Master Basic Algebra with Knapp's Comprehensive Textbook

[PieceOfPi]

Hi,

I wonder if I'm posting my question at a right place, but does anybody know if this is a good textbook for abstract algebra, especially for someone who's taking a "serious" math course for the first time?

BASIC ALGEBRA by Anthony W. Knapp
https://www.amazon.com/dp/0817632484/?tag=pfamazon01-20

The author has some sample pages on his website as well:
http://www.math.sunysb.edu/~aknapp/books/b-alg.html

Thanks

 

[morphism]

Can you find a copy at the library to try it out and see if you enjoy it?

 

[Hippo]

I have both the Basic and Advanced Algebra by Knaap. Is it any good? I dunno, I'm not a fan of Math so I can't really judge on it.

 

[qspeechc]

I looked at the preview of chapter 2, and if this is your first "serious" maths course, then it looks quite advanced to me, but wait for other opinions.

 

[PieceOfPi]

Can you find a copy at the library to try it out and see if you enjoy it?

It seems like a copy is not available for now (don't ask me why... it's supposed to be the textbook for the abstract algebra class this year). But one thing I can do is to buy this book at the campus book store, and if I didn't like it, I can return it while the return policy still works.

I looked at the preview of chapter 2, and if this is your first "serious" maths course, then it looks quite advanced to me, but wait for other opinions.

I think I should have clarified what I meant by a "serious" math course (although I think you got it right). I've already taken linear algebra, multivariable calculus, ODE, and some proof-oriented courses like number theory and elementary analysis. I haven't, however, taken any advanced undergraduate math courses such as abstract algebra, real analysis, and topology. So I was wondering if taking the abstract algebra course with that particular textbook would be appropriate for me. I think I have an enough preparation, though, but I would never know until I take the course.

 

[e8050991e]

Hi PieceOfPi,

Knapp's algebra course is very cleverly arranged.
It starts with basic number theory (unique prime
factorization, chinese remainder theorem etc. ),
some basics on systems of linear equations and
permutations.
Then comes linear algebra. I think it is a good start to repeat
some well known stuff from a more abstract point of view.

As a rule Knapp proceeds from the concrete to the more
abstract which is seldom in a book on this topic.

Knapp sometimes shows how you can improve on
a proof-idea which actually does not work for some reason.
For example in his chapter on Abelian groups he points out the
analogies to vector spaces. The categorization of finetely generated
Abelian groups starts with a proof-idea inspired by Gaussian elimination.
This try fails, because finitely generated groups can only almost
be viewed as vector spaces. Then he shows how to save this approach by
modifying the elimination process.

Knapp gives many examples and motivates the theory well. His proofs
are beautiful and not based on tricks, which leave you wondering
how someone can have such clever ideas.

You are certainly well prepared to work through Knapp's course.
I like this book and recommend it.