I am looking to go back and revise material that I have already learnt before. I'm, in particular, looking for suggestions for textbooks on the following subjects:
- Algebra: I self-studied abstract algebra last year out of Dummit and Foote's textbook. It was tough going to say the least, and it took me some time to cover the material from the first 10-12 or so chapters, excluding some specialized topics (p-groups etc.) or topics that were too advanced for me to fully comprehend back then (the proof of the fundamental theorem of Galois Theory etc.). So I am looking for a an algebra book to study that I can use to build on my knowledge gained from D&F, revise the previously learnt material, and learn new material. I don't think I'm ready to tackle Lang etc. at the moment.
- Calculus: I will most likely take Math GRE subject test later in the year, and I'm looking to dig into a good calculus textbook that covers all the material in a comprehensive manner. The presentation doesn't have to be completely rigorous, but complete. I can always practice additional questions out of a cookbook style book. Also, it'd be great if the book covers such topics as the beta function, gamma function, advanced integration techniques etc. as I'm very rusty on them. The only suggestion that comes to my mind is Apostol's Calculus: Volume I.
- "Methods:" I've never quite studied "mathematical methods" in detail. Bessel functions, Legendre Transform, Strum-Liouville problems, Laplace transform etc. I always avoided going over mathematical methods for physics/engineers textbook, as they presented the material in a purely cookbook style. So, I'm looking for suggestions for well-motivated textbooks on such topics. They don't have to be rigorous and contain only proofs, but they should be motivate the material and provide the relevant context. Or else, what's the point of going over scores of math books?