【书名】具体数学：计算机科学基础（英文版.第2版）
【原书名】Concrete Mathematics A Foundation for Computer Science(Second Edition)
【原出版社】Addison Wesley
【作者】（美）Ronald L.Graham,Donald E.Knuth,Oren Patashnik
【丛书名】经典原版书库
【出版社】机械工业出版社
【书号】7-111-10576-1
【开本】32开
【页码】680
【出版日期】2002-8-1
【版次】1-1
【文件语言】 中文
【文件格式】 PDF/PDG
【文件大小】
【内容简介】
作者
onald E.Knuth
算法和程序设计技术的先驱者，是计算机排版系统TEX和METAFONT的发明者。 Donald.E.Knuth(唐纳德.E.克努特，中文名高德纳)是斯坦福大学计算机程序设计艺术的荣誉退休教授，Knuth教授获得了许多奖项和荣誉，包括美国计算机协会图灵奖(ACM Turing Award)，美国前总统卡特授予的科学金奖(Medal of Science)，美国数学学会斯蒂尔奖(AMS Steele Prize)，以及1996年11月由于发明先进技术荣获的极受尊重的京都奖(KyotoPrize)。他因这些成就和大量创造性的影响深远的著作(19部书和160篇论文)而誉满全球。
This book introduces the mathematics that supports advanced computer Programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle Patterns in data. It is an indispensable text and reference not only for computer scientists--the authors themselves rely heavily on it! but for serious users Of mathematics in virtually every discipline. Concrete mathematics is a blending of continuous and disCRETE mathematics: "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas,using a collection of techniques for solving problems." The subject mater is primarily an expansion of the Mathematical Preliminaries section in Knuth's c1assic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study.
这本书介绍了数学，支持先进的计算机编程和算法分析。其著名作家的主要目的是提供一个坚实的数学技能和相关的基础-需要解决复杂问题的能力，评估可怕的款项，并发现数据微妙的模式。这是一个不可缺少的文本和参考不...这本书介绍了数学，支持先进的计算机编程和算法分析。其著名作家的主要目的是提供一个坚实的数学技能和相关的基础-需要解决复杂问题的能力，评估可怕的款项，并发现数据微妙的模式。这是一个不可缺少的文本和参考，不仅为计算机科学家 -作者自己很大程度上依赖于它！但对于几乎在每一个学科数学严重的用户。具体数学是连续和离散数学的混合：“更具体“的作者解释说，“这是数学公式操控，使用解决问题的技巧集合。“母校的主体主要是一个数学预赛在Knuth的计算机程序设计艺术节c1assic扩张，但表现风格更加悠闲，涵盖各个主题更深刻。一些新的课题已添加，并且最重要的想法已经追查到了自己的历史根源。书中收录500多练习，分为6类。提供完整的答案是所有练习，除了研究的问题，使书，特别是自学有价值。
目录 1 Recurrent Problems 1
1.1 The Tower of Hanoi 1
1.2 Lines in the Plane 4
1.3 The Josephus Problem 8
Exercises 17
2 Sums 21
2.1 Notation 21
2.2 Sums and Recurrences 25
2.3 Manipulation of Sums 30
2.4 Multiple Sums 34
2.5 General Methods 41
2.6 Finite and Infinite Calculus 47
2.7 Infinite Sums 56
Exercises 62
3 Integer Functions 67
3.1 Floors and Ceilings 67
3.2 Floor/Ceiling Applications 70
3.3 Floor/Ceiling Recurrences 78
3.4 !(R)mod! The Binary Operation 81
3.5 Floor/Ceiling Sums 86
Exercises 95
4 Number Theory 102
4.1 Divisibility 102
4.2 Primes 105
4.3 Prime Examples 107
4.4 Factorial Factors 111
4.5 Relative Primality 115
4.6 !(R)mod!ˉ: The Congruence Relati 123
4.7 Independent Residues 126
4.8 Additional Applications 129
4.9 Phi and Mu 133
Exercises 144
5 Binomial Coefficients 153
5.1 Basic Identities 153
5.2 Basic Practice 172
5.3 Tricks of the Trade 186
5.4 Generating Functions 196
5.5 Hypergeometric Functions 204
5.6 Hypergeometric Transformations 216
5.7 Partial Hypergeometric Sums 223
Exercises 230
6 Special Numbers
6.1 Stirling Numbers 243
6.2 Eulerian Numbers 253
6.3 Harmonic Numbers 258
6.4 Harmonic Summation 265
6.5 Bernoulli Numbers 269
6.6 Fibonacci Numbers 276
6.7 Continuants 287
Exercises 295
7 Generating Functions
7.1 Domino Theory and Change 306
7.2 Basic Maneuvers 317
7.3 Solving Recurrences 323
7.4 Special Generating Functions 336
7.5 Convolutions 339
7.6 Exponential Generating Functions 350
7.7 Dirichlet Generating Functions 356
Exercises 357
8 Discrete Probability
8.1 Definitions 367
8.2 Mean and Variance 373
8.3 Probability Generating Functions 380
8.4 Flipping Coins 387
8.5 Hashing 397
Exercises 413
9 Asymptotics
9.1 A Hierarchy 426
9.2 0 Notation 429
9.3 0 Manipulation 436
9.4 Two Asymptotic Tricks 449
9.5 Euler!ˉs Summation Formul 455
9.6 Final Summations 462
Exercises 475
A Answers to Exercises
B Bibliography
C Credits for Exercises
Index
List of Tables