"Casti Tours offers the most spectacular vistas of modern applied mathematics" a Nature
Mathematical modeling is about rulesa 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 languagea in the form of mathematical models of real-world phenomenaa that researchers use today to frame their views of reality.

Moving from the irreducible...

"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...

This Set contains: Reality Rules, Picturing the World in Mathematics, Volume 1, The Fundamentals by John Casti; Reality Rules, Picturing the World in Mathematics, Volume 2, The Frontier by John Casti

Kurt Godel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Godel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Godel's eccentricities, his close...

Der Lebensnerv aller intellektuellen und wissenschaftlichen Bestrebungen ist der standige Zustrom wichtiger, ungeloster, aber im Prinzip losbarer Probleme. Die projektive Geometrie zum Beispiel war fruher eine bluhende Ecke im mathemati schen Garten. Heute jedoch ist sie nicht mehr modern - einfach weil die Quelle wichtiger Probleme vor etwa hundert Jahren versiegte. Fur die heute so populare Chaostheorie dagegen interessierte sich vor einigen Jahrzehnten nur eine Handvoll weitsichtiger Abenteurer und Kenner des mathematisch Geheimnisvollen, bevor in jungerer Zeit die Arbeiten von Lorenz,...

Since the beginning of the fifties, the ruling paradigm in the discipline of economics has been that of a competitive general equilibrium. Associated dynamic analyses have therefore been preoccupied with the stability of this equilibrium state, corresponding simply to studies of comparative statics. The need to permeate the boundaries of this paradigm in order to open up new pathways for genuine dynamic analysis is now pressing. The contributions contained in this volume spring from this very ambition. A growing circle of economists have recently been inspired by two distinct but...

In May 1984 the Swedish Council for Scientific Research convened a small group of investigators at the scientific research station at Abisko, Sweden, for the purpose of examining various conceptual and mathematical views of the evolution of complex systems. The stated theme of the meeting was deliberately kept vague, with only the purpose of discussing alternative mathematically based approaches to the modeling of evolving processes being given as a guideline to the participants. In order to limit the scope to some degree, it was decided to emphasize living rather than nonliving processes and...

Der Lebensnerv aller intellektuellen und wissenschaftlichen Bestrebungen ist der standige Zustrom wichtiger, ungeloster, aber im Prinzip losbarer Probleme. Die projektive Geometrie zum Beispiel war fruher eine bluhende Ecke im mathemati- schen Garten. Heute jedoch ist sie nicht mehr modern - einfach weil die Quelle wichtiger Probleme vor etwa hundert Jahren versiegte. Fur die heute so populare Chaostheorie dagegen interessierte sich vor einigen Jahrzehnten nur eine Handvoll weitsichtiger Abenteurer und Kenner des mathematisch Geheimnisvollen, bevor in jungerer Zeit die Arbeiten von Lorenz,...