Ⅰ.
Artificial Intelligence 1

1.
History of Artificial Intelligence 1
1.1 What is Artificial Intelligence? 1
1.2 How has artificial intelligence evolved? 2

2.
Artificial Intelligence and Mathematics 4
2.1 How is mathematics used in artificial intelligence? 4

3.
Machine Learning 7
3.1 What is Machine Learning? 7
3.2 Example 8 of Learning Using Machine Learning
3.3 Machine Learning Methods 9

4.
Machine Learning and Artificial Neural Networks 10
4.1 Artificial Neural Networks 10
4.2 How Neural Networks Work 12
4.3 Neural Network Training 14
4.4 Artificial Neuron TLU 15
4.5 TLU's Logical Operations 15

5.
Perceptron 16
5.1 Perceptron 16
5.2 Logical Operations of Perceptrons 17
5.3 Limitations of the Perceptron: Inability to Implement Exclusive-OR 18

6.
Multilayer Perceptron 18
6.1 Multilayer Perceptron 18
6.2 Opa backpropagation method 20
6.3 Deep Neural Networks 21

7.
Deep Learning 22
7.1 Deep Learning 22
7.2 Characteristics of Deep Learning 22

8.
CNN 23, a representative deep learning model
8.1 ImageNet 23
8.2 ILSVRC Competition 23
8.3 Convolution 24
8.4 Convolutional Neural Networks 25
8.5 Feature Extraction Task of CNN 26

Ⅱ.
Data Representation for Data Processing 27

1.
Data and Matrices 27
1.1 Ordered Pairs and Vectors 27
1.2 Vector Operations 33
1.3 Matrices and Tensors 34
1.4 Matrix Operations 36
1.5 Types of Matrices 41

2.
Matrix Processing 47
2.1 Diagonalization and LU Decomposition 47
2.2 Principal Component Analysis 51
2.3 Convolutional Neural Networks 55

3.
Normalization 57
3.1 Overfitting 57
3.2 Normalization 59
3.3 Exponential and Logarithmic Functions 61

4.
Solution set of linear systems of equations 64
4.1 Systems of Linear Equations 64
4.2 Augmented matrix 66
4.3 Gaussian Elimination 67
4.4 Solution Sets of Systems of Linear Equations 69

5.
Orthogonal projection and least squares problem 71
5.1 Least Squares Problem 71
5.2 The Meaning of the Least Squares Problem 73
5.3 Orthogonal projection and least-squares solution 73
5.4 Finding a Curve That Fits the Data 76

Ⅲ.
Classification and Prediction 79

1.
Sequences and Statistics 79
1.1 Sequence 79
1.2 Random Variables and Probability Distributions 85
1.3 Mean, Variance, and Standard Deviation 89

2.
Bayes' Theorem 100
2.1 Joint probability 100
2.2 Conditional Probability 101
2.3 Bayes' Theorem 103

3.
Data Classification 107
3.1 Data Similarity 107
3.2 Distance 107
3.3 Norm 108
3.4 Comparison of data using angles 109
3.5 The Concept of Cosine Similarity 110
3.6 Inner product 110
3.7 angle 110
3.8 Calculating Cosine Similarity 111

Ⅳ.
Learning and Optimization 113

1.
Optimization and Decision Making 113
1.1 Loss Function 113
1.2 Gradient Descent 119

2.
The maximum and minimum of the function are 125
2.1 Limits of Functions 125
2.2 Left and Right Limits 125
2.3 Average rate of change 126
2.4 Slope of the Tangent Line 127
2.5 Differential Coefficient 129
2.6 Derivatives 130
2.7 Maximum and minimum of quadratic functions 132
2.8 Local maxima, local minima, and maximum and minimum values ​​of functions 133

3.
Activation function 135
3.1 Sigmoid function 135
3.2 ReLU function 137
3.3 Softmax Function 139

4.
Rational Decision Making 141
4.1 Rational Decision-Making Model 142

V.
Principal Component Analysis and Artificial Neural Networks 145

1.
Principal Component Analysis 145
1.1 Dimensional Reduction 145
1.2 Principal Component Analysis (PCA) 145
1.3 Computing Principal Component Analysis 147
1.4 Principal Component Analysis Case 148
1.5 Principal Component Analysis and Covariance Matrix 152
1.6 Principal Component Analysis and Linear Regression 154

[Reference] Data Visualization Using CODAP 155

Reference 161

Search 163