[套装书]具体数学：计算机科学基础（英文版·原书第2版）典藏版+数学分析原理（英文版·原书第3版·典藏版）（2册）

作者
[美]葛立恒（Ronald L. Graham）高德纳（Donald E. Knuth） 奥伦·帕塔什尼克（Oren Patashnik）（美）沃尔特·鲁丁（Walter Rudin）
丛书名
经典原版书库
出版社
机械工业出版社
ISBN
9781912191116
简要
简介
内容简介书籍计算机书籍 ---------------------------具体数学：计算机科学基础（英文版·原书第2版）典藏版--------------------------- 《具体数学：计算机科学基础(第 2版)》是一本在大学中广泛使用的经典数学教科书。书中讲解了许多计算机科学中用到的数学知识及技巧，教你如何把一个实际问题一步步演化为数学模型，然后通过计算机解决它，特别着墨于算法分析方面。其主要内容涉及和式、整值函数、数论、二项式系数、特殊的数、生成函数、离散概率、渐近式等，都是编程所必 备的知识。另外，《具体数学：计算机科学基础(第 2版)》包括了六大类500 多道习题，并给出了所有习题的解答，有助读者加深书中内容的理解。 《具体数学：计算机科学基础(第 2版)》面向从事计算机科学、计算数学、计算技术诸方面工作的人员，以及高等院校相关专业的师生 ---------------------------数学分析原理（英文版·原书第3版·典藏版）--------------------------- 本书涵盖了高等微积分学的丰富内容，最精彩的部分集中在基础拓扑结构、函数项序列与级数、多变量函数以及微分形式的积分等章节。
目录



---------------------------具体数学：计算机科学基础（英文版·原书第2版）典藏版---------------------------


Contents
1 递归问题Recurrent Problems
1.l河内塔 The Tower of Hanoi 1
1.2平面上的直线 Lines in the P1ane 4
1.3 约瑟夫的问题The Josephus Problem 8
习题Exercises 17
2和式 Sums
2.1 记号Notation 21
2.2和式和递归式 Sums and Recurrences 25
2.3 和式的处理Mainpulation of Sums 30
2.4 多重和式Mu1tip1e Sums 34
2.5一般性的方法 General Methods 4l
2.6 有限微积分和无线微积分Finite and Infinite Calcu1us 47
2.7无限和式 Infinite Sums 56
习题Exercises 62
3 整值函数Integer Functions
3.1 底和顶Floors and Ceilings 67
3.2底和顶的应用 Floor/Ceiling Applications 70
3.3底和顶的递归式 Floor/Ceiling Recurrences 78
3.4 mod：二元运算 '' mod '' ：The Binary Operation 81
3.5底和顶的和式 F1oor/Cei1ing Sums 86
习题Exercises 95
4数论 Number Theory
4.1 整除性Divisibility 102
4.2 素数Primes 105
4.3素数的例子 Prime Examples 107
4.4 阶乘的因子Factorial Factors 111
4.5 互素Relative Primality 115
4.6 mod ：同余关系 ''mod'': The Congruence Re1ation 123
4.7 独立剩余Independent Residues l26
4.8 进一步的应用Additional Applications 129
4.9函数和函数 Phi and Mu 133
习题Exercises 144
5二项式系数 Binomial Coefficients
5.1基本恒等式 Basic Identities l53
5.2基本练习 Basic Practice 172
5.3处理的技巧 Tricks of the Trade 186
5.4 生成函数Generating Functions 196
5.5 超几何函数Hypergeometric Functions 204
5.6 超几何变换Hypergeometric Transformations 216
5.7部分超几何和式 Partial Hypergeometric Sums 223
5.8机械求和法 Mechanical Summation 229
习题Exercises 242
6特殊的数 Special Numbers
6.1 斯特林数Stir1ing Numbers 257
6.2 欧拉数Eulerian Numbers 267
6.3 调和数Harmonic Numbers 272
6.4调和求和法 Harmoinc Summation 279
6.5伯努利数 Bernoulli Numbers 283
6.6斐波那契数 Fibonacci Numbers 290
6.7连项式 Continuants 301
习题Exercises 309
7生成函数 Generating Functions
7.1多米诺理论与换零钱 Domino Theory and Change 320
7.2基本策略 Basic Maneuvers 331
7.3解递归式 So1ving Recurrences 337
7.4特殊的生成函数 Special Generating Functions 350
7.5 卷积Convo1utions 353
7.6 指数生成函数Exponential Generating Functions 364
7.7狄利克雷生成函数 Dinchlet Generating Functions 370
习题Exercises 371
8 离散概率Discrete Probability
8.1定义 Definitions 381
8.2均值和方差 Mean and Variance 387
8.3 概率生成函数Probability Generating Functions 394
8.4 抛掷硬币Flipping Coins 401
8.5散列法 Hashing 411
习题Exercises 427
9 渐进式Asymptotics
9.1 量的等级A Hierarchy 440
9.2 大O记号 O Notation 443
9.3 O 运算规则O Manipulation 450
9.4 两个渐进技巧Two Asymptotic Tricks 463
9.5 欧拉求和公式Euler''s Summation Formula 469
9.6最后的求和法 Final Summations 476
习题Exercises 489
附录A习题答案 Answers to Exercises
附录B参考文献 B Bibliography
附录C 习题贡献者Credits for Exercises
索引Index
表索引List of Tables




