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Chapter 1 Preparation 3

Lesson 1 Some Elementary Expressions 3

1.1 Four Fundamental Operations 3

1.2 Signs of Equality and Inequality 3

1.3 Ratio and Proportion 4

1.4 Fractions and Decimals 4

1.5 Involution and Evolution 5

1.6 Elementary Fundamental Functions 5

1.7 Limit,Differentiation and Integration 6

1.8 Set Notation 7

1.9 Some other Symbols 7

1.10 Some Fundamental Operations by Matlab 8

Chapter 2 Professional Mathematical Fundamentals 15

Lesson 2 A Taste of Mathematics 15

2.1 Mathematics is Omnifarious 15

2.2 Mathematics is a Language of Science 16

2.3 Mathematics Has Two Categories 16

2.4 Mathematics Has Three Features 17

2.5 Math is Need by Everyone in the Modern Life 18

2.6 Three Mathematical Crises 19

2.7 One Mathematical Example by Matlab 24

Lesson 3 A Contour of Geometry 27

3.1 A Brief Introduction of Geometry 27

3.2 A Contour of Euclidean Geometry 27

3.3 A Contour of Analytic Geometry 30

3.4 A Contour of Non-Euclidean Geometry 31

3.5 Some Geometric Developing Trends 34

3.6 Two Geometric Examples by Matlab 34

Lesson 4 A Talk of Calculus 40

4.1 A Brief Introduction of Calculus 40

4.2 A Talk of Calculus of One Variable 42

4.3 A Talk of Calculus of Several Variable 45

4.4 Several Applications of Calculus 45

4.5 Some New Developments 46

4.6 Three Calculus Examples by Matlab 47

Lesson 5 A Walk through Algebra 51

5.1 A Walk through Algebra Contour 51

5.2 A Walk through Elementary Algebra 52

5.3 A Walk through Linear Algebra 54

5.4 Three Objects of Abstract Algebra 59

5.5 Three Algebraic Examples by Matlab 59

Lesson 6 A Journey of Mathematical Statistics 64

6.1 A Journey of Statistics 64

6.2 A Journey of Mathematical Statistics 66

6.3 A Journey of Probability Theory 69

6.4 A Journey of Monte Carlo Method 71

6.5 Three Statistical Examples by Matlab 74

Lesson 7 Math Will Rock the World 79

7.1 Some Bright Mathematical Prospects in the Internet World 79

7.2 The Dark Side of Mathematical Development 81

7.3 Pi in the Mathematical Development Sky 83

7.4 Calculus Ahead 86

7.5 Some Changes of the Private Lives 87

7.6 Two Modern Mathematical Examples by Matlab 88

Chapter 3 Information and Computation Science 95

Lesson 8 A Stroll about Information Theory 95

8.1 A Stroll about Information and Communication System 95

8.2 A Stroll about Information Theory 96

8.3 Two Key Concepts of Information Content 98

8.4 A Stroll about Information Science 101

8.5 Two signal Loading Examples by Matlab 102

Lesson 9 A Roam over Information Coding 106

9.1 A Roam over Information Explosion 106

9.2 A View of Digital Information 106

9.3 Information Needs to be Encoded 107

9.4 Two Scenarios about Two Coding Principles 108

9.5 Two Main Kinds of Information Coding 109

9.6 Two Common Coding Methods 111

9.7 Two Examples of Huffman Coding by Matlab 113

Lesson 10 An Impression of Ciphers 118

10.1 The Information is Insecurity 118

10.2 Ciphers are Efficient Ways to Protect Information 118

10.3 Two Common Encryption Algorithms 121

10.4 Data Encryption Standard—Modern Ciphers 123

10.5 Two Applications Examples by Matlab 124

Lesson 11 A Mathematical View of Digital Image Processing 130

11.1 A View of Digital Image Processing 130

11.2 Fourier Transform from the View of Signal Processing 132

11.3 A View of Image Interpolation 134

11.4 Image Rotation 136

11.5 A View of Image Sharpening 137

11.6 A View of Image Feature Extraction 139

11.7 Two Application Examples by Matlab 141

Lesson 12 A Tour of Algorithm Analysis 148

12.1 A Tour of Search Programs 148

12.2 A Tour of Algorithm 149

12.3 Five Characteristics of an Algorithm 150

12.4 How to Design an Algorithm 152

12.5 A Tour of Algorithm Analysis 153

12.6 Two Applications Examples by Matlab 156

Lesson 13 A Talk about Data Structures and Database 162

13.1 A Talk of Data Structures 162

13.2 A Database is a Data Storehouse 164

13.3 Management Information System(MIS) 166

13.4 Two Applications Examples by Matlab 169

Vocabulary 174

The Answers to Exercises 182