This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural network theory. Serving as a guide for students and researchers in mathematics and related fields, the book aims to equip readers with foundational knowledge on the topic. It prioritizes simplicity over generality, and presents rigorous yet accessible results to help build an understanding of the essential mathematical concepts underpinning deep learning.

翻译：本书介绍了深度学习的数学分析基础。内容涵盖逼近理论、优化理论和统计学习理论中的基本结果，这三个领域构成了深度神经网络理论的三大支柱。作为数学及相关领域学生和研究者的指南，本书旨在为读者提供该主题的基础知识。全书注重简明性而非普适性，通过严谨而易于理解的结论，帮助读者建立对深度学习核心数学概念的基本认识。