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Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling
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A Quest Towards a Mathematical Theory of Living Systems (Hardcover, 1st ed. 2017)
Loot Price: R2,967
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A Quest Towards a Mathematical Theory of Living Systems (Hardcover, 1st ed. 2017)
Series: Modeling and Simulation in Science, Engineering and Technology
Expected to ship within 10 - 15 working days
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This monograph aims to lay the groundwork for the design of a
unified mathematical approach to the modeling and analysis of
large, complex systems composed of interacting living things.
Drawing on twenty years of research in various scientific fields,
it explores how mathematical kinetic theory and evolutionary game
theory can be used to understand the complex interplay between
mathematical sciences and the dynamics of living systems. The
authors hope this will contribute to the development of new tools
and strategies, if not a new mathematical theory. The first chapter
discusses the main features of living systems and outlines a
strategy for their modeling. The following chapters then explore
some of the methods needed to potentially achieve this in practice.
Chapter Two provides a brief introduction to the mathematical
kinetic theory of classical particles, with special emphasis on the
Boltzmann equation; the Enskog equation, mean field models, and
Monte Carlo methods are also briefly covered. Chapter Three uses
concepts from evolutionary game theory to derive mathematical
structures that are able to capture the complexity features of
interactions within living systems. The book then shifts to
exploring the relevant applications of these methods that can
potentially be used to derive specific, usable models. The modeling
of social systems in various contexts is the subject of Chapter
Five, and an overview of modeling crowd dynamics is given in
Chapter Six, demonstrating how this approach can be used to model
the dynamics of multicellular systems. The final chapter considers
some additional applications before presenting an overview of open
problems. The authors then offer their own speculations on the
conceptual paths that may lead to a mathematical theory of living
systems hoping to motivate future research activity in the field. A
truly unique contribution to the existing literature, A Quest
Toward a Mathematical Theory of Living Systems is an important book
that will no doubt have a significant influence on the future
directions of the field. It will be of interest to mathematical
biologists, systems biologists, biophysicists, and other
researchers working on understanding the complexities of living
systems.
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