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C. Stanley Ogilvy
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Excursions in Number Theory (Dover Books on Mathematics)

by C. Stanley Ogilvy (Author), John T. Anderson (Author)
4.5 4.5 out of 5 stars 32 ratings
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"A splendidly written, well selected and presented collection … I recommend the book unreservedly to all readers, in or out of professional mathematics, who like to 'follow the gleam' of numbers." — Martin Gardner.
The theory of numbers is an ancient and fascinating branch of mathematics that plays an important role in modern computer theory. It is also a popular topic among amateur mathematicians (who have made many contributions to the field) because of its accessibility: it does not require advanced knowledge of higher mathematics.
This delightful volume, by two well-known mathematicians, invited readers to join a challenging expedition into the mystery and magic of number theory. No special training is needed — just high school mathematics, a fondness for figures, and an inquisitive mind. Such a person will soon be absorbed and intrigued by the ideas and problems presented here.
Beginning with familiar notions, the authors skillfully yet painlessly transport the reader to higher realms of mathematics, developing the necessary concepts along the way, so that complex subjects can be more easily understood. Included are thorough discussions of prime numbers, number patterns, irrationals and iterations, and calculating prodigies, among other topics.
Much of the material presented is not to be found in other popular treatments of number theory. Moreover, there are many important proofs (presented with simple and elegant explanations) often lacking in similar volumes. In sum, Excursions in Number Theory offers a splendid compromise between highly technical treatments inaccessible to lay readers and popular books with too little substance. Its stimulating and challenging presentation of significant aspects of number theory may be read lightly for enjoyment or studied closely for an exhilarating mental challenge.
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  1. ISBN-10
    0486257789
  2. ISBN-13
    978-0486257785
  3. Publisher
    Dover Publications
  4. Publication date
    November 1, 1988
  5. Language
    English
  6. Dimensions
    5.46 x 0.45 x 7.98 inches
  7. Print length
    192 pages
  8. See all details
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Product details

  • Publisher ‏ : ‎ Dover Publications (November 1, 1988)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 192 pages
  • ISBN-10 ‏ : ‎ 0486257789
  • ISBN-13 ‏ : ‎ 978-0486257785
  • Item Weight ‏ : ‎ 2.31 pounds
  • Dimensions ‏ : ‎ 5.46 x 0.45 x 7.98 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 32 ratings

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C. Stanley Ogilvy

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4.5 out of 5 stars
4.5 out of 5
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32 global ratings

Top reviews from the United States

BRUCE E HOGMAN
5.0 out of 5 stars Great fun in math
Reviewed in the United States on August 17, 2018
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Fun book for math nerds.
My own college professor, who made math interesting every lecture.
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Ky Xuan To
4.0 out of 5 stars Four Stars
Reviewed in the United States on December 20, 2016
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Good reading.
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aareal
5.0 out of 5 stars Wonderful!
Reviewed in the United States on December 9, 2012
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Short and to the point. Number Theory became my favorite class this semester because of this book! Helped out so much and left little confusions!
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Marc
5.0 out of 5 stars A popular math book, so no math required
Reviewed in the United States on February 20, 2012
This is not a math book from the point of learning number theory. It is a popular math book which gives a reader some basic understanding of a little bit of number theory.

The audience for this book are laypeople and the examples and subject matter is very casual.

For those who enjoy popular math books I have a warning: with the current explosion of popular math books you will probably have seen most of this material.

Math people will not find anything in this book, but hey it is a nice easy read for the casual reader.
2 people found this helpful
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Michael Wischmeyer
4.0 out of 5 stars An Enjoyable Romp Through Number Theory, Skipping from Topic to Topic
Reviewed in the United States on January 14, 2006
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)
15 people found this helpful
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Jerry Richardson
5.0 out of 5 stars Clear, short, and well illustrated math popularization
Reviewed in the United States on November 10, 2009
I am happy to recomend this book to anyone interested in mathematics. The presentation is clear and well illustrated. The book is thought-provking and enjoyable. The audience for this book is senior high school students and adults. It does touch a bit on calculus, but most of the book deals with less advanced mathematics. The book makes you think about mathematics and shows practical applications of some mathematical ideas that may suprise you.
3 people found this helpful
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newton fisher
3.0 out of 5 stars O.K.
Reviewed in the United States on November 25, 2000
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 not common to a U.S. vocabulary.
This book was originally published in 1966 by the Oxford Press. Brit maths notation is just `off' enough if, as me, you are not `into' it proofs are spoilt until the uncommon words are deciphered.
Maybe you recall in Alice in Wonderland the poem `... little Bat / how I wonder where your at'.--- `Bat' was a math prof at Oxford whose lectures and proofs were unaccustomed. Its not the maths which is Batty here but the nomenclature, the notation and the abruptness.
2 people found this helpful
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book reviewer
5.0 out of 5 stars I liked this book!
Reviewed in the United States on May 1, 2006
I really enjoyed Excursions in Mathematics. The author makes a variety of math topics interesting while explaining the mathematical ideas, using really interesting and easy to understand examples, taken from everyday experiences when applicable. There are a few puzzles which, if you give them a try are fun and might further clarify the math topics. I liked the light-hearted tone of the book, which was nice for those who may find math intimidating. There are notes at the end of the book which are more technically detailed on a few of the math topics. It was a fun, easy and informative read, a nice blend of fun and learning.
5 people found this helpful
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Top reviews from other countries

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P SBasu
5.0 out of 5 stars Good
Reviewed in India on December 1, 2023
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Good
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Cliente Amazon
4.0 out of 5 stars Buono
Reviewed in Italy on May 11, 2017
Verified Purchase
Per chi si avvicina la prima volta alla teoria dei numeri è perfetto. Chi ha letto altri testi divulgativi sull'argomento lo troverà elementare.
L'autore resta un ottimo divulgatore.
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M. F. Cayley
5.0 out of 5 stars Delightful and easily understandable. A gem of a book
Reviewed in the United Kingdom on March 1, 2013
Verified Purchase
This is a well-written exposition of some aspects of number theory. The prerequisites are just a knowledge of elementary arithmetic. Explanations are extremely lucid. Many of the topics chosen relate to prime numbers, including the frequency of prime numbers, a subject of continuing exploration by experts. Other chapters include an introduction to some aspects of the Fibonacci numbers, and a chapter on Diophantine equations - equations with whole number solutions. This book is a gentle introduction to some fascinating aspects of maths, and is a gem.
2 people found this helpful
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Three choruses
4.0 out of 5 stars Useful trip
Reviewed in the United Kingdom on October 7, 2017
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Very interesting subject. Whetted my appetite for more
2 people found this helpful
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Eoin
5.0 out of 5 stars Easy to read and informative
Reviewed in the United Kingdom on October 16, 2013
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This book was brilliantly written, relying on some anecdotal stories to maintain interest before explaining the maths behind it. It assumed no previous knowledge of number theory, and was a wonderful read.
3 people found this helpful
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