# Mathematics of Data Science

> Source: <https://arxiv.org/abs/2607.11938>
> Published: 2026-07-16 20:38:48+00:00

# Computer Science > Machine Learning

[Submitted on 11 Jul 2026]

# Title:Mathematics of Data Science

[View PDF](/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](/show-email/c0ae7ce9/2607.11938)]

**[v1]** Sat, 11 Jul 2026 08:31:44 UTC (15,747 KB)

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