Mathematics of Data Science

This book is about the mathematical foundations of data science.
1. Introduction
2. Curses, Blessings, and Surprises in High Dimensions
3. Singular Value Decomposition and Principal Component Analysis
4. Linear Regression and Regularization
5. Graphs, Networks, and Clustering
6. Nonlinear Dimension Reduction and Diffusion Maps
7. Linear Dimension Reduction via Random Projections
8. Optimization for Data Science
9. Classification
10. A Mathematical Introduction to Deep Learning
11. Large Sample Limit of Graph Laplacians
12. Community
13. Concentration of Measure and Gaussian Analysis
14. Matrix Concentration Inequalities
15. Compressive Sensing and Sparsity
16. Low-Rank Matrix Recovery