Universitext

p-adic Numbers

An Introduction

Authors: Gouvea, Fernando

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eBook $34.99
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  • ISBN 978-3-642-59058-0
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Softcover $49.95
price for USA
  • ISBN 978-3-540-62911-5
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About this Textbook

In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab­ stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor­ ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num­ bers have shown up in other areas of mathematics, and even in physics.

Reviews

From the reviews:

"This is a well-written introduction to the world of p-adic numbers. The reader is led into the rich structure of the fields Qp and Cp in a beautiful balance between analytic and algebraic aspects. The overall conclusion is simple: an extraordinarily nice manner to introduce the uninitiated to the subject. Not only giving the background necessary to pursue the matter, but doing it in such a way that a healthy 'hands-on experience'is generated in the process." Mededelingen van het wiskundig genootschap

"It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." The Mathematical Gazette

From the reviews of the second edition:

“If I had to recommend one book on the subject to a student – or even to a fully grown mathematician who had never played with p-adic numbers before – it would still be this book. … Gouvêa has succeeded admirably in taking a topic that is not standard in the undergraduate mathematics curriculum and writing a book accessible to undergraduates that allows its reader to play with some intriguing mathematics and explore a topic which is both fun and important.” (Darren Glass, The Mathematical Association of America, January, 2011)


Table of contents (7 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-59058-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-62911-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
p-adic Numbers
Book Subtitle
An Introduction
Authors
Series Title
Universitext
Copyright
1997
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-59058-0
DOI
10.1007/978-3-642-59058-0
Softcover ISBN
978-3-540-62911-5
Series ISSN
0172-5939
Edition Number
2
Number of Pages
VI, 306
Number of Illustrations and Tables
1 illustrations in colour
Topics