New Open-Access Textbook Maps the Math Behind Modern Data Science

Thomas Strohmer has posted a comprehensive textbook on arXiv covering the mathematical foundations that underpin data science and machine learning. The 16 chapters move from core linear-algebra machinery—singular value decomposition, principal component analysis, linear regression, and regularization—into the geometry of high-dimensional data, where phenomena like the ‘curse of dimensionality’ and concentration of measure govern how algorithms behave.

The later chapters build toward the tools driving contemporary ML: optimization methods, classification, a mathematical treatment of deep learning, and spectral techniques for graphs and clustering, including the large-sample limit of graph Laplacians. It also digs into the theory behind sparse and low-rank recovery, covering compressive sensing, matrix concentration inequalities, random projections, and diffusion maps for nonlinear dimension reduction.

Rather than a cookbook of techniques, the book aims to explain why the methods work, making it a reference for practitioners and students who want rigorous grounding rather than recipes. It is freely available as a PDF (roughly 15 MB) under a machine-learning listing on arXiv.