Abstract Algebra: book rankings.

[Schild'sLadder]

Could someone try to rank 'Abstract Algebra' textbooks, either undergraduate, or graduate level: By how rigorous they are, how they transfer to applicable subjects, and how well they're laid out, in a pedagogical manner.

Any answers would be appreciated.

Thanks in advance!

SL!

 

[Jorriss]

This would only be reasonable if you listed a few Abstract Algebra books you are interested in first.

Further, what does 'how they transfer to applicable subjects' mean? How applicable it is to the grand structure of mathematics? Physics? Engineering? Chemistry?

 

[artfullounger]

I really liked Fraleigh's book, it had some nice discussions of applications in automata, and it finished with some stuff on Galois theory which was interesting (in the 6th edition). It's definitely pitched at the undergrad level (I was using it for my first year linear algebra and groups sequence in the UK) and it's not terribly difficult to get into for non-mathematicians as well.

I don't think it's the most rigorous book out there, but if you're not hugely comfortable with mathematical abstraction and proof it's a good way to ease into the subject. I was mainly reading it to reinforce lectures and to look up important results I needed for proofs though, so I didn't do many of the questions.

 

[Improvisation]

Contemporary Abstract Algebra by Gallian is a good start.

 

[homerT]

Artin's first edition is spectacular, and most of the book is covered by these two video courses:

http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

http://www.math.upenn.edu/~ted/371S11/hw-371SchedTab.html