近些年来，深度学习在很多领域得到了成功应用。本文旨在研究深度学习方法获得广泛成功运用背后的数理支撑，本质是关于深度学习数理原理总结的读书笔记。文章从深度学习定义出发，描述了深度学习涉及的数学方法和统计方法，概述了深度学习中神经网络的操作流程以及在训练过程中运用到的三种核心算法，详细阐释了三种核心算法计算流程中运用到的激活函数和损失函数。此外，论文探究了循环式神经网络的数学原理。本次总结学习加深了作者对深度学习方法的理解，提升了作者运用机器学习方法解决实际问题的实战能力。

In recent years, deep learning has been successfully applied in many fields. The aim of this article is to investigate the mathematical underpinnings behind the widely successful use of deep learning methods, and is essentially a reading note on a summary of the mathematical principles of deep learning. Starting from the definition of deep learning, the article describes the mathematical and statistical methods involved in deep learning, outlines the operational process of neural networks in deep learning and the three core algorithms used in the training process, and explains in detail the activation and loss functions used in the computational process of the three core algorithms. In addition, the paper explores the mathematical principles of recurrent neural networks. This summary study deepens the authors' understanding of deep learning methods and enhances their practical ability to apply machine learning methods to solve real-world problems.