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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.

Surya
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  • 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) – Prahlad Vaidyanathan Nov 18 '13 at 14:11
  • @PrahladVaidyanathan I've edited the question. I am looking to refresh my pre calc algebra knowledge. – Surya Nov 18 '13 at 14:17
  • 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: http://math.stackexchange.com/questions/23740/good-book-for-high-school-algebra – Nate C-K Jun 04 '15 at 22:47

2 Answers2

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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.

Prahlad Vaidyanathan
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Along with the references provided by @Prahlad Vaidyanathan, you may also follow the following reference:

$1.~~$ Fundamentals of Abstract Algebra by D. S. Malik, John N. Mordeson, M. K. Sen
$~~~~~~~~~~~~~~~~$On this book, each chapter consists of definitions, theorems, proofs, and corollaries. There are also numerous examples that help illustrate the concepts. A unique feature of this text is the worked-out exercises that appear after every section. These worked-out exercises provide techniques of problem solving for students. Sprinkled throughout the text are comments dealing with the historical development of abstract algebra as well as profiles of notable mathematicians. Special topics, such as algebraic varieties, matrix rings, and Noetherian and Artinian rings, are also included for those instructors who want additional material.

$2.~~$ Topics in Abstract Algebra by M. K. Sen, S. Ghosh, P. Mukhopadhyay, S. K. Maity

$~~~~~~~~~~~~$This book gives a very good knowledge and problem solving ability in every aspects of Abstract Algebra, starting from Set Theory , and to every direction of Abstract Algebra like Group Theory, Subgroups, Ring, Fields etc. etc. With this book you can increase your ability to visualize what Abstract Algebra is, a person can think about the subject, can get new ideas in his/her mind.

nmasanta
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