Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra (Springer Monographs in Mathematics) - Hardcover

Prestel, Alexander; Delzell, Charles

Hardcover

ISBN 10: 3540412158 ISBN 13: 9783540412151

Publisher: Springer, 2001

Synopsis

Positivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of R^n which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations of such polynomials. It takes as starting point Hilbert's 17th Problem from 1900 and explains how E. Artin's solution of that problem eventually led to the development of real algebra towards the end of the 20th century. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed. Thus the monograph can also serve as the basis for a 2-semester course in real algebra.

About this title

Product Description

Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.

Review

From the reviews of the first edition:

"This is a nicely written introduction to ‘reality’ and ‘positivity’ in rings, and besides students and researchers it can also be interesting for anyone who would like to learn more on positivity and orderings." (Vilmos Totik, Acta Scientiarum Mathematicarum, Vol. 68, 2002)

"A book on ‘real algebra’ that serves as an introduction to the subject in addition to the main theme of the text. ... Well written with exercises for every chapter." (ASLIB Book Guide, Vol. 66 (11), 2001)

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 3540412158
• ISBN 13: 9783540412151
• Binding: Hardcover
• Number of pages: 276