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Graduate Texts in Mathematics

A Classical Introduction to Modern Number Theory

Authors: Ireland, K., Rosen, M.

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  • ISBN 978-1-4757-1779-2
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About this Textbook

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro­ ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis­ covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

Reviews

From the reviews of the second edition:

K. Ireland and M. Rosen

A Classical Introduction to Modern Number Theory

"Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution."

— MATHEMATICAL REVIEWS

"This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. … for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvêa, MathDL, January, 2006)


Table of contents (18 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4757-1779-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
A Classical Introduction to Modern Number Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
84
Copyright
1982
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-1779-2
DOI
10.1007/978-1-4757-1779-2
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIII, 344
Topics