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.

  • $\begingroup$ 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

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.


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