The Basic Theory of Power Series

The Basic Theory of Power Series

by Jesus M. Ruiz
     
 

Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these

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Overview

Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert's complex nullstellensatz, Risler's real nullstellensatz, Tougerons' implicit function theorem, and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. The present book opens another path: One gets acquaintance with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, and also some others.

Editorial Reviews

Booknews
For advanced undergraduate and early graduate mathematics students, explains power series techniques and theorems, and demonstrates their application in a number of branches of mathematics. Most students are exposed to power series only within the context of a specific application. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN-13:
9783528065256
Publisher:
Vieweg+Teubner Verlag
Publication date:
02/29/2012
Series:
Advanced Lectures in Mathematics Series
Edition description:
1993
Pages:
134
Product dimensions:
9.06(w) x 6.30(h) x (d)

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