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 Based on the authors' recently published and previously unpublished results, this book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations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

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 applied mathematics, data science, differential equations, online social networks. He has published numerous articles in scholarly journals and a book entitled, "Modeling Information Diffusion in Online Social Networks with Partial Differential Equations, Springer, 2020. Recently he developed and taught a course, Mathematical Methods in Data Science, at Arizona State University.

1. Linear Algebra 2. Probability 3. Calculus and Optimization 4. Network Analysis 5. Ordinary Differential Equations 6. Partial Differential Equations