Mathematics of Data Science

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[Submitted on 11 Jul 2026]

Title:Mathematics of Data Science

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

1. Curses, Blessings, and Surprises in High Dimensions

1. Singular Value Decomposition and Principal Component Analysis

1. Linear Regression and Regularization

1. Graphs, Networks, and Clustering

1. Nonlinear Dimension Reduction and Diffusion Maps

1. Linear Dimension Reduction via Random Projections

1. Optimization for Data Science

1. Classification

1. A Mathematical Introduction to Deep Learning

1. Large Sample Limit of Graph Laplacians

1. Community

1. Concentration of Measure and Gaussian Analysis

1. Matrix Concentration Inequalities

1. Compressive Sensing and Sparsity

1. Low-Rank Matrix Recovery

Subjects:

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

Cite as: arXiv:2607.11938 [cs.LG]

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

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

arXiv-issued DOI via DataCite

Submission history

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

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