- 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: 4.1 out of 5 stars See all reviews (25 customer reviews)
- Amazon Best Sellers Rank: #361,167 in Books (See Top 100 in Books)
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Elementary Number Theory (Springer Undergraduate Mathematics Series) Corrected Edition
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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."
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Top Customer Reviews
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.
Perhaps I never understood Abstract Algebra quite well enough because I did not have as strong as grasp in elementary number theory as I should have had, but Jones & Jones certainly present the subject matter in a way that a somewhat rusty college grad could quickly sink her teeth into and enjoy. In short, this helped me close ground, but fast, while at the same time it opened my eyes to other proofs in other courses that I had committed to memory yet never full appreciated.
In any case this book was money VERY well spent and worth its modest price of admission.
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. A book on number theory would also be incomplete without at least a brief discussion of Andrew Wiles and Fermat's Last Theorem. Of course, Elementary Number Theory steps up to the plate appropriately and gives an overview of the history of the theorem and a (necessarily) thin overview of Wiles' proof.
I think, however, one of the best features of the book is that Jones and Jones have attempted to make the text very readable, in the sense that you could sit in a bath and enjoy part of a chapter without any trouble. I have always enjoyed reading mathematics without pen and paper handy, mainly because it improves my memory and visualization when working through problems, and this text helps greatly in that regard. They do not go for the obscure, and realize that the people who are reading this text are doing so for the first time (hence the title) and will not be overly impressed if the authors had chosen to blind us with their brilliance. The authors understand that we are mere mortals with busy lives, and appreciate a smoothly flowing textbook without having to stumble through unique and cryptic notation or a difficult proof without any explanation.
The one thing this book does better than any other Number Theory book are the in-chapter questions. The questions are done so well that WANT to do them. You feel as if you are missing vital information by not doing them. This is one of the few books I can study for hours on end because you are constantly being engaged as you are working through the chapter, instead of mindlessly reading and hoping you remember everything you've just read. They questions aren't very difficult (full worked solutions for every problem if needed), but they are just hard enough to make you have to think.
That is also it's only downside. You cannot jump between sections sometimes. The book assumes you follow it from the beginning of a section to the end as it sometimes teaches you vital information via the in-chapter questions.
If you are looking to self-study then you will not find a better book. I've tried every Number Theory book with decent ratings on Amazon, and this is by far the best.