I am currently self-studying mathematics.
I have background readings of Stephen Abbott – Understanding analysis, a fair understanding on set-theory through online read-abouts, and E.A. Maxwell Advanced Algebra I & II. Along with a first semester course in Calculus.
I want to proceed with abstract Algebra, because I enjoy abstract thinking, and understanding how abstract thinking is possible, along with, formulating truths.
Having begun with Basic Algebra I by Jacobson, as it's most recommended by many on the web. I know i will find the content fairly difficult to grasp, but with time and maturity, I will understand the ideas. However, I wish to have supplementary notes (if available) to complement my reading and practice of the book.
Hence, I ask if anyone has open-sourced notes on this particular book?
Best Answer
To answer your question, I doubt there are notes specifically written for Jacobson's book.
If you want lecture notes to serve as parallel reading for parts of Jacobson, I might suggest the ones James Milne has published on his website, particularly on group theory, commutative algebra and field theory. There's more material in them about effective computations (including by computer).
If you want a book on algebra that has accompanying notes, George Bergman wrote A Companion to Lang's Algebra. It's available here.
Contrary to some of the comments, I don't think it's crazy to attempt Jacobson, especially given you've read the second volume of Maxwell. That being said, you need to be aware that Jacobson is at a higher level of difficulty than most books that cover similar material. Also, Jacobson probably implicitly assumes that the reader has seen more linear algebra than your background would indicate, so overall you may find that the problems are hard for you whenever there is some linear algebra involved. You may know most of the facts you need but not have used them in hard enough problems. I don't want to make it sound like this is an absolute prerequisite, but you can get up to speed quickly by reading a book like Halmos's concise Finite-Dimensional Vector Spaces.
If you find you need to take a step down in difficulty from Jacobson, a good book that also treats linear algebra from scratch and is still at a higher level than most undergraduate books is Algebra by Godement. (I would recommend skipping the chapter on logic, however.) On the whole, I'd say the problems in Godement are harder than in Artin or Dummit and Foote, but the subject isn't taken as far. Jacobson would make a good follow-on from Godement.