初等数论及其应用_在线百科全书查询
初等数论及其应用
图书信息
书 名: 初等数论及其应用作 者：罗森(KennethH.Rosen)
出版社： 机械工业出版社
出版时间： 2010年9月1日
ISBN: 9787111317982
开本： 16开
定价: 89.00元
内容简介
《初等数论及其应用(英文版)(第6版)》是数论课程的经典教材，自出版以来，深受读者好评，被美国加州大学伯克利分校、伊利诺伊大学、得克萨斯大学等数百所名校采用。
《初等数论及其应用(英文版)(第6版)》以经典理论与现代应用相结合的方式介绍了初等数论的基本概念和方法，内容包括整除、同余、二次剩余、原根以及整数的阶的讨论和计算。
作者简介
作者：（美国）罗森（Kenneth H.Rosen）
Kenneth H. Rosen 1972年获密歇根大学数学学士学位，1976年获麻省理工学院数学博士学位，1982年加入贝尔实验室，现为AT&T实验室特别成员，国际知名的计算机数学专家。Rosen博士对数论领域与数学建模领域颇有研究，并写过很多经典论文及专著。他的经典著作《离散数学及其应用》的中文版和影印版均已由机械工业出版社引进出版。
图书目录
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 wilson''s theorem and fermat''s little theorem 217
6.2 pseudoprimes 225
6.3 euler''s 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 fermat''s last theorem 530
13.3 sums of squares 542
13.4 pell''s 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
