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. 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. Many of the modern results have only been published in journals so far.

Covers its topic in greater depth than the typical standard books on polynomial algebra Includes supplementary material: sn.pub/extras

Autorentext

Victor Prasolov, born 1956, is a permanent teacher of mathematics at the Independent University of Moscow. He published two books with Springer, Polynomials and Algebraic Curves. Towards Moduli Spaces (jointly with M. E. Kazaryan and S. K. Lando) and eight books with AMS, including Problems and Theorems in Linear Algebra, Intuitive Topology, Knots, Links, Braids, and 3-Manifolds (jointly with A. B. Sossinsky), and Elliptic Functions and Elliptic Integrals (jointly with Yu. Solovyev).

Inhalt
Roots of Polynomials.- Irreducible Polynomials.- Polynomials of a Particular Form.- Certain Properties of Polynomials.- Galois Theory.- Ideals in Polynomial Rings.- Hilbert#x2019;s Seventeenth Problem.