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.