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Elementary Number Theory (Springer Undergraduate Mathematics Series) Corrected Edition

4.4 out of 5 stars 24 customer reviews
ISBN-13: 978-3540761976
ISBN-10: 3540761977
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Editorial Reviews

Review

From the reviews:

BULLETIN OF MATHEMATICS BOOKS

"?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."

 

G.A. Jones and J.M. Jones

Elementary Number Theory

"A welcome addition . . . a carefully and well-written book."―THE MATHEMATICAL GAZETTE

"This book would make an excellent text for an undergraduate course on number theory."

―MATHEMATICAL REVIEWS

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Product Details

  • Paperback: 200 pages
  • Publisher: Springer; Corrected edition (July 31, 1998)
  • Language: English
  • ISBN-10: 3540761977
  • ISBN-13: 978-3540761976
  • Product Dimensions: 7 x 0.7 x 9.2 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (24 customer reviews)
  • Amazon Best Sellers Rank: #226,498 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
I picked this up when I hit a small snag as I reviewed my undergraduate mathematics in order to return to graduate school for my master's in mathematics.
What started off as a small aside while reviewing another text (to recall some fundamentals, but in a rigorous way), turned into pure joy as I began a delightful excursion into "Elementary Number Theory," for its own sake, under the guidance of Jones & Jones.
Although many find Gallian and a host of others, Rudin included, to be the way to go, Jones & Jones [parallel to these authors] have a way of setting out proofs that appealed to me - for whatever that's worth.
ALL exercises have answers at the back, practically a sine qua non for all people who self-study and have to "grade" their own homework. The authors tie the relevance of the theories together without the sometimes heavy handed pop references to the Beatles, or to arcane things such as "yellow pigs." This is not to say the authors did not pay attention to the history and dates which they sprinkle in as they spin the development of the theories. Yet, they are always mindful of the mathematics which they teach and never get too cute.
It is the beauty of the number theory that is center stage, here, and like Zen, is achieved on the basis of its own elegant simplicity. But simplicity does not mean simple minded nor so brief that the authors lose the student. I felt in lock step with the authors page after page, proof after proof.
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Format: Paperback
A few weeks ago I ordered three books about Number Theory, and this is the one I like most. I am not a beginner in maths, but I am a beginner in Number Theory. This book start with the basics, and it has exercises with answers! I think this is a good book for self-study, it is easier to read than the books from Leveque.
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Format: Paperback
Ever since my undergraduate days aeons ago, I have always had an aversion to any number theory, but Jones and Jones have changed my mind completely. In the last year, I came across a few articles that made me want to learn more about the topic, but wasn't sure where to start, as I wanted a book that had proofs that I could follow, and yet also gave me some motivation to dive into more complicated mathematics such as elliptic curves. Elementary Number Theory fit the bill perfectly and has served as a wonderful introduction to the subject that I could follow and enjoy.

This book is the perfect blend of text and formulae for me, and seems an excellent combination of rigour and looseness, always trying to keep a steady pace for the reader without bogging down in pedantic details that are irrelevant to any but the most fastidious of readers. At the same time, the authors also ensure that the reader gains an appreciation of actually proving theorems about numbers, instead of relying on mere intuition or hunches.

As mentioned by other reviews here, the authors have included complete solutions to all of the exercises, which are sprinkled throughout each chapter, as well as at the end of each chapter. This is a welcome change to so many math texts that have "exercises left to the reader," and has been a requirement for me when reading a text in an unfamiliar subject. The exercises are selected appropriately to the content of the chapters and I found them to be a welcome complement to the rest of the book.

In addition, the book discusses applications of number theory to cryptography in a very readable fashion, with any additional mathematics required for the book (in this case some simple group theory and analysis) in two appendices.
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Format: Paperback
I bought this book while studying cryptography, a field that relies heavily on Number Theory for inspiration and from which it draws many, if not most, of its constructions. Most books on Cryptography summarily relegate the relevant number-theoretic aspects to short appendices that fail to build any intuition about what is going on. This book delivers precisely what is missing: a very readable, easily accessible introduction to the main topics of number theory that leaves the reader with a much better idea of how everything fits together. The book is very well suited for self-study, and includes answers to all exercises.
It should be noted, though, that the book does not address any of the computational aspects of Number Theory that are so dear to Cryptography (e.g it's easy to take square roots mod p if p is prime, hard to take square roots mod pq unless you know p,q). This, however, does not reduce its usefulness, since such results become very easy to absorb once one has a decent understanding of number theory and its workings. To fill the computational gaps, I would suggest Dana Angluin's "Lecture Notes on the Complexity of Some Problems in Number Theory" which are freely available on the web (the 2001 LaTeX'ed version)
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