Herb Kunze - Böcker

The fields of Artificial Intelligence (AI) and Machine Learning (ML) have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between mathematics and AI/ML and provides an overview of the current research streams.Engineering Mathematics and Artificial Intelligence: Foundations, Methods, and Applications discusses the theory behind ML and shows how mathematics can be used in AI. The book illustrates how to improve existing algorithms by using advanced mathematics and offers cutting-edge AI technologies. The book goes on to discuss how ML can support mathematical modeling and how to simulate data by using artificial neural networks. Future integration between ML and complex mathematical techniques is also highlighted within the book.This book is written for researchers, practitioners, engineers, and AI consultants.

The fields of Artificial Intelligence (AI) and Machine Learning (ML) have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between mathematics and AI/ML and provides an overview of the current research streams.Engineering Mathematics and Artificial Intelligence: Foundations, Methods, and Applications discusses the theory behind ML and shows how mathematics can be used in AI. The book illustrates how to improve existing algorithms by using advanced mathematics and offers cutting-edge AI technologies. The book goes on to discuss how ML can support mathematical modeling and how to simulate data by using artificial neural networks. Future integration between ML and complex mathematical techniques is also highlighted within the book.This book is written for researchers, practitioners, engineers, and AI consultants.

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters.  For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises.  This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences.  Herb Kunze is a professor of mathematics at the University of Guelph in Ontario.  Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan.   Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia.  Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo inOntario.  The major focus of their research is on fractals and the applications of fractals.

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters.  For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises.  This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences.  Herb Kunze is a professor of mathematics at the University of Guelph in Ontario.  Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan.   Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia.  Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo inOntario.  The major focus of their research is on fractals and the applications of fractals.

This book focuses on the recent development of methodologies and computation methods in mathematical and statistical modelling, computational science and applied mathematics.

This book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences.

This book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences.

This proceedings volume features a selection of peer-reviewed papers presented at the 6th AMMCS-International Conference on Applied Mathematics, Modeling, and Computational Science, held in Waterloo, Canada, from August 14–18, 2023.

Focusingon five main groups of interdisciplinary problems, this book covers a widerange of topics in mathematical modeling, computational science and appliedmathematics. It presents a wealth of new results in the development of modelingtheories and methods, advancing diverse areas of applications and promotinginterdisciplinary interactions between mathematicians, scientists, engineersand representatives from other disciplines.Thebook offers a valuable source of methods, ideas, and tools developed for avariety of disciplines, including the natural and social sciences, medicine,engineering, and technology. Original results are presented on both thefundamental and applied level, accompanied by an ample number of real-worldproblems and examples emphasizing the interdisciplinary nature and universalityof mathematical modeling, and providing an excellent outline of today’schallenges. Mathematical modeling,with applied and computational methods and tools, plays a fundamental role inmodern science and engineering. It provides a primary and ubiquitous tool inthe context making new discoveries, as well as in the development of newtheories and techniques for solving key problems arising in scientific andengineering applications.Thecontributions, which are the product of two highly successful meetingsheld jointly in Waterloo, Ontario, Canada on the main campus of Wilfrid LaurierUniversity in June 2015, i.e. the International Conference on AppliedMathematics, Modeling and Computational Science, and the Annual Meeting of theCanadian Applied and Industrial Mathematics (CAIMS), make the book a valuable resource for any reader interestedin a broader overview of the methods, ideas and tools involved in mathematicaland computational approaches developed for other disciplines, including thenatural and social sciences, engineering and technology.

Focusingon five main groups of interdisciplinary problems, this book covers a widerange of topics in mathematical modeling, computational science and appliedmathematics. It presents a wealth of new results in the development of modelingtheories and methods, advancing diverse areas of applications and promotinginterdisciplinary interactions between mathematicians, scientists, engineersand representatives from other disciplines.Thebook offers a valuable source of methods, ideas, and tools developed for avariety of disciplines, including the natural and social sciences, medicine,engineering, and technology. Original results are presented on both thefundamental and applied level, accompanied by an ample number of real-worldproblems and examples emphasizing the interdisciplinary nature and universalityof mathematical modeling, and providing an excellent outline of today’schallenges. Mathematical modeling,with applied and computational methods and tools, plays a fundamental role inmodern science and engineering. It provides a primary and ubiquitous tool inthe context making new discoveries, as well as in the development of newtheories and techniques for solving key problems arising in scientific andengineering applications.Thecontributions, which are the product of two highly successful meetingsheld jointly in Waterloo, Ontario, Canada on the main campus of Wilfrid LaurierUniversity in June 2015, i.e. the International Conference on AppliedMathematics, Modeling and Computational Science, and the Annual Meeting of theCanadian Applied and Industrial Mathematics (CAIMS), make the book a valuable resource for any reader interestedin a broader overview of the methods, ideas and tools involved in mathematicaland computational approaches developed for other disciplines, including thenatural and social sciences, engineering and technology.