[2607.11938] Mathematics of Data Science

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arXiv:2607.11938 (cs)

[Submitted on 11 Jul 2026]

Title:Mathematics of Data Science

Authors:Afonso S. Bandeira, Amit Singer, Thomas Strohmer<br>View a PDF of the paper titled Mathematics of Data Science, by Afonso S. Bandeira and Amit Singer and Thomas Strohmer

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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

Subjects:

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Probability (math.PR)

Cite as:<br>arXiv:2607.11938 [cs.LG]

(or<br>arXiv:2607.11938v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.11938

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arXiv-issued DOI via DataCite

Submission history<br>From: Thomas Strohmer [view email]<br>[v1]<br>Sat, 11 Jul 2026 08:31:44 UTC (15,747 KB)

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