初等數論及其應用 [Elementary Number Theory （6th Edition）] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

[美] 羅森（KennethH·Rosen） 著

齣版社： 機械工業齣版社

ISBN：9787111317982

版次：1

商品編碼：10350852

品牌：機工齣版

包裝：平裝

叢書名： 華章數學·統計學原版精品係列

外文名稱：Elementary Number Theory （6th Edition）

開本：16開

齣版時間：2010-09-01

頁數：752

正文語種：英文

編輯推薦

通過豐富的實例和練習，將數論的應用引入瞭更高的境界，同時更新並擴充瞭對密碼學這一熱點論題的討論。
·內容與時俱進。不僅融閤瞭最新的研究成果和新的理論，而且還補充介紹瞭相關的人物傳記和曆史背景知識。
·習題安排彆齣心裁。書中提供兩類由易到難、富有挑戰的習題：一類是計算題，另一類是上機編程練習。這使得讀者能夠將數學理論與編程技巧實踐聯係起來。此外，《初等數論及其應用（英文版）（第6版）》在上一版的基礎上對習題進行瞭大量更新和修訂。

內容簡介

《初等數論及其應用（英文版）（第6版）》是數論課程的經典教材，自齣版以來，深受讀者好評，被美國加州大學伯剋利分校、伊利諾伊大學、得剋薩斯大學等數百所名校采用。
《初等數論及其應用（英文版）（第6版）》以經典理論與現代應用相結閤的方式介紹瞭初等數論的基本概念和方法，內容包括整除、同餘、二次剩餘、原根以及整數的階的討論和計算。

作者簡介

Kenneth H. Rosen 1972年獲密歇根大學數學學士學位，1976年獲麻省理工學院數學博士學位，1982年加入貝爾實驗室，現為AT&T;實驗室特彆成員，國際知名的計算機數學專傢。Rosen博士對數論領域與數學建模領域頗有研究，並寫過很多經典論文及專著。他的經典著作《離散數學及其應用》的中文版和影印版均已由機械工業齣版社引進齣版。

目錄

list of symbols x
what is number theory?
1 the integers 5
1.1 numbers and sequences 5
1.2 sums and products 16
1.3 mathematical induction 23
1.4 the fibonacci numbers 30
1.5 divisibility 36

2 integer representations and operations 45
2.1 representations of integers 45
2.2 computer operations with integers 54
2.3 complexity of integer operations 61
3 primes and greatest common divisors 69
3.1 prime numbers 70
3.2 the distribution of primes 79
3.3 greatest common divisors and their properties 93
3.4 the euclidean algorithm 102
3.5 the fundamental theorem of arithmetic 112
3.6 factorization methods and the fermat numbers 127
3.7 linear diophantine equations 137

4 congruences 145
4.1 introduction to congruences 145
4.2 linear congruences 157
4.3 the chinese remainder theorem 162
4.4 solving polynomial congruences 171
4.5 systems of linear congruences 178
4.6 factoring using the pollard rho method 187

5 applications of congruences 191
5.1 divisibility tests 191
5.2 the perpetual calendar 197
5.3 round-robin tournaments 202
5.4 hashing functions 204
5.5 check digits 209

6 some special congruences 217
6.1 wilsons theorem and fermats little theorem 217
6.2 pseudoprimes 225
6.3 eulers theorem 234

7 multiplicative functions 239
7.1 the euler phi-function 239
7.2 the sum and number of divisors 249
7.3 perfect numbers and mersenne primes 256
7.4 misbius inversion 269
7.5 partitions 277

8 cryptology 291
8.1 character ciphers 291
8.2 block and stream ciphers 300
8.3 exponentiation ciphers 318
8.4 public key cryptography 321
8.5 knapsack ciphers 331
8.6 cryptographic protocols and applications 338

9 primitive roots 347
9.1 the order of an integer and primitive roots 347
9.2 primitive roots for primes 354
9.3 the existence of primitive roots 360
9.4 discrete logarithms and index arithmetic 368
9.5 primality tests using orders of integers and primitive roots 378
9.6 universal exponents 385

10 applications of primitive roots and the
order of an integer 393
10.1 pseudorandom numbers 393
10.2 the eigamal cryptosystem 402
10.3 an application to the splicing of telephone cables 408

11 quadratic residues 415
11.1 quadratic residues and nonresidues 416
11.2 the law of quadratic reciprocity 430
11.3 the jacobi symbol 443
11.4 euler pseudoprimes 453
11.5 zero-knowledge proofs 461

