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Hi,have you a good reference (books) for the study of polynomials with one variable or many variables ? Thanks for your help.

Don't hesitate to correct my English.

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I think you should try to be more specific... Why are you interested in polynomials? Or if you have no reason other than pure curiosity, it would still be very helpful to say that. – Kevin Lin Mar 12 2010 at 3:28

An idiosyncratic but very interesting book is Schinzel's "Topics on Polynomials" (not 100% sure that's the exact title, book is at my office).

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"Selected topics on polynomials", MR0649775 (84k:12010) ams.org/mathscinet-getitem?mr=649775 – lhf Mar 12 2010 at 2:39

McKee and Smyth, eds., Number Theory and Polynomials, being the proceedings of a workshop held at Bristol University, 3-7 April 2006.

Langevin and Waldschmidt, eds., Cinquante Ans de Polynomes - Fifty Years of Polynomials, proceedings of a conference held in Paris, 26-27 May 1988,

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For those with an inclination towards number theory, "Squares" by Rajwade might be interesting.

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J. V. Uspensky, Theory of Equations

It is actually the theory of polynomial equations...

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Serge Lang once gave me a nice little booklet with a red cover. The title was something like "Polynomials: A beautiful high school topic". I remember it had some stuff about the abc conjecture. I can't seem to find my copy right now, though. I can't find it online, either.

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 Perhaps it mutated into "Math Talks for Undergraduates"? – Franz Lemmermeyer Mar 11 2010 at 21:24

There is Polynomials by E.Barbeau contains all the basics, and has a lot of exercises too.

On a similar spirit is Polynomials by V.V. Prasolov.

I've found the treatment in both these books very nice, with lots of examples/applications and history of the results.

Oh, and in case you are interested in orthogonal polynomials, I believe the standard reference is SzegĂ¶'s book.

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