I am a college sophomore in the US with a major in mathematics and am an aspiring mathematician in the fields of computational complexity theory and cryptography. I would like to seek your advice and recommendations on comprehensive, insightful, and challenging books for abstract algebra and abstract linear algebra. I had looked through some books and pulled out some possible candidates:
- Linear Algebra: Friedberg/Insel/Spence, Hoffman/Kunze, and Axler
- Abstract Algebra: Herstein (Topics in Algebra), Artin, Dummit/Foote, and MacLane/Birkhoff (Algebra)
This will be my first introduction to abstract algebra and linear algebra. I would like to start with challenging, detailed books as I think my mathematical maturity and knowledge will grow much better than with easy, toned-down books.
As for my background, I studied single-variable calculus using Serge Lang (A First Course in Calculus) and acquired proof-writing skill using the proof-teaching book Chartrand's Mathematical Proofs.
I apologize for any grammatical errors, and look forward to your advice and recommendations!