Customer Reviews

Number Theory (Dover Books on Mathematics)

5 star:		(7)
4 star:		(4)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

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.

I have a background in logic but absolutely none in elementary number theory or abstract algebra and I am using this as a first-time study guide. I find it very good. I have to mull over some of the proofs and examples since certain shortcuts are not immediately evident to me, but everything is generally clear and easy to follow. There are very few historical remarks which may or may not be a bonus for some. And as Dover does, they are practically giving this thing away.

Despite the deceptively small size of the text compared to many of its type, be sure to carry at least twice as many sheets of paper to fully get all you can out of it. George Andrew's pedagogical style of using combinatorics (basic gambling probability) to explain advanced concepts in number theory is executed brilliantly, and leaves even first-year undergraduates like me without a doubt in the world.

It is essential to do the problems in this book! Do not skip them thinking writing down the definitions and theorems will be enough-- some of the problems will kill you if you go in only knowing the written theorems, without any proper thought into the subject. Like any mathematical subject, it requires rigorous thinking and hours of reading before even considering going on to more advanced topics, like algebraic number theory, abstract algebra, or residue theory.

Breaking down the book into parts, I find it slightly disconcerting that despite the small nature of the book, the concept of quadratic congruences are only introduced in a less-than-introductory fashion, in comparison to other number theory books. It may be true that the author's main research was based off partition theory (the largest section in the book), but quadratic congruences have large applied mathematical influences, and should be considered to be read on, after the book as been finished.

Despite that, this text is an incredible foray into elementary number theory, and is a recommended buy for all those interested in the mathematical world.

This book is great for the price and if you can handle the terseness of a Dover book I would say it is great in general. The back of the book indicates it would be good for liberal arts majors. That is just crazy. However, you don't need much more than a solid foundation in mathematics through the Calculus of sequences and series. To get the most out of this book, you should do as many of the exercises as you can, even the ones without answers. Also, plan on supplementing the text with some online research. A general review of generating functions may be useful. Chapter 3 is a bit out of place and easy to lose patience with. Perhaps it can be read following Part 1. With that said, you can get a lot out of this book with regard to number theory (which arguably may not be generally useful).

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.

I love number theory but this book exposed me to combinatorics, which I though was the theory of permutation. So now I have a new interest. Book is new and shipped in quick time with good wrapping and perfect shape.
Great seller and who could not love Dover Publications?

This is one of the classic texts on Number Theory. It is a challenging book for anyone. The problem sets range from easy to hard. There are some hints, but those are few and far between. Like most Dover math books, it's dry and concise. There are better books on the market, but not for this price.

Price is a factor and Hardy is the classic text.
This one by George E. Andrews is well written has good examples and exercises
and doesn't cost an arm and leg used.It has a good prime section and a good quadratic section. I found stuff I hadn't seen before here.
It is going to take me a while to get everything out of this one!

I don't like how some theorems are proved with pictures and long paragraphs. There are more rigorous introductory texts out there. Also, the author doesn't explain some important steps in his picture proof. There was one question where the answer used modulo, but the author hasn't explained what it is yet.

The author tries to make things easy, and he succeeds in most parts. However, some proofs seem to be simple, but they actually involve complicated reasoning. My suggestion is that the author should not try to hide these difficult parts by reformulating abstract things into simple objects because it doesn't really help. I'd rather see difficulties in proofs than follow them with no idea why they have to be like that.