12 decimal fractions and continued fractions 469
12.1 decimal fractions 469
12.2 finite continued fractions 481
12.3 infinite continued fractions 491
12.4 periodic continued fractions 503
12.5 factoring using continued fractions 517

13 some nonlinear diophantine equations 521
13.1 pythagorean triples 522
13.2 fermats last theorem 530
13.3 sums of squares 542
13.4 pells equation 553
13.5 congruent numbers 560

14 the gaussian integers 577
14.1 gaussian integers and gaussian primes 577
14.2 greatest common divisors and unique factorization 589
14.3 gaussian integers and sums of squares 599
appendix a axioms for the set of integers 605
appendix b binomial coefficients 608
appendix c using maple and mathematica for number theory 615
c.1 using maple for number theory 615
c.2 using mathematica for number theory 619
appendix d number theory web links 624
appendix e tables 626
answers to odd-numbered exercises 641
bibliography 721
index of biographies 733
index 735
photo credits 752

精彩書摘

Experimentation and exploration play a key role in the study of number theory. Theresults in this book were found by mathematicians who often examined large amounts ofnumerical evidence, looking for patterns and making conjectures. They worked diligentlyto prove their conjectures； some of these were proved and became theorems, others wererejected when counterexamples were found, and still others remain unresolved. As youstudy number theory, I recommend that you examine many examples, look for patterns,and formulate your own conjectures. You can examine small examples by hand, much asthe founders of number theory did, but unlike these pioneers, you can also take advantageof todays vast computing power and computational engines. Working through examples,either by hand or with the aid of computers, will help you to learn the subject——and youmay even find some new results of your own！

前言/序言

　　My goal in writing this text has been to write an accessible and inviting introduction to number theory. Foremost， I wanted to create an effective tool for teaching and learning.I hoped to capture the richness and beauty of the subject and its unexpected usefulness.Number theory is both classical and modem， and， at the same time， both pure and applied. In this text， I have strived to capture these contrasting aspects of number theory. I have worked hard to integrate these aspects into one cohesive text.
　　This book is ideal for an undergraduate number theory course at any level. No formal prerequisites beyond college algebra are needed for most of the material， other than some level of mathematical maturity. This book is also designed to be a source book for elementary number theory; it can serve as a useful supplement for computer science courses and as a primer for those interested in new developments in number theory and cryptography. Because it is comprehensive， it is designed to serve both as a textbook and as a lifetime reference for elementary number theory and its wide-ranging applications.
　　This edition celebrates the silver anniversary of this book. Over the past 25 years，close to 100，000 students worldwide have studied number theory from previous editions.Each successive edition of this book has benefited from feedback and suggestions from many instructors， students， and reviewers. This new edition follows the same basic approach as all previous editions， but with many improvements and enhancements. I invite instructors unfamiliar with this book， or who have not looked at a recent edition， to carefully examine the sixth edition. I have confidence that you will appreciate the rich exercise sets， the fascinating biographical and historical notes， the up-to-date coverage， careful and rigorous proofs， the many helpful examples， the rich applications， the support for computational engines such as Maple and Mathematica， and the many resources available on the Web.

評分☆☆☆☆☆

國內對數論不重視，書也很少。正文是英文版的，不知道能不能看懂。

評分☆☆☆☆☆

《初等數論及其應用(英文版)(第6版)》是數論課程的經典教材，自齣版以來，深受讀者好評，被美國加州大學伯剋利分校、伊利諾伊大學、得剋薩斯大學等數百所名校采用。

評分☆☆☆☆☆

內容簡介

評分☆☆☆☆☆

This edition celebrates the silver anniversary of this book. Over the past 25 years，close to 100，000 students worldwide have studied number theory from previous editions

評分☆☆☆☆☆

通過豐富的實例和練習，將數論的應用引入瞭更高的境界，同時更新並擴充瞭對密碼學這一熱點論題的討論。

評分☆☆☆☆☆

·內容與時俱進。不僅融閤瞭最新的研究成果和新的理論，而且還補充介紹瞭相關的人物傳記和曆史背景知識。

評分☆☆☆☆☆

比較好的數論書，簡單有趣，但難度不夠

評分☆☆☆☆☆

買瞭一直沒看，還不知道怎麼樣

評分☆☆☆☆☆

《初等數論及其應用（英文版）（第6版）》以經典理論與現代應用相結閤的方式介紹瞭初等數論的基本概念和方法，內容包括整除、同餘、二次剩餘、原根以及整數的階的討論和計算。