基本信息
- 原书名：Elementary Number Theory and Its Applications,Fourth Edition
- 原出版社： Addison Wesley/Pearson
- 作者： （美）Kenneth H.Rosen
- 丛书名： 经典原版书库
- 出版社：机械工业出版社
- ISBN：9787111138150
- 上架时间：2004-2-17
- 出版日期：2004 年2月
- 开本：16开
- 页码：638
- 版次：4-1
- 所属分类：数学 > 代数，数论及组合理论 > 数论及应用
教材
内容简介
书籍
数学书籍
本书主要介绍数论的应用，包括整数、素数与最大公约数、同余变换、递增函数、密码学、本原根、二
次剩余与反比、小数与连分数、非线性丢番图方程等内容。
本书没有刻板的说教，而是以别致的方式，使学习数论变得轻松。此外，别出心裁的习题安排是本书的另一特色。每一节中都含有两类练习题，一类是笔答题，另一类是上机编程练习，这使得读者能够将书中的数学内容与实际的编程技巧联系起来。
本书自出版以来，深受读者好评，并已在数百所大学中被广泛采用。第4版除继承了前几版的优点之外，具备以下方面更加出色的特点：
通过大量实例将数论的应用引入了更高的境界。
更新并扩充了对密码学这一热点论题的介绍。
新增了关于默比乌斯反演与解多项式同余方程的内容。
证明更加严谨完善。
经过更加仔细的审核以确保内容的准确性。
给出了一些关于数论的网站地址。
数学书籍
本书主要介绍数论的应用，包括整数、素数与最大公约数、同余变换、递增函数、密码学、本原根、二
次剩余与反比、小数与连分数、非线性丢番图方程等内容。
本书没有刻板的说教，而是以别致的方式，使学习数论变得轻松。此外，别出心裁的习题安排是本书的另一特色。每一节中都含有两类练习题，一类是笔答题，另一类是上机编程练习，这使得读者能够将书中的数学内容与实际的编程技巧联系起来。
本书自出版以来，深受读者好评，并已在数百所大学中被广泛采用。第4版除继承了前几版的优点之外，具备以下方面更加出色的特点：
通过大量实例将数论的应用引入了更高的境界。
更新并扩充了对密码学这一热点论题的介绍。
新增了关于默比乌斯反演与解多项式同余方程的内容。
证明更加严谨完善。
经过更加仔细的审核以确保内容的准确性。
给出了一些关于数论的网站地址。
作译者
Kenneth H．Rosen密歇根大学数学学士，麻省理工学院数学博士。曾就职于科罗拉多大学、俄亥俄州立大学、缅因大学，后加盟贝尔实验室，现为AT&T实验室特别成员。
Rosen博士在数论领域与数学建模领域著有大量的论文及专著，除本书外，还著有经典作品《离散数
学及其应用》(本书中文版己由机械工业出版社引进出版)，此外，他还与人合著有《UNIX System V Re-
lease 4：An Introduction》、《UNIX：The Complete Reference and Best UNIX Tips Ever》等书，并担任
CRC离散数学丛书的主编。
Rosen博士在数论领域与数学建模领域著有大量的论文及专著，除本书外，还著有经典作品《离散数
学及其应用》(本书中文版己由机械工业出版社引进出版)，此外，他还与人合著有《UNIX System V Re-
lease 4：An Introduction》、《UNIX：The Complete Reference and Best UNIX Tips Ever》等书，并担任
CRC离散数学丛书的主编。
目录
What is Number Theory? 1
1 The Integers 5
1.1 Numbers, Sequences, and Sums
1.2 Mathematical Induction 18
1.3 The Fibonacci Numbers 24
1.4 Divisibility 31
2 Integer Representations and Operations 39
2.1 Representations of Integers 39
2.2 Computer Operations with Integers 49
2.3 Complexity of Integer Operations 56
3 Primes and Greatest Common Divisors 65
3.1 Prime Numbers 66
3.2 Greatest Common Divisors 80
3.3 The Euclidean Algorithm 86
3.4 The Fundamental Theorem of Arithmetic 97
3.5 Factorization Methods and the Fermat Numbers 109
3.6 Linear Diophantine Equations 119
4 Congruences 127
4.1 Introduction to Congruences 127
4.2 Linear Congruences 139
1 The Integers 5
1.1 Numbers, Sequences, and Sums
1.2 Mathematical Induction 18
1.3 The Fibonacci Numbers 24
1.4 Divisibility 31
2 Integer Representations and Operations 39
2.1 Representations of Integers 39
2.2 Computer Operations with Integers 49
2.3 Complexity of Integer Operations 56
3 Primes and Greatest Common Divisors 65
3.1 Prime Numbers 66
3.2 Greatest Common Divisors 80
3.3 The Euclidean Algorithm 86
3.4 The Fundamental Theorem of Arithmetic 97
3.5 Factorization Methods and the Fermat Numbers 109
3.6 Linear Diophantine Equations 119
4 Congruences 127
4.1 Introduction to Congruences 127
4.2 Linear Congruences 139
前言
In olden times (well, before 1970) number theory had the reputation as the purest part of mathematics. It was studied for its long and rich history, its wealth of easily accessible
and fascinating questions, and its intellectual appeal. But, in the past few years, people
have looked at number theory in a new way. Today, people study number theory bothfor the traditional reasons and for the compelling reason that number theory' has become essential for cryptography. The first edition of this book was the first text to integrate the modem applications of elementary number theory with traditional topics. This fourth edition builds on the basic approach of the original text. No other number theory text presents elementary number theory and its applications in as thoughtful a fashion as this book does. Instructors will be pleasantly surprised to see how modem applications can be seamlessly woven into their number theory course when they use this text.
This book is designed as a text for an undergraduate number theory course at any level. No formal prerequisites are needed for most of the material, other than some level of mathematical maturity. This book is also designed to be a useful supplement for computer science courses and as a number theory primer for people interested in learning about new developments in number theory and cryptography.
This fourth edition has been designed to preserve the strengths of previous editions while providing substantial enhancements and improvements. Instructors familiar with previous editions will be comfortable with this new edition. Those examining this book for the first time will see a text suitable for the new millennium, integrating gems of number theory dating back thousands of years with developments less than ten years old. Those familiar with previous editions will find that this book has become more flexible, easier to each from, and more interesting and compelling. They will also find that additional emphasis has also been placed on the historical context of results and on the experimental side of number theory.
and fascinating questions, and its intellectual appeal. But, in the past few years, people
have looked at number theory in a new way. Today, people study number theory bothfor the traditional reasons and for the compelling reason that number theory' has become essential for cryptography. The first edition of this book was the first text to integrate the modem applications of elementary number theory with traditional topics. This fourth edition builds on the basic approach of the original text. No other number theory text presents elementary number theory and its applications in as thoughtful a fashion as this book does. Instructors will be pleasantly surprised to see how modem applications can be seamlessly woven into their number theory course when they use this text.
This book is designed as a text for an undergraduate number theory course at any level. No formal prerequisites are needed for most of the material, other than some level of mathematical maturity. This book is also designed to be a useful supplement for computer science courses and as a number theory primer for people interested in learning about new developments in number theory and cryptography.
This fourth edition has been designed to preserve the strengths of previous editions while providing substantial enhancements and improvements. Instructors familiar with previous editions will be comfortable with this new edition. Those examining this book for the first time will see a text suitable for the new millennium, integrating gems of number theory dating back thousands of years with developments less than ten years old. Those familiar with previous editions will find that this book has become more flexible, easier to each from, and more interesting and compelling. They will also find that additional emphasis has also been placed on the historical context of results and on the experimental side of number theory.
