Paer one：Mathematical Foundations 基础数学

1 Introduce and Motivation 书籍的介绍和出书缘由

• 1.1 Finding Words for Intuitions 直观描述
• 1.2 Two Ways to Read This Book 阅读这本书的两种方法
• 1.3 Exercises and Feedback 练习和反馈

2 Linear Algebra 线性代数

• 2.1 System of Linear Equations 线性方程组
• 2.2 Matricies 矩阵
• 2.3 Solving System of Linear Equations 解线性方程组
• 2.4 Vector Spaces 向量空间
• 2.5 Linear Independence 线性独立
• 2.6 Basis and Rank 基&秩
• 2.7 Linear Mappings 线性映射
• 2.8 Affine Spaces 仿射空间
• 2.9 Exercises 第一章习题指导

3 Analytic Geometry 解析几何

• 3.1 Norms 标准
• 3.2 Inner Products 内积
• 3.3 Lengths and Distances
• 3.4 Angles and Orthogonality
• 3.5 Orthonorma Basis
• 3.6 Orthogonal Complement
• 3.7 Inner Product of Functions
• 3.8 Orthogonal Projections
• 3.9 Rotations
• 3.10 Further Reading Exercises

4 Matrix Decompositions 矩阵分解

• 4.1 Determinant and Trace
• 4.2 Eigenvalues and Eigenvectors
• 4.3 Cholesky Decomposition
• 4.4 Eigendecomposition and Diagonalization
• 4.5 Singular Value Decomposition
• 4.6 Matrix Approximation
• 4.7 Matrix Phylogeny
• 4.8 Further Reading Exercises

5 Vector Calculus 向量微积分

• 5.1 Differentiation of Univariate Functions
• 5.2 Partial Differentiation and Gradients
• 5.3 Gradients of Vector-Valued Functions
• 5.4 Gradients of Matrices
• 5.5 Useful Identities for Computing Gradients
• 5.6 Backpropagation and Automatic Differentiation
• 5.7 Higher-Order Derivatives
• 5.8 Linearization and Multivariate Taylor Series
• 5.9 Further Reading Exercises

6 Probability and Distributions 概率&分布

• 6.1 Construction of a Probability Space
• 6.2 Discrete and Continuous Probabilities
• 6.3 Sum Rule，Product Rule，and Bayes‘ Theorem
• 6.4 Summary Statistics and Independence
• 6.5 Gaussian Distribution
• 6.6 Conjugacy and the Exponential Family
• 6.7 Change of Variables/Inverse Transform
• 6.8 Further Reading Exercises

7 Continuous Optimization 连续优化

• 7.1 Optimization Using Gradient Descent
• 7.2 Constrained Optimization and Lagrange MultipliersMultipliers
• 7.3 Convex Optimization
• 7.4 Further Reading Exercises

Part two：Center Machine Learning Problems

8 When Models Meet Data

9 Liner Regression

10 Dimensionality Reduction with Principal Component Analysis

11 Density Estimation with Gaussian Mixture Models

12 Classification with Support Vector Machines

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