Mathematical Foundations of Data Sciences
Sampling, representation, information, and learning: read the mathematics, then explore how its conclusions change as you vary the parameters. Each experiment sits beside its corresponding book figure and retains the publication’s numbering.
Painting detail by Louis Peyré (1923–2012). About the paintings.
Preface¶
This book presents the mathematical and numerical foundations of modern data science.
It covers signal and image processing (Fourier analysis, wavelets, denoising, and compression), imaging science (inverse problems, sparsity, and compressed sensing), and machine learning (regression, classification, and deep learning).
The chapters develop the underlying tools—linear operators, nonlinear approximation, probability, and convex optimization—and show how these tools lead to efficient algorithms.
The book also serves as a theoretical companion to the Numerical Tours (https://