Berlyand L. Mathematics of Deep Learning. An Introduction...2ed 2026

Textbook in PDF format

This course aims at providing a mathematical perspective to some key elements of the so-called deep neural networks (DNNs). Much of the interest on deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far. The book focuses on deep learning techniques and introduces them almost immediately. Other techniques such as regression and SVM are briefly introduced and used as a steppingstone for explaining basic ideas of deep learning. Throughout these notes, the rigorous definitions and statements are supplemented by heuristic explanations and figures. The book is organized so that each chapter introduces a key concept. When teaching this course, some chapters could be presented as a part of a single lecture whereas the others have more material and would take several lectures