Excursions in Number Theory (Dover books explaining science) (Paperback)

by C. Stanley Ogilvy (Author)

Editorial Reviews

Product Description

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. ". . . splendidly written, well selected and presented collection . . ." — Martin Gardner.

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Product Details Paperback: 168 pages Publisher: Dover Publications (November 1, 1988) Language: English ISBN-10: 0486257789 ISBN-13: 978-0486257785 Product Dimensions: 7.8 x 5.3 x 0.5 inches Shipping Weight: 5.6 ounces (View shipping rates and policies) Average Customer Review: 3.9 out of 5 stars See all reviews (7 customer reviews) Amazon.com Sales Rank: #176,570 in Books (See Bestsellers in Books) Popular in these categories: (What's this?) #40 in  Books > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Number Theory #44 in  Books > Science > Mathematics > Pure Mathematics > Number Theory

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Front Cover | Table of Contents | First Pages | Back Cover

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Citations (learn more)

17 books cite this book:

• Elementary Number Theory with Applications by Thomas Koshy on 6 pages
• Mathematical Mysteries: The Beauty and Magic of Numbers (Helix Books) by Calvin C. Clawson in Back Matter (1), and Back Matter (2)
• Identification Numbers and Check Digit Schemes (Classroom Resource Materials) by Joseph Kirtland on page 25, and Back Matter
• Smarandache Notions, Vol. 14 by W.B. Vasantha Kandasamy on page 250
• Lakatos' Philosophy of Mathematics (Studies in the History and Philosophy of Mathematics) by T. Koetsier in Back Matter

See all 17 books citing this book

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What Do Customers Ultimately Buy After Viewing This Item?

	60% buy the item featured on this page: Excursions in Number Theory (Dover books explaining science) 3.9 out of 5 stars (7) $8.95
	12% buy Elementary Theory of Numbers (Dover books on advanced mathematics) 4.4 out of 5 stars (5) $9.95
	12% buy Number Theory (Dover Books on Advanced Mathematics) 4.5 out of 5 stars (8) $10.36
	8% buy Recreations in the Theory of Numbers 4.6 out of 5 stars (8) $10.17

