Mathematical Methods in Data Science covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probability and differential equations. Based on the authors’ recently published and previously unpublished results, this book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for data analysis and prediction. With data science being used in virtually every aspect of our society, the book includes examples and problems arising in data science and the clear explanation of advanced mathematical concepts, especially data-driven differential equations, making it accessible to researchers and graduate students in mathematics and data science. Combines a broad spectrum of mathematics, including linear algebra, optimization, network analysis and ordinary and partial differential equations for data science - Written by two researchers who are actively applying mathematical and statistical methods as well as ODE and PDE for data analysis and prediction - Highly interdisciplinary, with content spanning mathematics, data science, social media analysis, network science, financial markets, and more - Presents a wide spectrum of topics in a logical order, including probability, linear algebra, calculus and optimization, networks, ordinary differential and partial differential equations "This book is an interesting introduction to mathematical methods for data science. It covers ordinary differential equations and partial differential equations, and this is a main feature that distinguishes the book from others. The first chapters start gently to build some mathematical background on linear algebra, probability, calculus, and optimization. In the fourth chapter, the book presents real-world use of these mathematical tools for network analysis. Then the book goes deeper into the subject and discusses the methodologies of ordinary differential equations and partial differential equations, as well as their applications. Overall, the book is suitable for advanced undergraduate and beginning graduate students interested in mathematical data science methods." --Liangzu Peng, zbMATHOpen Introduces a new approach to integrate big data into the framework of ordinary and partial differential equations for data analysis and prediction Data science is built on top of mathematics. This book covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probability and differential equations. The book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for data analysis and prediction. The mathematics is accompanied with examples and problems arising in data science and demonstrate advanced mathematics, in particular, data-driven differential equations are useful in data science. There are a number of books on mathematical methods in data science. Currently all these related books primarily focus on linear algebra, optimization, statistical methods. However, network analysis, ordinary and partial differential equation models play an increasingly important role in data science. For example, ordinary differential equation models, for example, SIR models, have been extensively used for infectious disease modelling and prediction. With the availability of unprecedented amount of clinical, epidemiological and social COVID-19 data, data-driven differential equation models have become more useful for infection prediction and analysis with mitigation measures and vaccination. The three chapters for network analysis, ordinary and partial differential equations are based on some recent published and unpublished results by the authors in recent years. This book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for data analysis and prediction. She received the Ph.D. degree in applied mathematics from Beijing Institute of Technology, Beijing, China, in 2004. Her research interests include data science, applied mathematics, and applied statistics. She conducted five Projects of National Nature Science Foundation of China, one Alexander von Humboldt Fellowship for Experienced Researcher, and five Provincial Projects. She has published numerous articles in scholarly journals, such as Acta Mater.、Appl. Phys. Lett.、IEEE Trans. SMC、Infor. Sci.、J. Stat. Phys.、J. Nonlinear Sci.、 Phys. Rev. B、Phys. Rev. E、Sci. China Math.、Sci. China Phys. and Sci. China Mater., etc. He completed his doctorate in mathematics, while also earning a master's degree in computer science at Michigan State University in 1997. He worked as a full-time software engineer in industry for almost ten years before joining Arizona State University. Dr. Wang’s research interests include