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An Introduction to the Theory of Numbers 5th Edition

3.7 out of 5 stars 7 customer reviews
ISBN-13: 978-0471625469
ISBN-10: 0471625469
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Editorial Reviews

About the Author

Hugh Montgomery is a Professor of Mathematics at the University of Michigan.

Larry Niven (left) is the Hugo and Nebula Award-winning author of such classics as "Ringworld, The Integral Trees", and "Destiny's Road". He has also collaborated with both Jerry Pournelle and Steven Barnes on "The Legacy of Heorot, Beowulf's Children", and the bestselling "Dream Park" series. He lives in Chatsworth, California.

Larry Niven and Jerry Pournelle were the joint winners of the 2005 Robert A. Heinlein Award.

Sy Montgomery is a naturalist, author, documentary scriptwriter, and radio commentator who writes for children as well as adults. Among her award-winning books are "The Good Good Pig, Journey of the Pink Dolphins", "Spell of the Tiger", and "Search for the Golden Moon Bear". She has made four trips to Peru and Brazil to study the pink dolphins of the Amazon; and on other expeditions, she was chased by an angry silverback gorilla in Zaire; bitten by a vampire bat in Costa Rica; undressed by an orangutan in Borneo; and hunted by a tiger in India. She also worked in a pit crawling with eighteen thousand snakes in Manitoba; handled a wild tarantula in French Guiana; and swum with piranhas, electric eels, and dolphins in the Amazon. Research for this book included travel to China and Mongolia to see the latest discoveries of giant bird fossils, and to Australia to see the most dangerous birds in the world. She lives in New Hampshire.

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Product Details

  • Hardcover: 544 pages
  • Publisher: Wiley; 5 edition (January 1991)
  • Language: English
  • ISBN-10: 0471625469
  • ISBN-13: 978-0471625469
  • Product Dimensions: 6.2 x 1.2 x 9.6 inches
  • Shipping Weight: 2 pounds
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #129,774 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By A Customer on September 8, 2000
Format: Hardcover
I have started my studies in Number Theory reading this book from the preface to the last word. It is amazing! I think it is a better introduction to the subject than the classical Hardy and Wright...it is "more objective" and almost 100% elementary...a good high school reader could do well with it. The chapter of diophantine equations has some divine proofs, very clever and very beautiful. And there is an easy proof of the irracionality of Pi. The only negative point is the existence of some points where the authors could be less concise and a bit clearer, stating the theorems before giving the demonstrations, instead of saying at the end of the paragraph "we then have proved the theorem of..." Its a good book for self-study. It has many exercises.
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By A Customer on January 9, 2002
Format: Hardcover
This book (5th edition) cover the topics of undergraduate number theory well. The chapters are -
(1)divisibility
(2)congruences
(3)quadratic reciprocity and quadratic forms
(4)some funtions of number theory
(5)some diophantine equations
(6)farey fractions and irrational numbers
(7)simple continued fractions
(8)prime estimates and multiplicative number theory
(9)algebraic numbers
(10)partition funtion
(11)density of sequences of integers.
It also contains basic cryptography, basic group theory and basic elliptical curves in some of the chapters. The authors give notes on the end of each chapter about some research results, which I enjoy reading.
However, the author give too much hints spoling the fun of solving the problems. Eg 32-36, 40-3, 59-53, 108-36, 136-17, 312-8, and most of the problems in chapter 8. The author should put these hints at the back of the book. I suggest you look up IMO (imo.math.ca) for problems suitable for chapter 1-7 because IMO is well-knowned for its excellent number theory problems (especially 1990-3).
Overall this is an excellent book. I give it a rating of 4.5/5, I don't give it 5 because of the author give too much hints to problems instead of putting hints at back of the book.
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Format: Hardcover
This is a fantastic book on number theory. It covers far more ground than most introductory text (comparable to Hardy and Wright in depth with much less concern for the big O). It covers material usually only available in separate texts: Rational points on elliptic curves, the partition function, and Dirchlet series. Quite readable chapters, well motivated theoretically, although the historic motivation for the subject matter comes largely in the end-of-the-chapter notes. It's an excellent refresher and reference for non-specialist who find themselves using an algorithm or formula they've forgotten (number theory now playing a role in physics and CS, like never before). It is well cross-referenced with regards to methods of proofs the can be accomplished in different section by different methods - this again making it an excellent reference.
Alas, it is pre-FLT. So you'll have to look elsewhere for that.
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Format: Hardcover Verified Purchase
This is an excellent book on the theory of numbers appropriate for a beginning graduate student who completed undergraduate introductory courses in number theory, advanced calculus, and linear algebra. In order to comprehend the material in this book, the student must poccess mathematically maturity, as they will be required to prove a good number of theorems throughout each chapter. I had the opportunity to use this book when I did my graduate level coursework in Number Theory.

I especially like the chapters on Diophantine equations and continued fractions.
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