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p-adic Numbers Fernando Q. Gouvea

p-adic Numbers By Fernando Q. Gouvea

p-adic Numbers by Fernando Q. Gouvea

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Summary

There are numbers of all kinds: rational, real, complex, p-adic. 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.

p-adic Numbers Summary

p-adic Numbers: An Introduction by Fernando Q. Gouvea

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

p-adic Numbers Reviews

This book was intended to be for undergraduates and it was really an excellent place to start, with a good choice of subjects and many exercises, and this third edition is even better. ... It is really an excellent book with a vivid style, pleasant to read, with 360 exercises going from easy computations by hand of an example to more advanced conceptual or computational exercises. (Daniel Barsky, Mathematical Reviews, March, 2022)

About Fernando Q. Gouvea

Fernando Q. Gouvea is a number theorist and historian of mathematics. In number theory he has been interested in the connection between p-adic modular forms and deformations of Galois representations. As a historian his main focus is on the early history of algebraic number theory, but he has also written on other historical topics. He enjoys books and has written many book reviews for a wide range of publications. For many years he served as editor of MAA Focus and of MAA Reviews. His current project is a forthcoming book on the history of p-adic numbers and p-adic analysis in the first decades of the twentieth century. Gouvea's other books include Arithmetic of p-adic Modular Forms, A Guide to Groups, Rings, and Fields, and (with William P. Berlinghoff) Math through the Ages: A Gentle History for Teachers and Others.

Table of Contents

1 Aperitif.- 2 Foundations.- 3 The p-adic Numbers.- 4 Exploring p.- 5 Elementary Analysis in p.- 6 Vector Spaces and Field Extensions.- 7 Analysis in p.- 8 Fun With Your New Head.- A Sage and GP: A (Very) Quick Introduction.- B Hints and Comments on the Problems.- C A Brief Glance at the Literature.- Bibliography.- Index.

Additional information

NLS9783030472948
9783030472948
3030472949
p-adic Numbers: An Introduction by Fernando Q. Gouvea
Fernando Q. Gouvea
Universitext
New
Paperback
Springer Nature Switzerland AG
2020-06-20
366
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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