Mathematics of Data Science: A Comprehensive Book.

This publication, titled "Mathematics of Data Science," serves as a foundational textbook exploring the core mathematical principles essential for understanding and applying data science methodologies. The book is structured to guide readers through a wide array of topics, starting with an introduction to high-dimensional data challenges and opportunities. Key areas covered include fundamental linear algebra concepts like Singular Value Decomposition (SVD) and Principal Component Analysis (PCA), various regression techniques, and the mathematics behind graphs, networks, and clustering algorithms. It also delves into advanced topics such as nonlinear dimension reduction, optimization methods crucial for machine learning, and classification techniques. Furthermore, the book provides a mathematical introduction to deep learning, explores large sample limits of graph Laplacians, and covers advanced statistical concepts like concentration of measure, Gaussian analysis, matrix concentration inequalities, compressive sensing, and low-rank matrix recovery. This comprehensive scope makes it a valuable resource for anyone seeking a deep theoretical understanding of data science.