---------------------------数学分析原理（英文版·原书第3版·典藏版）---------------------------


Prefacevii
Chapter 1 The Real and Complex Number Systems1
Introduction 1
Ordered Sets 3
Fields 5
The Real Field 8
The Extended Real Number System 11
The Complex Field 12
Euclidean Spaces 16
Appendix 17
Exercises21
Chapter 2 Basic Topology 24
Finite, Countable, and Uncountable Sets 24
Metric Spaces 30
Compact Sets 36
Perfect Sets 41 Connected Sets42
Exercises43
Chapter 3 Numerical Sequences and Series 47
Convergent Sequences 47
Subsequences 51
Cauchy Sequences 52
Upper and Lower Limits 55
Some Special Sequences 57
Series 58
Series of Nonnegative Terms 61
The Number e63
The Root and Ratio Tests 65
Power Series 69
Summation by Parts70
Absolute Convergence 71
Addition and Multiplication of Series72
Rearrangements 75
Exercises78
Chapter 4 Continuity83
Limits of Functions 83
Continuous Functions 85
Continuity and Compactness 89
Continuity and Connectedness 93
Discontinuities94
Monotonic Functions 95
Infinite Limits and Limits at Infinity 97
Exercises 98
Chapter 5 Differentiation 103
The Derivative of a Real Function 103
Mean Value Theorems 107
The Continuity of Derivatives 108
L'Hospital's Rule 109
Derivatives of Higher Order 110
Taylor’s Theorem 110
Differentiation of Vector-valued Functions 111
Exercises 114
Chapter 6 The Riemann-Stieltjes Integral 120
Definition and Existence of the Integral 120
Properties of the Integral 128
Integration and Differentiation133
Integration of Vector-valued Functions 135
Rectifiable Curves 136
Exercises138
Chapter 7 Sequences and Series of Functions,143
Discussion of Main Problem 143
Uniform Convergence 147
Uniform Convergence and Continuity149
Uniform Convergence and Integration 151
Uniform Convergence and Differentiation 152
Equicontinuous Families of Functions 154
The Stone-Weierstrass Theorem 159
Exercises165
Chapter 8 Some Special Functions 172
Power Series 172
The Exponential and Logarithmic Functions 178
The Trigonometric Functions 182
The Algebraic Completeness of the Complex Field 184
Fourier Series185
The Gamma Function 192
Exercises196
Chapter 9 Functions of Several Variables 204
Linear Transformations 204
Differentiation211
The Contraction Principle220
The Inverse Function Theorem221
The Implicit Function Theorem 223
The Rank Theorem228
Determinants 231
Derivatives of Higher Order 235
Differentiation of Integrals 236
Exercises 239
Chapter 10 Integration of Differential Forms 245
Integration 245
Primitive Mappings 248
Partitions of Unity 251
Change of Variables 252
Differential Forms 253
Simplexes and Chains266
Stokes’ Theorem 273
Closed Forms and Exact Forms 275
Vector Analysis 280
Exercises 288
Chapter 11 The Lebesgue Theory300
Set Functions 300
Construction of the Lebesgue Measure 302
Measure Spaces310
Measurable Functions310
Simple Functions 313
Integration 314
Comparison with the Riemann Integral 322
Integration of Complex Functions 325
Functions of Class [WTHT]L[WT]\+2 325
Exercises 332
Bibliography 335
List of Special Symbols 337
Index 339



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