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p-adic Numbers

An Introduction

  • Textbook
  • © 1997

Overview

Authors:
  1. Fernando Q. Gouvêa

    1. Department of Mathematics, Colby College, Waterville, USA

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Part of the book series: Universitext (UTX)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-vi
    Download chapter PDF

  2. Introduction

    • Fernando Q. Gouvêa
    Pages 1-5

  3. Apéritif

    • Fernando Q. Gouvêa
    Pages 7-21

  4. Foundations

    • Fernando Q. Gouvêa
    Pages 23-41

  5. p-adic Numbers

    • Fernando Q. Gouvêa
    Pages 43-85

  6. Elementary Analysis in ℚp

    • Fernando Q. Gouvêa
    Pages 87-132

  7. Vector Spaces and Field Extensions

    • Fernando Q. Gouvêa
    Pages 133-185

  8. Analysis in ℂp

    • Fernando Q. Gouvêa
    Pages 187-233

  9. Back Matter

    Pages 235-305
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Keywords

About this book

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)

Authors and Affiliations

  • Department of Mathematics, Colby College, Waterville, USA

    Fernando Q. Gouvêa

Bibliographic Information

  • Book Title: p-adic Numbers

  • Book Subtitle: An Introduction

  • Authors: Fernando Q. Gouvêa

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-642-59058-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • eBook ISBN: 978-3-642-59058-0Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: VI, 306

  • Number of Illustrations: 1 illustrations in colour

  • Topics: Number Theory

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