image I have for it is the same mental image I have for partitions, which leaves out a lot of information. How do you think about proofs that depend on symbolic manipulation? Should I just start memorizing? I can work my way through most of the homework problems, but it takes me a lot of time and even though they seemed challenging and interesting, I forget a great deal of them later-unlike graph theory homework, roughly equally challenging, where I remember just about everything. In the lectures particularly, I am usually a minute or two behind the professor and absorb little.