Mathematics of Data Science

arXiv:2607.11938v1 Announce Type: cross Abstract: 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

Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph
Lectures on AI for Mathematics
Unicorn: Scaling High-Dimensional Time Series Forecasting via Universal Correlation Modeling
Why Architecture Choice Matters in Symbolic Regression
Position: LLM Serving Needs Mathematical Optimization and Algorithmic Foundations, Not Just Heuristics

Source: arXiv cs.AI | 2026-07-15

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