Nathan Jacobson's books "Basic Algebra I, II" and "Lectures in Abstract Algebra – Volumes I, II, III (GTM 30, 31, 32)". What are the differences between these two books?
1) The subject.
The material of the two books overlap, which one is better?
2) Does "Lectures in Abstract Algebra" aim to undergraduate?
3) "Basic Algebra I, II" Cannot edit a word! Really?
4) Is it necessary to read the two books?
Thanks a lot!
Best Answer
The Basic texts are much more modern in content and organization than the Lectures. The Lectures are based on Jacobson's graduate lectures on algebra at John Hopkins and Yale in the 1940's and early 1950's-consequently, the style is far more classical and categorical/homological methods are nearly completely missing. Basic also covers quite a bit more than the Lectures. That being said, the Lectures are very careful and comprehensive and it's interesting to compare the 2 via the state of the field in the different time frames if you can get a copy relatively cheap.