Fernando Q. Gouvea's Books

Arithmetic of p-adic Modular Forms

By: Fernando Q. Gouvea

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Arithmetic of p-adic Modular Forms

By: Fernando Q. Gouvea

The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.

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Page Count

129

Publisher

Springer

Published Date

ISBN 10

3540388540

ISBN 13

9783540388548

p-adic Numbers

An Introduction

By: Fernando Q. Gouvea

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p-adic Numbers

An Introduction

By: Fernando Q. Gouvea

p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

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Page Count

285

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662222787

ISBN 13

9783662222782

Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

By: William P. Berlinghoff,Fernando Q. Gouvêa

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Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

By: William P. Berlinghoff,Fernando Q. Gouvêa

Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.

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Page Count

331

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147046456X

ISBN 13

9781470464561

p-adic Numbers

An Introduction

By: Fernando Q. Gouvea

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p-adic Numbers

An Introduction

By: Fernando Q. Gouvea

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Page Count

285

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662222787

ISBN 13

9783662222782

A Guide to Groups, Rings, and Fields

By: Fernando Q. Gouvêa

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A Guide to Groups, Rings, and Fields

By: Fernando Q. Gouvêa

Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

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Page Count

329

Publisher

MAA

Published Date

ISBN 10

0883853558

ISBN 13

9780883853559

Book's by Fernando Q. Gouvea

Arithmetic of p-adic Modular Forms

Arithmetic of p-adic Modular Forms

p-adic Numbers

p-adic Numbers

Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

p-adic Numbers

p-adic Numbers

A Guide to Groups, Rings, and Fields

A Guide to Groups, Rings, and Fields

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