具体数学计算机科学基础（英文版·第2版）

　　《具体数学：计算机科学基础》（英文版第2版）是一本全英文版的具体数学计算机科学基础的参考书。

　　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.

【目录】
目录
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
1

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