Mathematics of Data Science

arXiv cs.LG Papers
mathematics data-science foundations book arxiv machine-learning

Summary

This book covers the mathematical foundations of data science, including high-dimensional analysis, SVD, PCA, regression, graphs, clustering, deep learning, and more.

arXiv:2607.11938v1 Announce Type: new 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
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# Mathematics of Data Science
Source: [https://arxiv.org/abs/2607.11938](https://arxiv.org/abs/2607.11938)
[View PDF](https://arxiv.org/pdf/2607.11938)

> 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

## Submission history

From: Thomas Strohmer \[[view email](https://arxiv.org/show-email/c0ae7ce9/2607.11938)\] **\[v1\]**Sat, 11 Jul 2026 08:31:44 UTC \(15,747 KB\)

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