p-adic Numbers

Beschreibung

Every single other work on p-adic numbers is written for more advanced students. In general, they presuppose more mathematical material, move more quickly through the subject, and get much deeper into advanced material. This book can almost be viewed as an introduction to be read in preparation for reading these more advanced texts.
Includes supplementary material: sn.pub/extras

Autor*in

Fernando Quadros Gouvea

Themen in »p-adic Numbers«

Algebra absolute values on fields calculus finite field number theory p-adic analysis p-adic numbers valuations

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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)

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