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A Classical Introduction to Modern Number Theory

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This book is in the MAA's basic library list.

MAA Review

Ireland and Rosen's A Classical Introduction to Modern Number Theory hardly needs another good review from me... but hey, I'm going to give it one anyway. 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.

The title gives a good idea of what's in the book. The approach is "classical", which means fairly concrete and based on explicit, computable examples. But the topics are chosen with an eye to what is important in number theory today, from reciprocity laws to elliptic curves. The result is a book that does exactly what it proposes to do, opening up modern number theory to students who are not quite ready for group schemes and Galois representations.

In most universities and colleges, there is no course for which this book would be the ideal text. Courses on number theory tend to be either very elementary or too advanced and specialized. But 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 is Professor of Mathematics at Colby College and the co-author, with William P. Berlinghoff, of Math through the Ages. He somehow finds time to also be the editor of MAA Reviews.

BLL*** — The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

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