After about six months of study (over the course of about 16 months total) I’m coming to the end of Ch. 3 (on modules) in Lang’s Algebra (third edition) and I don’t know if it’s the high I’m feeling now that I actually feel pretty comfortable with the content, and am making connections between different parts of the book, and am actually understanding what he’s writing and why it’s significant (generally feeling that I’ve mathematically matured a lot in the 150ish pages it’s taken me to get this far) but I’m a bit jittery for higher peaks, and I’m curious to know what advantages or disadvantages there might be in going on to any one of the following at the end of the chapter:
Going on to Ch. 4 in Lang, on polynomials, and then on to Galois Theory
Going to part 3 in Lang, on Representation Theory
Complex Made Simple
Galois Groups and Fundamental Groups
Topology: A Categorical Approach
Topology and Groupoids
Gunning's books on Holomorphic Functions
Something more on Ring Theory or Module Theory
Aside from the first three chapters of Lang, I studied Spivak’s Calculus up to the part on infinite series, and Lang’s Linear Algebra. I don’t have any particularly great mathematical interest right now that might make me choose one over the other, but I’ve vicariously felt the allure of Galois Theory for some time (actually the reason I began Lang), but I’d say right now, I know equally little (and am just as interested to learn) about all topics listed above. Any other suggestions are welcome of course.