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7 Reviews 5 star:  (2) 4 star:  (3) 3 star:  (1) 2 star:  (1) 1 star:    (0)           Average Customer Review 3.9 out of 5 stars (7 customer reviews)		Share your thoughts with other customers:
Most Helpful Customer Reviews 15 of 15 people found the following review helpful: 4.0 out of 5 stars An amusing and short book covering the "fun" of numbers., July 7, 1996 By A Customer Written for anyone with an interest in numbers, this booktalks about some of the "neat" things about numbers withoutrequiring more than high school mathematical knowledge. Topics covered include prime number, geometric numbers, repeated fractions, and other chestnuts in mathematical recreations. This book is written at precisely the right level to interest a wide range of readers. For college mathematics students, a higher level book, such as "Fundamentals of Number Theory" by Leveque would be recommended as a primer to the theory of numbers. 4 of 4 people found the following review helpful: 4.0 out of 5 stars An Enjoyable Romp Through Number Theory, Skipping from Topic to Topic, January 14, 2006 By  Michael Wischmeyer (Houston, Texas) - See all my reviews (TOP 500 REVIEWER)    (REAL NAME)       Excursions in Number Theory (Oxford, publ. 1966; Dover reprint 1988) is a brief pleasure trip across the realm of number theory. C. Stanley Ogilvy's and John T. Anderson's enjoyable text only requires that readers have familiarity with algebra and have a penchant for puzzles. For those interested in more mathematics twenty pages of explanatory notes are found in the appendix. Using carefully selected examples, the authors present key topics with surprisingly clarity. Although congruences (arithmetic, not geometric), Diophantine equations, and continued fractions may be unfamiliar, the reader rather quickly appreciates the critical roles played by these concepts and tools. For example, congruences prove to be exceedingly helpful in solving a wide range a numeric problems and also reappear in later discussions on irrationals, iterations, and Diophantine equations. The study of prime numbers is fundamental to number theory, but as yet we have no known formula to produce all primes. Even more disturbing, we have no procedures that are even guaranteed to produce only primes (i.e., not yield an unpredictable mix of primes and composite numbers). There is something fundamental about primes that we seem not to understand. The short chapter, Prime Numbers as Leftover Scrap, offers a fascinating perspective that I have not encountered elsewhere. Other chapters are more playful, offering curios, puzzles, and oddities. Some examples appear to be little more than amusing numeric coincidences while other oddities prove to have theoretical significance. I am not an avid fan of mathematical puzzles, but I thoroughly enjoyed these diversionary chapters. As a follow-up to Ogilvy and Anderson, I am now reading: Number Theory and Its History by Oystein Ore (1948), available as a Dover reprint (1988), is now rather old, even pre-dating computer use in number theory research. The difficulty level is moderate. The historical background is interesting. (3 stars) Elementary Theory of Numbers (1962) by William J. LeVeque offers detailed proofs underlying number theory and should appeal to readers that enjoy studying mathematics. Topics include congruences, powers of an integer modulo m, continued fractions, Gaussian integers, and Diophantine equations. The Dover reprint suffers from a small font size. (3.5 stars) Yet another Dover reprint, Number Theory (1971) by George Andrews also targets more serious readers. Andrews uses an interesting combinatorial approach to number theory. Good font size and open page layouts. (4 stars) 4 of 4 people found the following review helpful: 4.0 out of 5 stars A Wonderful Trip, December 22, 2000 By  Hugh Alley (San Francisco, CA United States) - See all my reviews Unlike other Dover books, this text does not require an extensive background in math and fluency in the language of proofs. It is, as the title suggests, a delightful excursion through number theory that will ignite your interest in the subject and move you to further study. I found the author's annotations helpful and I did not mind the occasional use of British vernacular. At many points in the text, Ogilvy & Anderson prompt the reader to pursue a question on their own, rather than walk through a full proof or explanation. This may seem abrupt, but it keeps the text focused and leaves the reader wanting to know more about number theory. I hope Dover continues to reach out to a general audience with books like this. It condenses a difficult subject into everyday language without condescending to the reader.		Ad feedback   Most Recent Customer Reviews 5.0 out of 5 stars Great service When I purchase products directly from Amazon, I receive them fast. What I like more from Amazon is that it can combine the shipping to reduce my cost. Read more Published 9 months ago by Y Nhi 5.0 out of 5 stars Fantastic Journey This is a reprint of one of the books that most inspired my interest in mathematics as a boy. I highly recommend it to any high school student interested in... Read more Published on November 17, 2001 by anon2001 3.0 out of 5 stars O.K. This is one of the Dover Math Series which is `flawed'. Some of this series are really nice while others are, as this one, abrupt, written [generally by Englishmen] using words... Read more Published on November 25, 2000 by newton fisher 2.0 out of 5 stars Not too difficult... ...but I could not tell how current this reprint edition of a 1966 book is. This short volume is filled with curiosities about numbers and their theory, but the explanations... Read more Published on August 19, 2000 by Stephen Armstrong Search Customer Reviews Only search this product's reviews

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Product Details

• Paperback: 168 pages
• Publisher: Dover Publications (November 1, 1988)
• Language: English
• ISBN-10: 0486257789
• ISBN-13: 978-0486257785
• Product Dimensions: 7.8 x 5.3 x 0.5 inches
• Shipping Weight: 5.6 ounces (View shipping rates and policies)
• Average Customer Review: 3.9 out of 5 stars See all reviews (7 customer reviews)
• Amazon.com Sales Rank: #176,570 in Books (See Bestsellers in Books)

  Popular in these categories: (What's this?)

