Elementary Number Theory, 5th edition

• Publisher:   Addison Wesley
• Number Of Pages:   744
• Publication Date:   2004-10-29
• ISBN-10 / ASIN:   0321237072
• ISBN-13 / EAN:   9780321237071

Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years.

For a good number of the odd problems the solution manual is good at working out the problem and coming to an answer. However, some of the answers are identical to what is in the back of the Number Theory textbook.

The description is misleading. The solutions manual only contains the solutions to odd problems. The same 'answers' that are available at the back of the book are explained in a little bit more detail in the solutions manual. If you are looking for solutions to even numbered problems as well then don't buy this.

This book is wordy, but less clear than I think it could be. It moves slowly, yet omits helpful ways of looking at concepts in the interest of being elementary. Also, it does not pave the way for future study of the material, nor does it pave the way for later study of connections to algebra, analysis, or combinatorics. This book overlooks intuitive, visual ways of representing basic concepts. For example, lattice/Hasse diagrams helped me understand divisibility and GCD's, but this book does not even mention this way of looking at divisibility. Congruence relations can be visualized in a number of ways, but this book only treats them using basic algebra. A book that moves as slowly and is as elementary as this one should really explore these sorts of visual presentations of concepts. Since this book is elementary, it does not explore any connections to groups, rings and ideals, fields, or lattices, and I think this is a shame because these structures make number theory make more sense. I think the book would do better to introduce a few of these structures in a very basic way. The book also passes up the opportunity to introduce generating functions, a critical and fairly elementary topic in number theory, which are only touched in one exercise. The first few chapters of Wilf's Generatingfunctionology and Newman's "Analytic Number Theory" show that generating functions can be presented at an elementary level. There are blurbs of history interspersed throughout the text, and I like the idea, but the history focuses almost exclusively on biographical information, with a tiny bit of history of famous problems and conjectures. There is little discussion of how the core mathematical ideas in the book were discovered and evolved over time. This book would do well to cut out the biographies and replace them with richer discussion of the historical development of the subject itself. I like the idea of a number theory book that focuses on applications, but this book does so at the expense of other things: its treatment of truly fascinating topics (such as continued fractions) is so weak that I do not think it's worth the trade-off. The book does nothing to pave the way towards the study of either analytic or algebraic number theory. The Zeta function only gets a token mention. This book is usable as a textbook or for self-study, but it is not outstanding for either of these goals, nor is it useful as a reference for advanced students. Studying from this book alone won't help one develop a good sense of intuition in number theory. Stillwell's thin book is about as easy to follow as this one, and yet it slowly introduces ideals and other algebraic concepts by the end of the book. My favorite book on number theory is Apostol's "Analytic Number Theory". It is considerably more advanced than this one, but I think that students with a strong background will actually find it easier to learn from. I have not yet found a truly elementary book on number theory that I liked; I think students would be better off to first acquire enough background and mathematical maturity to dive right into some of these more advanced texts, than to spend their time working through a book like this.

This book is awesome. Tons of material covered, but at a decent pace and with good examples. All the reader needs is a good working knowledge of how to read and construct proofs, and the time and patience to get through the material. The exercises range from the computational to the theoretical, from the routine to the extremely challenging. Many of the examples and exercises are intriguing, well-known results. The author touches on a large amount of subject matter and has many references for those interested in further reading. He makes no use of any of the methods that come from the main branches of Mathematics, namely Algebra, Analysis, etc. (though he mentions a few famous results), but he also mentions that he will not be using these methods in the beginning. It starts off a bit easy but gets moderately challenging. This book will never leave my shelf, and has sparked an interest inside of me that shows no signs of burning out. Again, an excellent book.

I bought this book as a supplemental study guide - my course was a mix of Number Theory, Abstact Algebra, Finite Fields and Probablility (pre-requisites for Cryptography study). The professor used lectures with hand-written supplements as primary study media. I found this text to be well-written, each concept was dealt with separately and concisely, then later assimilated with others to form broader ideas. Even though the text is directed at Number Theory, many of the other related concepts I studied were mentioned or covered in this text. This book will stay on my bookshelf for quite a while.

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