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### 基本信息

- 原书名：Concrete Mathematics A Foundation for Computer Science(Second Edition)
- 原出版社： Addison Wesley

### 编辑推荐

【新书推荐】具体数学:计算机科学基础:第2版(中文版)

### 内容简介

计算机书籍

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.

### 目录

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

### 前言

and [N]. We are especially pleased to be able to inaugurate the Euler Family of typefaces in this book, because Leonhard Euler's spirit truly lives on every pare: Concrete mathematics is Eulerian mathematics. The authors are extremely grateful to Andrei Broder, Ernst Mayr, Andrew Yao, and Frances Yao, who contributed greatly to this book during the years that they taught Concrete Mathematics at Stanford. Furthermore we offer 1024 thanks to the teaching assistants who creatively transcribed what took place in class each year and who helped to design the examination questions; their names are listed in Appendix C. This book, which is essentially a compendium of sixteen years' worth of lecture notes, would have been impossible without their first-rate work. Many other people have helped to make this book a reality. For examples, we wish to commend the students at Brown, Columbia, CUNY, Princeton, Rice, and Stanford who contributed the choice of graffiti and helped to debug our first drafts. Our contacts at Addison-Wesley were especially efficient and helpful; in particular, we wish to thank our publisher (Peter Gordon), production supervisor (Bette Aaronson), designer (Roy Brown), and copy editor (Lyn Dupré). The National Science Foundation and the Office of Naval Research have given invaluable support. Cheryl Graham was tremendously helpful as we prepared the index. An above all, we wish to thank our wives (fan, Jill, and Amy) for their patience, support, encouragement, and ideas. This second edition features a new Section 5.8, which describes some important ideas that Doron Zeilberger discovered shortly after the first edition went to press. Additional improvements to the first printing can also be found on almost every page. We have tried to produce a perfect book, but we are imperfect authors. Therefore we solicit help in correcting any mistakes that we've made. A reward of $2.56 will gratefully be paid to the first finder if any error, whether it is mathematical, historical, or typographical.