Synopses & Reviews
With a refreshingly contemporary approach, Alternate Realities: Mathematical Models of Nature and Man brings together many of the strands of modern dynamical system theory for an incisive treatment of the theory and practice of mathematical modeling. The focus is on going from the observed behavior of natural and human systems to the development of formal mathematical models of such behavior. The book probes these problems in a "user-friendly" mathematical environment. The chapters discuss model-making in biology, cognitive processes, ecological and natural resource systems, fluid flow, evolution, artistic forms, games of chance and other engaging, real-world topics. These subjects are approached using such system-theoretic concepts as complexity, self-organization, adaptation, bifurcation, resilience, surprise, and uncertainty, together with other mathematical structures. Discussion questions, problems, and exercises follow each chapter, reinforcing and amplifying the concepts considered. Extensive notes and references are also included for every chapter. For teachers, students, and researchers in mathematical modeling and/or general applied mathematics, Alternate Realities: Mathematical Models of Nature and Man presents an exciting and refreshing approach to capturing the processes of nature and man in formal mathematical terms.
Praise for Alternate Realities Mathematical Models of Nature and Man "
covers the major topics completely and accurately within the context of current knowledge. Indeed, to my knowledge, there is no book which does so nearly as completely and well." George Leitmann, University of California, Berkeley "Surveys an extensive amount of modern mathematics
introduces and outlines some of these basic modern ideas for the non-specialist." Donald G. Saari, Northwestern University "A sophisticated and modern text on mathematical modelling
much more comprehensive than any of its competitors currently on the market." George Klir, State University of New York at Binghamton "Castis approach is fearless in constructing conceptual mappings between reality and mathematical notions. The book is pioneering in nature." Myron B. Allen, University of Wyoming
An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
About the Author
About the author John L. Casti is a Professor at the Institute for Econometrics, Operations Research, and System Theory at the Technical University of Vienna, Austria. He is the author or editor of nine books, including, most recently, Linear Dynamical Systems and Paradigms Lost: Conflicting Visions of Reality in Modern Science, a science book for the general reader. In addition, he has published over 70 research papers. Professor Casti received his PhD in mathematics from the University of Southern California, Los Angeles, in 1970.
Table of Contents
The Ways of Modelmaking: Natural Systems and Formal Mathematical Representations.
Pattern and the Emergence of Living Forms: Cellular Automata and Discrete Dynamics.
The Analytical Engine: A Newtonian View of Brains, Minds and Mechanisms.
Catastrophes and Life: The Singularities of Ecological and Natural Resource Systems.
Order in Chaos: Turbulence and Pattern in the Flow of Fluids, Populations and Money.
Strategies for Survival: Competition, Games and the Theory of Evolution.
Taming Nature and Man: Control, Anticipation and Adaptation in Social and Biological Processes.
The Geometry of Human Affairs: Connective Structure in Art, Literature and Games of Chance.
How Do We Know?: Myths, Models and Paradigms in the Creation of Beliefs.
Problems and Exercises.
Notes and References.