Polynomials [Paperback]

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

This comprehensive book covers both long-standing results in the theory of polynomials and recent developments. After initial chapters on the location and separation of roots and on irreducibility criteria, the book covers more specialized polynomials.

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 Hilberts 17^th 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)