p-adic Numbers: An Introduction (Universitext) [Paperback]

Fernando Quadros Gouvea (Author)

Book Description

ISBN-10: 3540629114 | ISBN-13: 978-3540629115 | Publication Date: August 5, 2003 | Edition: 2nd

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "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

Editorial Reviews

Review

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

Product Details

• Paperback: 312 pages
• Publisher: Springer; 2nd edition (August 5, 2003)
• Language: English
• ISBN-10: 3540629114
• ISBN-13: 978-3540629115
• Product Dimensions: 9.1 x 6.1 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #193,228 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

39 of 41 people found the following review helpful:

5.0 out of 5 stars This is a wonderful book for several reasons., December 27, 1999

By A Customer

This review is from: p-adic Numbers: An Introduction (Universitext) (Paperback)

This book really grabbed me on a number of points. First, in addressing a rather abstract topic (often not included in a basic undergraduate curriculum) it does a good job trying to compute concrete examples. It stays broad, as not to lose the reader on the messy details of any particular part of the theory. Hence the book is good even for students who are a little weak on their background. It is well-organized and exposed for an introductory-level text.

In particular, its proofs are rather clear, concise, and meaningful. There are only a couple points where Gouvea uses trickery (a la Rudin) to prove things, and he is honest enough to warn before they come. Indeed, the footnotes are quite entertaining, especially for one who has read enough math books to catch his jokes. Overall, the read is casual. It is good for independent reading.

The problems in the book are also worthy of praise. They are interspersed after proofs and in the middle of exposition, as ways to make sure the reader is following. Indeed, they are always pertinent and carefully planned. In addition, they point out ways in which mathematics authors often skip over details which the reader should actually verify for him/herself. Specifically, they perpare a student for reading graduate-level texts (which are notoriously full of this occurrence). Pedagogically, therefore, this is a very important tool, and useful book for a budding math student.

Finally, for the graduate student who wants to go down the path of p-adics, Gouvea does a good job of pointing the reader in the several different directions the literature can guide him/her. He gives references to other texts, giving just a taste of their contents, throughout. His eye towards further study is keen.

I must point out again that it is a joyful and entertaining read, in addition to being an exposition of a deeply fascinating (and deeply odd) area of math. This book, because of its clarity, its organization, its promotion of good mathematical reading skills, and its wonderful style occupies a spot on the very exclusive shelf of highest-quality texts in mathematics.

26 of 27 people found the following review helpful:

5.0 out of 5 stars I only wish I could give more stars..., October 21, 2002

By 

Cameron McLeman (Flint, MI) - See all my reviews

This review is from: p-adic Numbers: An Introduction (Universitext) (Paperback)

This is the best introduction-level mathematics textbook I have ever read, and I have read (and own) many. Every theorem and definition is well-motivated, and problems for the reader are interspersed within the text to make sure that every subtle nuance of the exposition is understood. Though introductory, Gouvea manages to incorporate some relatively advanced topics, (as far as undergraduate mathematics goes) such as the Weierstrass Preparation Theorem, local rings, and analysis in C_p. All this and the topic at hand is fascinating to boot. p-adic numbers are perfect for anyone wishing to pick up an amazingly interesting topic not found in most undergraduate or graduate courses. In conclusion, I recommend this book to the set of people interested in p-adic numbers, and its complement.

20 of 23 people found the following review helpful:

5.0 out of 5 stars enthousiasm-adique, July 11, 2000

By 

Bahram Houchmandzadeh (France) - See all my reviews
(REAL NAME)   

This review is from: p-adic Numbers: An Introduction (Universitext) (Paperback)

You're curious about beautifull topics in math, but reading a classical texbook, browsing through a list of lemma and therorems just get you sleep ? Read this one. The idea behind theorems, and why and how they came alive are so nicely exposed that this book can replace your favorite bed time one.