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Algebraic Number Theory, Second Edition (Discrete Mathematics and Its Applications) Hardcover – January 5, 2011

ISBN-13: 978-1439845981 ISBN-10: 1439845980 Edition: 2nd

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Algebraic Number Theory, Second Edition (Discrete Mathematics and Its Applications) + Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics)
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Product Details

  • Series: Discrete Mathematics and Its Applications
  • Hardcover: 442 pages
  • Publisher: Chapman and Hall/CRC; 2 edition (January 5, 2011)
  • Language: English
  • ISBN-10: 1439845980
  • ISBN-13: 978-1439845981
  • Product Dimensions: 1.1 x 6.9 x 9.9 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #2,527,184 in Books (See Top 100 in Books)

Editorial Reviews


This is an introductory text in algebraic number theory that has good coverage … . This second edition is completely reorganized and rewritten from the first edition. … Very Good Features: (1) The applications are not limited to Diophantine equations, as in many books, but cover a wide range, including factorization into primes, primality testing, and the higher reciprocity laws. (2) The book has a large number of mini-biographies of the number theorists whose work is being discussed. …
MAA Reviews, April 2011
This book is in the MAA's basic library list. The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

Praise for the First Edition
This is a remarkable book that will be a valuable reference for many people, including me. The book shows great care in preparation, and the ample details and motivation will be appreciated by lots of students. The solid punches at the end of each chapter will be appreciated by everybody. It deserves success with many adoptions as a text.
—Irving Kaplansky, Mathematical Sciences Research Institute, Berkeley, California, USA

An extremely well-written and clear presentation of algebraic number theory suitable for beginning graduate students. The many exercises, applications, and references are a very valuable feature of the book.
—Kenneth Williams, Carleton University, Ottawa, Ontario, Canada

This is a unique book that will be influential.
—John Brillhart, University of Arizona, Tucson, USA

About the Author

Richard A. Mollin is a professor in the Department of Mathematics and Statistics at the University of Calgary. In the past twenty-five years, Dr. Mollin has founded the Canadian Number Theory Association and has been awarded six Killam Resident Fellowships. He has written more than 200 publications, including Advanced Number Theory with Applications (CRC Press, August 2009), Fundamental Number Theory with Applications, Second Edition (CRC Press, February 2008), An Introduction to Cryptography, Second Edition (CRC Press, September 2006), Codes: The Guide to Secrecy from Ancient to Modern Times (CRC Press, May 2005), and RSA and Public-Key Cryptography (CRC Press, November 2002).

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Customer Reviews

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Most Helpful Customer Reviews

9 of 9 people found the following review helpful By A Customer on April 25, 2003
Format: Hardcover
I learned a tremendous amount about Algebraic Number Theory from this excellent source. I have looked at other books that just skim the topics. This one covers them in depth and even has applications to cryptography (the author shuld have put that in the title). Even more advanced topics such as the higher reciprocity laws are covered with rigorous detail and extreme clarity. I read the AMS review for this book by Charles Parry and it is right on! This book should replace the old standards such as Janusz's and Marcus' books for instance. I'd say that this is a gem to be enjoyed.
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3 of 3 people found the following review helpful By Ellipsic on September 7, 2006
Format: Hardcover
I used this book in a one on one course in algebraic number theory in my fourth year of college. We finished just before ramification.

My background at the time included a year of undergraduate linear algebra, a year of undergraduate abstract algebra, a semester of intro. graduate algebra, intro. Galois theory, and intro. commutative algebra. The only things I used were Galois theory, my second abstract algebra course, and my second linear algebra course. Commutative algebra helped, but wasn't necessary in that abstract setting.

Organization: The book is very well organized with helpful appendices on abstract algebra basics (Groups, Rings, Fields) and Galois theory. The first chapter is slow-paced and provides a strong historical background for the material. A reviewer below suggested that there were "logical leaps" in the text--I never found such stuff, and I am always very picky about details. The author uses easy propositions that are assigned for homework sometimes, but they're mostly straightforward.

Exercises: They range from straightforward to quite thought-invoking... I remember one in particular, a starred problem, in which I had to use three "tricks" to solve.

Content: I like this book a lot. It's not super abstract on the level of Lang, but has hints of great generality throughout, and it's not some trivial algebraic number theory full of history, anecdotes, useless junk book with "Fermat's Last Theorem" misleadingly stated in the title somewhere. This book has a lot of stuff on applications to cryptography.
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4 of 9 people found the following review helpful By Abhik R. Roy on March 25, 2006
Format: Hardcover
I am a graduate student specializing in Ring Theory and I have to tell you this is the absolute worst book I have ever had. Not only does the author make these humongous jumps in each section, he also has massive logical gaps. There are plenty of errors in the text starting right from the first section. You could easily spend a whole year deciphering (with a massive headache) the first chapter. The author is definetly wrong in assuming that all you need is a basic undergraduate number theory class and basic abstract algebra. You could have 2 comprehensive years of graduate modern algebra and still not be ready for the massive logical gaps in the book. Sure if we were all Galois and Eulers, the book would be easier, but I'd bet they'd even be scratching their heads often enough. My advice is stay away from the text at all cost. You'll regret paying the outrageous price for a text that is worth firepaper.
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