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

Book 11 of 187: Springer Monographs in Mathematics

Prestel, Alexander; Delzell, Charles

 
9783540412151: Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra (Springer Monographs in Mathematics)
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.

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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)

"About this title" may belong to another edition of this title.

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

Other Popular Editions of the Same Title

9783642074455: Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra (Springer Monographs in Mathematics)

Featured Edition

ISBN 10:  3642074456 ISBN 13:  9783642074455
Publisher: Springer, 2011
Softcover