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Number Theory: 10 (Dover Books on Mathematics) Paperback – 2 Jan 2000

4.5 out of 5 stars 2 customer reviews

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Product details

  • Paperback: 259 pages
  • Publisher: Dover Publications Inc.; New edition edition (2 Jan. 2000)
  • Language: English
  • ISBN-10: 0486682528
  • ISBN-13: 978-0486682525
  • Product Dimensions: 13.8 x 1.5 x 21.9 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 174,236 in Books (See Top 100 in Books)

Product Description

About the Author

The Holy Grail of Number Theory
George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.
In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.
In the Author's Own Words:
"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews

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Format: Paperback Verified Purchase
Very interesting introduction to number theory. The book starts by introducing Peano's axioms, as well as groups and semigroups, but quickly moves onto more advanced topics. The book is rigorous, proofs are given for each theorem.
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Format: Paperback Verified Purchase
An excellent book.
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Most Helpful Customer Reviews on (beta) 4.4 out of 5 stars 36 reviews
127 of 128 people found the following review helpful
5.0 out of 5 stars Excellent text by expert in the field 22 Dec. 2000
By D. Taylor - Published on
Format: Paperback Verified Purchase
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.
36 of 36 people found the following review helpful
5.0 out of 5 stars An incredible text in elementary number theory 5 Jan. 2009
By Calvin D. Woo - Published on
Format: Paperback
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.
29 of 29 people found the following review helpful
1.0 out of 5 stars Don't buy the e-book 28 May 2014
By Amazon Customer - Published on
Format: Kindle Edition
I made the mistake of trying the electronic version of this book. This is the first mathematics book I have tried doing that with and it was a huge mistake. This book is based on formulae and their isn't a way to view them properly in the e-book version with the Kindle App. The formulas are too tiny to see and it makes it impossible to read the book. I can't recommend this as an e-book until they fix the problem with the formula viewing.
43 of 47 people found the following review helpful
4.0 out of 5 stars chimpanzee oven mitts 2 July 2005
By M. J. De - Published on
Format: Paperback
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.
17 of 17 people found the following review helpful
4.0 out of 5 stars Might as well be renamed 'Combinatorial Number Theory' 23 Feb. 2012
By Native of Neptune - Published on
Format: Paperback Verified Purchase
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.
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