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Algorithms and Computation in Mathematics #11: Polynomials

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Algorithms and Computation in Mathematics #11: Polynomials Cover

 

Synopses & Reviews

Publisher Comments:

This comprehensive book covers both long-standing results in the theory of polynomials and recent developments which have until now only been available in the research literature. After initial chapters on the location and separation of roots and on irreducibility criteria, the book covers more specialized polynomials, including those which are symmetric, integer-value or cyclotomic, and those of Chebyshev and Bernoulli. There follow chapters on Galois theory and ideals in polynomial rings. Finally there is a detailed discussion of Hilbert's 17th problem on the representation of non-negative polynomials as sums of squares of rational functions and generalizations. From the reviews: "... Despite the appearance of this book in a series titled Algorithms and Computation of Mathematics, computation occupies only a small part of the monograph. It is best described as a useful reference for one's personal collection and a text for a full-year course given to graduate or even senior undergraduate students. [.....] the book under review is worth purchasing for the library and possibly even for one's own collection. The author's interest in the history and development of this area is evident, and we have pleasant glimpses of progress over the last three centuries. He exercises nice judgment in selection of arguments, with respect to both representativeness of approaches and elegance, so that the reader gains a synopsis of and guide to the literature, in which more detail can be found. ..." E. Barbeau, SIAM Review 47, No. 3, 2005 "... the volume is packed with results and proofs that are well organised thematically into chapters and sections. What is unusual is to have a text that embraces and intermingles both analytic and algebraic aspects of the theory. Although the subject is about such basic objects, many tough results of considerable generality are incorporated and it is striking that refinements, both in theorems and proofs continued throughout the latter part of the Twentieth Century. [...] There is a plentiful of problems, some of which might be challenging even for polynomial people; solutions to selected problems are also included." S.D.Cohen, MathSciNet, MR 2082772, 2005 "Problems concerning polynomials have impulsed resp. accompanied the development of algebra from its very beginning until today and over the centuries a lot of mathematical gems have been brought to light. This book presents a few of them, some being classical, but partly probably unknown even to experts, some being quite recently discovered. [...] Many historical comments and a clear style make the book very readable, so it can be recommended warmly to non-experts already at an undergraduate level and, because of its contents, to experts as well." G.Kowol, Monatshefte für Mathematik 146, Issue 4, 2005

Synopsis:

Covers its topic in greater depth than the typical standard books on polynomial algebra

Synopsis:

The theory of polynomials constitutes an essential part of university of algebra and calculus. Nevertheless, there are very few books entirely devoted to this theory. This book provides an exposition of the main results in the theory of polynomials, both classical and modern. Many of the modern results have only been published in journals so far. Considerable attention is given to Hilbert's 17th problem on the representation of non-negative polynomials by the sums of squares of rational functions and its generalizations. Galois theory is discussed primarily from the point of view of the theory of polynomials, not from that of the general theory of fields and their extensions.

Table of Contents

Foreword.- Roots of Polynomials.- Irreducible Polynomials.- Polynomials of a Particular Form.- Certain Properties of Polynomials.- Galois Theory.- Ideals in Polynomial Rings.- Hilbert's Seventeenth Problem.- Appendix.- Bibliography.

Product Details

ISBN:
9783540407140
Translator:
Leites, D.
Publisher:
Springer
Translator:
Leites, D.
Author:
Leites, Dimitry
Author:
Prasalov, Victor V.
Author:
Prasolov, Victor V.
Author:
Leites, D.
Subject:
Algebra - General
Subject:
Galois theory
Subject:
Irreducible polynomials
Subject:
Hilberts seventeenth problem
Subject:
Grbner bases
Subject:
Algebra
Subject:
Mathematics - Algebra
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Algorithms and Computation in Mathematics
Series Volume:
11
Publication Date:
January 2004
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
316
Dimensions:
235 x 155 mm 580 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » General

Algorithms and Computation in Mathematics #11: Polynomials New Hardcover
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$99.25 In Stock
Product details 316 pages Springer Berlin Heidelberg - English 9783540407140 Reviews:
"Synopsis" by , Covers its topic in greater depth than the typical standard books on polynomial algebra
"Synopsis" by , The theory of polynomials constitutes an essential part of university of algebra and calculus. Nevertheless, there are very few books entirely devoted to this theory. This book provides an exposition of the main results in the theory of polynomials, both classical and modern. Many of the modern results have only been published in journals so far. Considerable attention is given to Hilbert's 17th problem on the representation of non-negative polynomials by the sums of squares of rational functions and its generalizations. Galois theory is discussed primarily from the point of view of the theory of polynomials, not from that of the general theory of fields and their extensions.
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