Number Theory (Dover Books on Mathematics)

I recently took a one-semester course using this text. I found it to be one of the best textbooks I've used so far. The exposition was clear and easy to digest, with just the right number of clarifications and examples. The exercises were numerous, challenging and illuminating. No background beyond very basic set theory is assumed, and in fact the writer goes very far out of his way to keep his exposition separate from abstract algebra. This is most evident in the chapter on primitive roots. I can't speak for the second half of the book, on additivity, but I can say with certainty that the first nine chapters are worth the effort.

George Andrews is the reigning expert on partitions in the mathematical community who has written many seminal papers on the subject over the past half-century! If you don't know what partitions are in the theoretical sense, don't worry, the text provides ample introduction. I don't think you can find a more elementary introduction to the difficult, but extraordinarily powerful and elegant theory of partitions. The book covers the basics of number theory well, but it is the chapters on partitions that make this text stand out. It covers the Rogers-Ramanujan identities as well as the Jacobi triple product identity. It is rare in the mathematical community that an expert in a subject also writes a ground-level introductory text - but that's what you have here. Thanks to the dover edition, it's now quite affordable.

A few years ago, I read this book by George Andrews of Penn State University into chapter 8 and this 1971 textbook by him already shows his long interest in both combinatorics and number theory. Where I stopped reading was when the author's proofs started being multiple pages long. Here are the titles of the chapters with their starting pages: // PART I Multiplicativity-Divisibility // 1. Basis Representation-3 / 2. The Fundamental Theorem of Arithmetic-12 / 3. Combinatorial and Computational Number Theory-30 / 4. Fundamentals of Congruences-49 / 5. Solving Congruences-58 / 6. Arithmetic Functions-75 / 7. Primitive Roots-93 / 8. Prime Numbers-100 // PART II Quadratic Congruences // 9. Quadratic Residues-115 / 10. Distribution of Quadratic Residues-128 // PART III Additivity // 11. Sums of Squares-141 / 12. Elementary Partition Theory-149 / 13. Partition Generating Functions-160 / 14. Partition Identities-175 // PART IV Geometric Number Theory // 15. Lattice Points-201 / There are four mathematical appendices and the full set of indices after the 15 chapters--213-259. From the complicated table of contents above, one can see a broad sweep of combinatorial number theory. Part I is mostly pretty straight number theory, and that is what I did read. Part III on additivity is almost fully combinatorics more than number theory though. Still the price of this book is quite low to have access to all of this big range of mathematics to pick and choose what is most interesting to any given reader. Recommended.

Definitely not an easy read, but it was lots of fun and I liked it.

Excellent book for the subject

Number theory is both easy and difficult. This book does a good job of highlighting some of these aspects in a clear and straightforward way. It also does a good job of discussing the role technology is playing for some in the field today.

Good book if you have someone with you but it has a really hard introduction. The proof is not for the faint of heart and is beautiful if you understand it but I would recommend a different book (probably not from springer either if you are self teaching lol)./

I had a number theory class back in the dark ages when i was studying Mathematics at OSU. Before I started this book I reviewed another number theory book. It was like deja vu - the method was exactly what I had seen before. In fact, it may have been the same book. Then I picked this up to go a little more in depth. I was a little thrown off at first. Pretty much the same things were covered but from such a vastly different angle it almost seemed like a whole different field of mathematics. I can't say which viewpoint is the correct one (they both are, I guess) but, since the books are so inexpensive, I would suggest try each or using both. It is often eye-opening to see the same conclusion derived from attacking the problem from more than one angle.

Really a great book, consider theory plus many problems, but if you are just starting then don't go and try to solve everything from this book, as Many as you can solve,cuz more you do the more you will get familiar with the patterns and then you will be able to solve the problem you left. And I will also sujest that see some vedios of number theory in YouTube before buying, then you will not feel disheartened or unconfident. Happy solving.

good book

いわゆる平方剰余までの初等整数論の解説書であるが、数学専攻の学生を視野においた組み合わせ数学も随所に取り入れている。記述はふんだんに実例を取り上げて丁寧であるが定理等は簡潔にまとめられている。日本では、高木貞治の初等整数論が名著とされてはいるが、これは数学専攻の学生を対象としたかなり難解な書で、初学者にはハードルは高い。その点Number theoryは初学者には取っ付きやすく、高校の数学Aで学んだ学生にはスムーズに接続されるであろう。整数論は理科系の学生には基礎科目としては、通常カリキュラムには入っていない。しかし昨今ネットの暗号化、仮想通貨のブロックチェーンなどの時代の要請を鑑みると、整数論を学ぶことは理科系学生には必須と考えられる。その点で、このNumber theoryは英語も平易であるから整数論を学ぶ教科書として、十分選択肢になりうる。

A classic book that covers elementary number theory and some advanced topics as well. The author used a "discovery" approach that it's not common in most modern texts on Number Theory. Each chapter and section is about a "question" that the author explores, and then uses to establish the theorems and proofs. The exercises aren't too difficult, but they are good enough to keep you engaged. As a downside, I should say that the approach is not as easy to revisit as other books that go directly into "theorem/proof" without too much exposure.

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