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P-Adic Numbers : An Introduction - Fernando Q. Gouvea

P-Adic Numbers

An Introduction

Paperback Published: 22nd May 2003
ISBN: 9783540629115
Number Of Pages: 306

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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.

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. ... Gouvea 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)

Aperitif
Foundations
p-adic Numbers
Elementary Analysis in Qp
Vector Spaces and Field Extensions
Analysis in Cp
Hints and Comments on the Problems
A Brief Glance at the Literature.
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540629115
ISBN-10: 3540629114
Series: Structure and Bonding
Audience: General
Format: Paperback
Language: English
Number Of Pages: 306
Published: 22nd May 2003
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.68
Weight (kg): 0.45
Edition Number: 2
Edition Type: Revised

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