2
$\begingroup$

I am looking for an elementary or Intermediate Algebra book which has proofs. I would like book to present proofs for statements like

If $P(x)$ is a polynomial of degree n then will have exactly n zeroes, some of which may repeat. EDIT: This should be 'at most n zeros'

I have looked at couple of books so far I couldnt find one which has proofs.

Basically, I am looking for a book in definition-> theorem -> proof -> example format.

EDIT: I am at undergraduate level. EDIT: I am looking for a book at this level http://www.amazon.com/Intermediate-Algebra-Connecting-Concepts-Applications/dp/0534496369/ref=sr_1_29?ie=UTF8&qid=1384785496&sr=8-29&keywords=intermediate+algebra But books like these seem to skip proofs.

$\endgroup$
  • $\begingroup$ There are literally a thousand such algebra books. You have to tell us a little more about what level you are at: under-graduate/graduate/etc. (And btw, the statement you mention is true only over $\mathbb{C}$ - or an algebraically closed field - not in general) $\endgroup$ – Prahlad Vaidyanathan Nov 18 '13 at 14:11
  • $\begingroup$ @PrahladVaidyanathan I've edited the question. I am looking to refresh my pre calc algebra knowledge. $\endgroup$ – Surya Nov 18 '13 at 14:17
  • $\begingroup$ The problem is that the Fundamental Theorem of Algebra doesn't have a proof that relies only on the theory that you covered at that level. If you really want a rigorous version of algebra, I think you might as well just move on to abstract algebra. If what you really want is to refresh your pre-calc knowledge, see this question: math.stackexchange.com/questions/23740/… $\endgroup$ – Nate C-K Jun 4 '15 at 22:47
0
$\begingroup$

The following are good books, IMHO, for what you are looking for (I think) :

  1. Herstein's Topics in Algebra or Abstract Algebra

  2. Michael Artin's Algebra

  3. Joseph Gallian's Contemporary Abstract Algebra

Each of them has pluses and minuses, so have a look at all of them before picking one.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.