具体数学：计算机科学基础 英文版

　　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 Knuths 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.

暂缺《具体数学：计算机科学基础 英文版》作者简介

1 Recurrent Problems                  
 1.l The Tower of Hanoi 1                  
 1.2 Lines in the P1ane 4                  
 1.3 The Josephus Problem 8                  
 Exercises 17                  
 2 Sums                  
 2.1 Notation 21                  
 2.2 Sums and Recurrences 25                  
 2.3 Mainpulation of Sums 30                  
 2.4 Mu1tip1e Sums 34                  
 2.5 General Methods 4l                  
 2.6 Finite and Infinite Calcu1us 47                  
 2.7 Infinite Sums 56                  
 Exercises 62                  
 3 Integer Functions                  
 3.1 Floors and Ceilings 67                  
 3.2 Floor/Ceiling Applications 70                  
 3.3 Floor/Ceiling Recurrences 78                  
 3.4 'mod" The Binary Operation 81                  
 3.5 F1oor/Cei1ing Sums 86                  
 Exercises 95                  
 4 Number Theory                  
 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 'mod': The Congruence Re1ation 123                  
 4.7 Independent Residues l26                  
 4.8 Additional Applications 129                  
 4.9 Phi and Mu 133                  
 Exercises 144                  
 5 Binomial Coefficients                  
 5.1 Basic Identities l53                  
 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                  
 5.8 Mechanical Summation 229                  
 Exercises 242                  
 6 Special Numbers                  
 6.1 Stir1ing Numbers 257                  
 6.2 Eulerian Numbers 267                  
 6.3 Harmonic Numbers 272                  
 6.4 Harmoinc Summation 279                  
 6.5 Bernoulli Numbers 283                  
 6.6 Fibonacci Numbers 290                  
 6.7 Continuants 301                  
 Exercises 309                  
 7 Generating Functions                  
 7.1 Domino Theory and Change 320                  
 7.2 Basic Maneuvers 331                  
 7.3 So1ving Recurrences 337                  
 7.4 Special Generating Functions 350                  
 7.5 Convo1utions 353                  
 7.6 Exponential Generating Functions 364                  
 7.7 Dinchlet Generating Functions 370                  
 Exercises 371                  
 8 Discrete Probability                  
 8.1 Definitions 381                  
 8.2 Mean and Variance 387                  
 8.3 Probability Generating Functions 394                  
 8.4 Flipping Coins 401                  
 8.5 Hashing 411                  
 Exercises 427                  
 9 Asymptotics                  
 9.1 A Hierarchy 440                  
 9.2 O Notation 443                  
 9.3 O Manipulation 450                  
 9.4 Two Asymptotic Tricks 463                  
 9.5 Euler's Summation Formula 469                  
 9.6 Final Summations 476                  
 Exercises 489                  
 A Answers to Exercises                  
 B Bibliography                  
 C Credits for Exercises                  
 Index                  
 List of Tables