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Advanced Methods in Mathematics and Data Science: Concepts and Applications provides a comprehensive guide to topics in which mathematical modelling and applications play a pivotal role, including computational models in physics and chemistry, statistical models in life science, data analysis in engineering, as well as finance and social science applications. The book provides a clear and step-by-step presentation of advanced mathematical methods at the intersection of machine learning, artificial intelligence, big data analytics, and statistics, including control theory, topology, and nonlinear dynamic systems. The book progresses from concepts and foundational methods in the early chapters, to inter-disciplinary applications in computational mathematics, mathematical biology, fractional calculus, nonlinear dynamical systems, and data-driven optimization. The methods used to analyze data using a particular computational model are thoroughly explained through real-world and publicly available data sets. Examples of real-world data sets from a variety of academic disciplines are provided so that a wide audience can learn to analyze data in their research. The book provides tips, recommendations, and strategies to troubleshoot common issues, as well as definitions of key terms. The book helps readers enhance their conceptual understanding and practical application of computational methods to real-world data sets, and enables readers to gain competency at the intersection of advanced mathematics and AI, which is an important skill in today’s data-driven market.Presents the concepts of computational mathematics, control theory, topology, fractional calculus, and nonlinear dynamical systems in conjunction with data science methods such as AI, Machine Learning, computational statistics, big data analytics, optimization, and data-driven decision makingProvides readers with conceptual understanding and practical application of computational models to real-world data sets, along with methods for the worked examplesAddresses topics where mathematical modelling and applications play a pivotal role, including computational models in physics and chemistry, statistical models in life science, analysis in science and engineering, as well as finance and social science methods