Reality Rules, 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 o 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 inmeaningful 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.

Advance acclaim for Reality Rules... " A first rate text, up-to-date and provocative, written by a master modeler, expositor and critic of the methodology of modeling." -- Philip J. Davis Coauthor, The Mathematical Experience " Along with a fascinating variety of models and mathematics, Casti has added a generous supply of workable exercises, making Reality Rules a realistic classroom text as well as a great read." -- Reuben Hersh Professor of Mathematics University of New Mex Alternate Realities Mathematical Models of Nature and Man John L. Casti A thoroughly modern account of the theory and practice of mathematical modeling with a treatment focusing on system-theoretic concepts such as complexity, self-organization, adaptation, bifurcation, resilience, surprise and uncertainty, and the mathematical structures needed to employ these in a formal system. Includes extensive problem sets and discussion questions. " Surveys an extensive amount of modern mathematics... introduces and outlines some of these basic modern ideas for the nonspecialist." -- Donald G. Saari Northwestern University " Casti' s approach is fearless in constructing conceptual mappings between reality and mathematical notions. The book is pioneering in nature." -- Myron B. Allen University of Wyoming 1989 (0 471-61842-X) 493 pp.