Customer Reviews

Elementary Number Theory (5th Edition)

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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. I also found most proofs to be written with the proper balance of clarity and brevity.

While there is no attempt at an exposition of any algebraic or analytic methods, which are certainly some of the most beautiful results in number theory, the reader should not expect any, as evidenced by the word "elementary" in the title. As such, knowledge of these topics is not required for reading this book. The chapters on cryptography are also well written and serve as motivation for anyone wondering what all this stuff can be used for. Though the subject matter is still worthy of study, regardless of any particular application.

This book will never leave my shelf, and has sparked an interest in me that shows no signs of burning out. Again, an excellent book.

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.

Great book! Rosen explains tough concepts well and the homework problems really drive it home. The computational homework for programmers is especially nice. However, some of the problems are worded in such a way that it obscures the intent of the question. Then again, this IS number theory.

The book itself is a fine book. However, the book is not in good shape. It was marked as in good condition and it is falling apart. I am very disappointed and will think twice about buying books on here again.