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The Higher Arithmetic: An Introduction to the Theory of Numbers Paperback – August 21, 2008

ISBN-13: 978-0521634465 ISBN-10: 0521634466 Edition: 7th

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Product Details

  • Paperback: 241 pages
  • Publisher: Cambridge University Press; 7 edition (January 28, 2000)
  • Language: English
  • ISBN-10: 0521634466
  • ISBN-13: 978-0521634465
  • Product Dimensions: 6 x 0.6 x 9 inches
  • Shipping Weight: 12 ounces
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #2,513,771 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer's opinion, is far superior for this purpose to any other book in English." Bulletin of the American Mathematical Society

"It is a pleasant experience to see a book on Number theory in its seventh edition." Monatshefte fur Mathematik

Book Description

Updated in a seventh edition The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in depth knowledge of the theory of numbers, but also touches upon matters of deep mathematical significance.'Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewers opinion, is far superior for this purpose to any other book in English'--From a review of the first edition in Bulletin of the American Mathematical Society

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Customer Reviews

4.2 out of 5 stars
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Most Helpful Customer Reviews

67 of 70 people found the following review helpful By Anthony Varilly on June 7, 2000
Format: Paperback
This book is an AMAZING introduction to the Theory of Numbers. It assumes no previous exposure to the subject, or any technical mathematical knowledge for that matter. Its prose is lucid and the style appealing. Davenport chose NOT to write a lemma-theorem-proof kind of book, and the result is a marvelous, eminently readable introduction to the subject. Its wonderful to read a book where good prose is used to appropiately substitute a massive collection of uninviting symbols. I've also been reading other books on Number Theory, such as Hardy & Wright, but none are as clear as this one.
I found the chapter on quadratic residues (which includes the reciprocity law) to be especially well written. The section on computers and number theory is excelent as well. A concise and coherent discussion of crytography and the RSA system is included here. The organization of the book's chapters is fantastic. Each chapter builds up on results proven in the previous ones, showing well the connections between the different aspects of Number Theory. The exercises of the book range from simple to challenging, but are all accesible to someone willing to put effort into them.
This would be an excelent source for learning number theory for mathematical competition purposes, such as the ASHME, AIME, USAMO, and even for the International Mathematical Olympiad. The book contains much more than what is needed for these competitions, but the olympiad/contest reader will benefit greatly from a study of Davenport's work.
The book can certainly be used for an undergraduate course in Number Theory, though it might need supplementary materials, to cover a semester's worth of work.
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6 of 7 people found the following review helpful By Dave the Math Guy on January 1, 2012
Format: Paperback
The principal virtue of this text is that it can be taken up by readers with no more than ordinary high school level mathematical maturity yet it can aptly serve as the text for an undergraduate level first course in Number Theory. It is a model of clear and concise mathematical enunciation.
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Format: Paperback
The higher arithmetic is more commonly known as number theory and is one of the most enjoyable and complex areas of mathematics. Simultaneously simple and hard, the problems are generally easy to understand yet can be horrendously difficult to solve. Furthermore, the initial areas of number theory are easy to comprehend; in general it only takes a basic knowledge of algebra to manage the main points.
In this book, Davenport takes you through the basics of number theory, starting with prime factorization and going through some simple Diophantine equations. The chapter titles are:

*) Factorization and the primes
*) Congruences
*) Quadratic residues
*) Continued fractions
*) Sums of squares
*) Quadratic forms
*) Some Diophantine equations

This book is a solid introduction to number theory and can be understood by the advanced high school student. The primary drawback for the modern reader is that there is no coverage of the use of number theory in modern encryption techniques.
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