Reality Rules Picturing the World in Mathematics--The Frontier

Mathematical modeling is about rules-the rules of reality. Reality Rules explores the syntax and semantics of the language in which these rules are written, the language of mathematics. Characterized by the clarity and vision typical of the author's previous books, Reality peting dialects of this language-in the form of mathematical models of real-world phenomena-that researchers use today to frame their views of reality. Moving from the irreducible basics of modeling to the upper reaches of scientific and philosophical speculation, Volumes I and II, The Fundamentals and The Frontier, are ideal complementary texts, equally matched in difficulty, yet unique in their coverage of issues central to the contemporary modeling of complex systems. The Frontier introduces a number of application areas and/or associated techniques of modeling that complement the ideas presented in The Fundamentals. Chapter 5 shows how dynamical system theory and concepts from game theory can be brought together to shed new light on problems of population biology and ecology. This chapter also gives a mathematical account of the controversial problem of sociobiology. Chapter 6 introduces the notion of control system within the confines of linear processes. The ideas of reachability and observability are given special emphasis and used to illustrate how "good" models are constructed directly from observed data. Chapter 7 deals with the selection mechanism for inputs that,are chosen to maximize or minimize some measure of system performance, while Chapter 8 addresses the ways in which patterns in art, literature, and other fields outside of the natural sciences can be formulated in meaningful mathematical terms. Chapter 9 focuses on computation, showing why there is no difference between a computer program, a dynamical system, and a deductive logical system. The practical tutorial design of Reality Rules allows students to fully master conceptual material, while fostering creative thought. The end-of-section exercises within each chapter and the discussion questions and problems sections high-light key areas and enhance classroom and at home study. The book's many examples not only introduce new applications of theoretical results, but also illustrate how to use the theory in a wide array of realistic situations. A Solutions Manual is also available for instructional use and self-study. Lucidly written and handsomely illustrated, Reality Rules is a fascinating journey into the conceptual underpinnings of reality itself, one that examines the major themes in dynamical system theory and modeling and the issues related to mathematical models in the broader contexts of science and philosophy. Far-reaching and far-sighted, Reality Rules is destined to shape the thought and work of students, researchers and scholars in mathematics, science, and the social sciences for generations to come.Casti, John L. is the author of 'Reality Rules Picturing the World in Mathematics--The Frontier' with ISBN 9780471577980 and ISBN 0471577987.