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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.
- Sales Rank: #277845 in Books
- Published on: 1998-08-01
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.00" w x 6.14" l, 1.66 pounds
- Binding: Hardcover
- 394 pages
Review
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. Gouv�a, MathDL, January, 2006)
Most helpful customer reviews
33 of 36 people found the following review helpful.
Simply Amazing
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.
36 of 40 people found the following review helpful.
Best book on the subject
By Adam Massey
I am currently finishing my third year of undergraduate math at Brown University, and have just completed a course that used this particular book. I have to say it's the most WELL WRITTEN math book I've ever read, and I've read many, many math books by now (more than I'm willing to count as I'm typing this). Professor Rosen (and Ken Ireland, God rest his soul) have made a book that has both fun and interesting problems as well as clear explanations of proofs in the text. It does of course require that you know the basics of abstract algebra (in particular, one is expected to know that "1" is a unit and therefore cannot be prime, so of course when we discuss problems involving factorization into primes, one will of course ignore the number 1). One is also expected to know the basics of formal logic (i.e. understanding how a proof by induction works, how a proof by contradiction works, and knowing that any proper subset of the natural numbers will have a least element), and I choose to point this out simply because MrBigBeast's review makes it obvious that all these facts were not understood. Despite the fairly large amount of assumed knowledge (this is a book intended for advanced undergrads and first year grad students, afterall), this book takes one on an amazing adventure through the depths of elementary number theory, as well as introduces you to very advanced topics in both algebraic and analytic number theory (ever want to know about Zeta Functions? This book treats the topic quite nicely, making a fairly difficult concept accessible). Truly a gem of a book and worth buying even if you never use it for a course.
18 of 20 people found the following review helpful.
Great Text!
By A Customer
This a great introduction to number theory, with a lot of the material directed to modern research. They discuss zeta functions, algebraic number theory, and elliptic curves. It is a helpful link from introductory number theory toward the vast fields of research in the area.
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