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A Classical Introduction to Modern Number Theory [Hardcover]

Kenneth Ireland , Michael Rosen
4.3 out of 5 stars  See all reviews (6 customer reviews)
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Book Description

Aug. 1 1998 038797329X 978-0387973296 2nd ed. 1990. Corr. 5th printing 1998

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

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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."


"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)

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First Sentence
As a first approximation, number theory may be defined as the study of the natural numbers 1, 2, 3, 4, . . . . Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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2 of 2 people found the following review helpful
5.0 out of 5 stars IGNORE KWIRTHEERY'S REVIEW July 3 1999
By A Customer
The unfortunate thing about these Amazon reviews is that anyone can write a review, regardless of their credentials. I am a ex-philosopher who took to mathematics, and now I am a mathematician. The review of kwirtheery demonstrates, on the other hand, that he is a philosopher (allegedly) who does not know a single thing about mathematics. The thing is, I actually understand kwirtheery's language, but I also understand the language of mathematics. The same can't be said of K. His comment about the zeta function is obtuse and irrelevant. His comments are aimed not at all to the concerned book, but to mathematics in general which he does not know a thing about. I give the book 5 stars, and K's review a 0. Talk about something you know about, K., otherwise keep your "opinion" to yourself.
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5.0 out of 5 stars Simply Amazing May 25 2003
By A Customer
I picked up this book as a junior in college and was simply stunned. The flow of ideas is so natural that there are times when you can even read the book like a novel. The exposition is clean, and the proofs are elegant.
However, keep in mind that this book IS a GTM. Hence, it requires pre-requisites by way of approximately a year of abstract algebra. As the author says in the preface, it's possible to read a the first 11 chapters without it. However, to appreciate the beauty of the theory, I would sincerely recommend algebra as pre-req.
The first 12 chapters can be considered 'elementary' (not easy, just fundamental). The others are specialized algebraic topics. For instance, the chapter on elliptic curves is useful to get a flavor of the subject. However, it includes very few proofs.
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5.0 out of 5 stars A Modern Classic Dec 6 1999
If ever there was a textbook of which one could say that it was a thing of beauty, this has to be it. The book is very clearly written, and it is readily accessible even to those without a deep understanding of algebra or analysis; despite this, it manages to touch upon a great deal of relatively sophisticated material, and in a way that makes clear the links between the problems of the past and those of the present. I'd imagine that the book would constitute an essential item of reference for anyone with more than a passing interest in number theory.
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