Mathematical Methods in Data Science

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three chapters for network analysis, ordinary and partial differential equations are based on some recent published and unpublished results by the authors in recent years.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. This book is the first of this king that combines a broad of mathematics including linear algebra, optimization, network analysis and ordinary and partial differential equations for data science. Its highly novel approach is based on network analysis to integrate ordinary and partial differential equations for data analysis and prediction Written by two researchers who are actively in applying mathematical, statistical methods as well as ODE and PDE for data analysis and prediction The book is highly interdisciplinary and its topics span among mathematics, data science, social media analysis, network science, financial markets and others. Data science is used in virtual every section of our society From pedagogical point of view, the book presents a wide spectrum of topics in a logical order. Specifically, probability, linear algebra, calculus and optimization, networks, ordinary differential and partial differential equations