UTiCS系列：计算机科学入门与现代教学视角

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"《什么是计算机科学》（What Is Computer Science? An Information Security Perspective）是一本针对大学本科阶段计算机科学和信息科学学生精心编撰的教材系列。该系列由Daniel Page和Nigel Smart两位在各自领域内享有盛誉的专家撰写，旨在提供高质量的教学内容，覆盖计算机科学的核心基础理论、高级主题以及实际应用。这些书籍的特点是采用新颖、精炼且现代的教学方法，适合自我学习或作为一学期至两学期课程的补充教材。书中不仅包含扎实的理论知识，还注重实践性，提供了大量实例和问题供读者练习，许多章节甚至包括完整的解题步骤，方便学生理解和掌握。该系列书目的目标是确保学生能够全面理解计算机科学的基础概念，同时培养他们的实践能力和解决实际问题的能力。《什么是计算机科学？一个信息安全视角》这一具体书籍，可能侧重于信息安全领域，将计算机科学的理论与信息安全实践相结合，让学生对这一交叉学科有深入理解。系列编辑Ian Mackie以及国际顾问委员会的审阅，保证了教材的权威性和深度。如果你对后续的系列内容感兴趣，可以访问Springer出版社的网址www.springer.com/series/7592获取更多相关资源。《Undergraduate Topics in Computer Science》系列为学生提供了一个系统、严谨的学习平台，帮助他们在计算机科学领域打下坚实的基础，并提升他们的专业素养。"

Contents

Part I Foundations of Computer Science

1 Compressing and Correcting Digital Media ............. 3

1.1 A Compact Disk =a Sequence of Numbers ............ 5

1.1.1 DecimalandBinaryRepresentation............ 6

1.1.2 DecimalandBinaryNotation ............... 9

1.1.3 Grouping Bits into Bytes . . . .............. 10

1.2 DataCompression......................... 11

1.2.1 A Run-Length Based Approach .............. 13

1.2.2 A Dictionary-Based Approach .............. 15

1.3 ErrorCorrection.......................... 18

1.3.1 An Error Detection Approach . .............. 18

1.3.2 An Error Correction Approach .............. 21

1.4 Recasting Error Correction as Matrix Arithmetic ......... 23

1.4.1 AnOverviewofVectors.................. 24

1.4.2 AnOverviewofMatrices ................. 25

1.4.3 Addition and Multiplication Modulo 2 .......... 27

1.4.4 UsingMatricesforErrorCorrection............ 28

1.4.5 Generalising the Matrix-Based (7, 4)-Code........ 31

References ................................ 31

2 Writing and Comparing Algorithms ................. 33

2.1 Algorithms............................. 33

2.1.1 WhatIsanAlgorithm?................... 34

2.1.2 WhatIsnotanAlgorithm? ................ 37

2.2 Algorithms for Multiplication ................... 38

2.3 Algorithms for Exponentiation .................. 42

2.4 Computational Complexity .................... 44

2.4.1 Step Counting and Dominant Steps ............ 45

2.4.2 Problem Size and Step Counting Functions ........ 46

xvi Contents

2.4.3 Ignoring Small Problems and Minor Terms ........ 47

2.4.4 Studying the Growth of Functions ............. 49

References ................................ 51

3 Playing Hide-and-Seek with Virus Scanners ............. 53

3.1 ComputersandPrograms ..................... 55

3.1.1 A Theoretical Computer .................. 56

3.1.2 AReal,Harvard-StyleComputer ............. 57

3.1.3 A Real, von Neumann-Style Computer .......... 59

3.2 HarvardVersusvonNeumannComputers............. 66

3.2.1 Beyond Straight-Line Programs .............. 67

3.2.2 TowardSelf-ModifyingPrograms............. 68

3.3 ASelf-ModifyingVirus ...................... 70

3.3.1 UsingXORtoMaskNumbers............... 70

3.3.2 AVirusthatMasksthePayload.............. 71

3.3.3 Preventing the Virus Without a Virus Scanner . . .... 73

References ................................ 74

4 How Long Is a Piece of String? .................... 77

4.1 StringDataStructures....................... 78

4.1.1 Problem#1:RepresentingCharacters........... 80

4.1.2 Problem#2:RepresentingStrings............. 82

4.2 StringAlgorithms ......................... 84

4.2.1 strlen: Finding the Length of a String ......... 84

4.2.2 toupper: Converting a String to Upper-Case . . .... 86

4.2.3 strcmp: Testing if One String Is the Same as Another . 89

4.2.4 strcat: Concatenating Two Strings Together . . .... 91

4.2.5 Problem #3: Repeated Concatenation ........... 95

References ................................ 97

5 Demystifying Web-Search: the Mathematics of PageRank ..... 99

5.1 PageRank: the Essence of Google Web-Search .......... 100

5.1.1 What Actually Is Web-Search? .............. 100

5.1.2 Web-Search Before Google ................ 101

5.1.3 Web-Search After Google ................. 102

5.2 Using Graph Theory to Model and Explore the Web . . . .... 103

5.2.1 GraphTraversal ...................... 105

5.2.2 GraphExploration..................... 109

5.3 Using Probability Theory to Model Web-Browsing ........ 110

5.3.1 Sanitising the Web-Graph to Avoid a Subtle Problems . . 113

5.3.2 A Mathematical Approach to Computing PageRank . . . 114

5.4 Putting It All Together: Using PageRank to Produce Web-Search

Results............................... 121

References ................................ 123

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