  #40 in	Books > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Number Theory
  #44 in	Books > Science > Mathematics > Pure Mathematics > Number Theory

Customer Reviews

Most Helpful Customer Reviews

15 of 15 people found the following review helpful:

4.0 out of 5 stars An amusing and short book covering the "fun" of numbers., July 7, 1996

By A Customer

Written for anyone with an interest in numbers, this booktalks about some of the "neat" things about numbers withoutrequiring more than high school mathematical knowledge. Topics covered include prime number, geometric numbers, repeated fractions, and other chestnuts in mathematical recreations. This book is written at precisely the right level to interest a wide range of readers. For college mathematics students, a higher level book, such as "Fundamentals of Number Theory" by Leveque would be recommended as a primer to the theory of numbers.

4 of 4 people found the following review helpful:

4.0 out of 5 stars An Enjoyable Romp Through Number Theory, Skipping from Topic to Topic, January 14, 2006

By	Michael Wischmeyer (Houston, Texas) - See all my reviews (TOP 500 REVIEWER)    (REAL NAME)

Excursions in Number Theory (Oxford, publ. 1966; Dover reprint 1988) is a brief pleasure trip across the realm of number theory. C. Stanley Ogilvy's and John T. Anderson's enjoyable text only requires that readers have familiarity with algebra and have a penchant for puzzles. For those interested in more mathematics twenty pages of explanatory notes are found in the appendix.

Using carefully selected examples, the authors present key topics with surprisingly clarity. Although congruences (arithmetic, not geometric), Diophantine equations, and continued fractions may be unfamiliar, the reader rather quickly appreciates the critical roles played by these concepts and tools. For example, congruences prove to be exceedingly helpful in solving a wide range a numeric problems and also reappear in later discussions on irrationals, iterations, and Diophantine equations.

The study of prime numbers is fundamental to number theory, but as yet we have no known formula to produce all primes. Even more disturbing, we have no procedures that are even guaranteed to produce only primes (i.e., not yield an unpredictable mix of primes and composite numbers). There is something fundamental about primes that we seem not to understand. The short chapter, Prime Numbers as Leftover Scrap, offers a fascinating perspective that I have not encountered elsewhere.

Other chapters are more playful, offering curios, puzzles, and oddities. Some examples appear to be little more than amusing numeric coincidences while other oddities prove to have theoretical significance. I am not an avid fan of mathematical puzzles, but I thoroughly enjoyed these diversionary chapters.

As a follow-up to Ogilvy and Anderson, I am now reading:

Number Theory and Its History by Oystein Ore (1948), available as a Dover reprint (1988), is now rather old, even pre-dating computer use in number theory research. The difficulty level is moderate. The historical background is interesting. (3 stars)

Elementary Theory of Numbers (1962) by William J. LeVeque offers detailed proofs underlying number theory and should appeal to readers that enjoy studying mathematics. Topics include congruences, powers of an integer modulo m, continued fractions, Gaussian integers, and Diophantine equations. The Dover reprint suffers from a small font size. (3.5 stars)

Yet another Dover reprint, Number Theory (1971) by George Andrews also targets more serious readers. Andrews uses an interesting combinatorial approach to number theory. Good font size and open page layouts. (4 stars)

4 of 4 people found the following review helpful:

4.0 out of 5 stars A Wonderful Trip, December 22, 2000

By	Hugh Alley (San Francisco, CA United States) - See all my reviews

Unlike other Dover books, this text does not require an extensive background in math and fluency in the language of proofs. It is, as the title suggests, a delightful excursion through number theory that will ignite your interest in the subject and move you to further study.

I found the author's annotations helpful and I did not mind the occasional use of British vernacular. At many points in the text, Ogilvy & Anderson prompt the reader to pursue a question on their own, rather than walk through a full proof or explanation. This may seem abrupt, but it keeps the text focused and leaves the reader wanting to know more about number theory.

I hope Dover continues to reach out to a general audience with books like this. It condenses a difficult subject into everyday language without condescending to the reader.