Reality Rules, The Fundamentals (Wiley Professional: Reality Rules: Picturing the World in Mathematics) (Volume 1) (Paperback)

by John Casti (Author) "What do you think of when you hear the word "model"?..." (more)
Key Phrases: New York, Morse's Theorem, Academic Press (more...)

Editorial Reviews

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Solutions Manual available. -- The publisher, John Wiley & Sons --This text refers to the Paperback edition.

Product Description
"Casti Tours offers the most spectacular vistas of modern applied mathematics" —Nature

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 Rules is a window onto the competing 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 1 and 2, The Fundamentals and The Frontier, are ideal complements, equally matched in difficulty, yet unique in their coverage of issues central to the contemporary modeling of complex systems.

Engagingly 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 insight and work of students, researchers, and scholars in mathematics, science, and the social sciences for generations to come.

Of related interest . . .

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.

1989 0-471-61842-X 493pp.

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Product Details

• Paperback: 416 pages
• Publisher: Wiley-Interscience (March 27, 1997)
• Language: English
• ISBN-10: 0471184357
• ISBN-13: 978-0471184355
• Product Dimensions: 9.9 x 7 x 0.8 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
• Amazon.com Sales Rank: #2,670,684 in Books (See Bestsellers in Books)

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5.0 out of 5 stars Models of the world based on more abstract concepts such as automata and chaos, November 10, 2008

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

This review is from: Reality Rules, The Fundamentals (Volume 1) (Hardcover)

Mathematical models of the world are the toolset that we use to build everything, from the simplest machine to the largest skyscraper. For example, when a large and tall building is being planned, the foundations are laid based on the models for the type of soil, width of the building, the weight of the materials and the height. It is all constructed in model form before the first shovel lifts the first piece of dirt. The fact that it is a rare occasion when a building or anything else spontaneously comes crashing down demonstrates how sound our mathematical models are.
In this book, Casti presents some of the more recent and abstract models of the world, these models are not nearly as precise. These are not basic equations, but generally ideas regarding how models can be constructed. The chapters are:

*) The ways of model making: natural systems and formal mathematical representations - this chapter introduces the idea of a system being modeled by a set of states and transitions between those states in response to events.
*) Catastrophes, dynamics and life: the singularities of ecological and natural resource systems - this chapter covers the models for systems that reach cusps of dramatic change, such as populations of living creatures where the model contains cusps. The most interesting graph in this chapter is on page 131. It is a graph of Scottish witchcraft trials from 1600 to 1700 plotted so the graph is linear.
*) Pattern and the emergence of living forms: cellular automata and discrete dynamics - in this chapter the models of cellular and finite automata are presented and used to describe some types of biological activity.
*) Order in chaos- the mathematics of chaos theory are presented and used to describe some situations such as population cycles, free markets and the spread of disease.

As the contents of the chapters demonstrate, this is not a book on simple modeling; the topics require a degree of mathematical sophistication. However, if your interest is in these models of the world, then this is an excellent resource. There is a small set of exercises at the end of each section and larger sets of discussion questions and problems at the ends of the chapters.