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  Product Details:   Author:
 George E. Andrews  Paperback:
 259 pages  Publisher:
 Dover Publications  Publication Date:
 October 12, 1994  Language:
 English  ISBN:
 0486682528  Product Length:
 8.64 inches  Product Width:
 5.44 inches  Product Height:
 0.6 inches  Product Weight:
 0.66 pounds  Package Length:
 8.4 inches  Package Width:
 5.3 inches  Package Height:
 0.7 inches  Package Weight:
 0.7 pounds  Average Customer Rating:
 based on 23 reviews 
   Customer Reviews:  
Average Customer Review:
( 23 customer reviews )
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113 of 114 found the following review helpful:
Excellent text by expert in the fieldDec 22, 2000
By D. Taylor George Andrews is the reigning expert on partitions in the mathematical community who has written many seminal papers on the subject over the past halfcentury! 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 RogersRamanujan 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 groundlevel introductory text  but that's what you have here. Thanks to the dover edition, it's now quite affordable.
39 of 41 found the following review helpful:
chimpanzee oven mittsJul 02, 2005
By M. J. De I have a background in logic but absolutely none in elementary number theory or abstract algebra and I am using this as a firsttime 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.
25 of 25 found the following review helpful:
An incredible text in elementary number theoryJan 05, 2009
By Calvin D. Woo 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 firstyear 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 lessthanintroductory 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.
11 of 11 found the following review helpful:
Fresh AirJun 07, 2011
By J. Mohr I recently took a onesemester 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.
10 of 10 found the following review helpful:
Might as well be renamed 'Combinatorial Number Theory'Feb 23, 2012
By Native of Neptune 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 MultiplicativityDivisibility // 1. Basis Representation3 / 2. The Fundamental Theorem of Arithmetic12 / 3. Combinatorial and Computational Number Theory30 / 4. Fundamentals of Congruences49 / 5. Solving Congruences58 / 6. Arithmetic Functions75 / 7. Primitive Roots93 / 8. Prime Numbers100 // PART II Quadratic Congruences // 9. Quadratic Residues115 / 10. Distribution of Quadratic Residues128 // PART III Additivity // 11. Sums of Squares141 / 12. Elementary Partition Theory149 / 13. Partition Generating Functions160 / 14. Partition Identities175 // PART IV Geometric Number Theory // 15. Lattice Points201 / There are four mathematical appendices and the full set of indices after the 15 chapters213259.
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.
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