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Mathematical Methods in Data Science 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 to demonstrate advanced mathematics, in particular, data-driven differential equations used. Chapters also cover network analysis, ordinary and partial differential equations based on recent published and unpublished results. Finally, 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.
There are a number of books on mathematical methods in Data Science. Currently, all these related books primarily focus on linear algebra, optimization and statistical methods. However, network analysis, ordinary and partial differential equation models play an increasingly important role in Data Science.
Data Science is an interdisciplinary field that aims to use scientific approaches to extract meaning and insights from data. Today almost all kinds of organizations are generating exponential amounts of data. A closely related and overlapping field, Machine Learning, uses computer algorithms to find patterns and features in massive amounts of data in order to make decisions and predictions. To be able to truly understand data science and machine learning, it is important to appreciate the underlying mathematics and statistics, as well as computing algorithms. Mathematical knowledge in linear algebra, calculus, optimization, probability, and statistics is essential for data science. For historical reasons, courses in data science and machine learning tend to be taught in statistical and computer science departments, where the emphasis is on statistics and computer algorithms.
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.
Preface
Linear algebra
Probability
Calculus and optimization
Network analysis
Ordinary differential equations
Partial differential equations