New 'Mathematics of Data Science' book covers deep learning foundations

A new comprehensive textbook titled 'Mathematics of Data Science' has been released on arXiv by authors Afonso S. Bandeira (ETH Zurich), Amit Singer (Princeton), and Thomas Strohmer (UC Davis). The book, spanning 16 chapters, systematically covers the mathematical underpinnings of modern data science and machine learning. It begins with fundamental concepts like the curse and blessing of dimensionality, then moves through singular value decomposition, principal component analysis, linear regression, and regularization techniques. Later chapters delve into graph theory, network clustering, nonlinear dimension reduction via diffusion maps, and random projections.

The second half of the book tackles optimization for data science, classification methods, and a rigorous mathematical introduction to deep learning. Advanced topics include large sample limits of graph Laplacians, community detection, concentration of measure, matrix concentration inequalities, compressive sensing, and low-rank matrix recovery. The authors aim to provide a unified framework that connects classical statistics, signal processing, and modern AI. The resource is freely available on arXiv (arXiv:2607.11938) and is intended for graduate students and researchers seeking a deep theoretical grounding.