安德伍德·达德利：初等数论 德堡大学数学名誉教授 Elementary Number Theory

基本信息

Series:Dover Books on Mathema 1.4tics

Format:Paperback / softback 272 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486469317

Published:26 Dec 2008

Weight:276g

Dimensions:133 x 208 x 13 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

这本生动有趣的教材非常适合作为数论的一门课程，只需要熟悉初等代数和实数的性质。作者安德伍德·达德利 (Underwood Dudley) 曾撰写过一系列流行的数学书籍，他认为学习数学的好方法是解决问题。为了遵循这一理念，本书包括近 1,000 个练习和问题 - 一些是计算性的，一些是经典的，许多是原创的，还有一些有完整的解决方案。

开篇章节对初等数论的基础知识进行了合理的解释，并发展了整数和同余的基本性质。后续章节提供了费马和威尔逊定理的证明，介绍了数论函数，并探讨了二次互反定理。接下来是三个独立的部分，考察了数字的表示、丢番图方程和素数。本书后附有 260 个额外的问题、三个有用的附录以及对选定练习和问题的答案。

Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems—some computational and some classical, many original, and some with complete solutions.

The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.

作者简介

安德伍德·达德利（1937 年 1 月 6 日出生）是美国数学家和作家。他的几本畅销书描述了伪数学家的古怪数学，这些伪数学家错误地认为自己解决了问题或做了其他不可能的事情。安德伍德·达德利是德堡大学数学名誉教授。

Underwood Dudley (born January 6, 1937) is an American mathematician and writer. His popular works include several books describing crank mathematics by pseudomathematicians who incorrectly believe they have squared the circle or done other impossible things. Underwood Dudley is Professor Emeritus of Mathematics at DePauw University.