"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.
Most Helpful Customer Reviews
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.
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...
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.
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