Enhanced descriptions from Syndetics:

"Casti is one of the great science writers." -San Francisco Examiner
"Casti's gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." -Christian Science Monitor
Following up the acclaimed Five Golden Rules, another quintet of gleaming math discoveries
With Five More Golden Rules, readers are treated to another fascinating set of theoretical gems from acclaimed popular science author John Casti. Injecting all-new ingredients into his trademark recipe of real-world examples, historical anecdotes, and straightforward explanations, Casti once again brings math to thrilling life. All who enjoyed the unique pleasures of the original will love this follow-up survey highlighting the creme de la creme of math in the last century.
Explores how knot theory informs the classic tale of Alexander the Great and the Gordian Knot
* Considers how the Shannon Coding Theory applies to decoding the human genome
John L. Casti, PhD (Santa Fe, NM), a resident member of the Santa Fe Institute, is a professor at the Technical University of Vienna and the author of Would-Be Worlds (Wiley) and Cambridge Quintet.

Table of contents provided by Syndetics

• Chapter 1 The Alexander Polynomial: Knot Theory (p. 1)
• Knot History, Mathematics
• Have Knot, Will Unravel
• What Color Is Your Knot?
• Unwinding DNA
• Alexander's Great Invariant
• Getting Physical
• All Tangled Up
• Appendix Knots and Energy
• Chapter 2 The Hopf Bifurcation Theorem: Dynamical System Theory (p. 35)
• What Is a Dynamical System?
• In the Long Run
• Stability
• At the Center of Things
• Forks in the Flow
• Gradient Dynamical Systems and Elementary Catastrophes
• A Strangeness in the Attraction
• Up, Up, Down and Away
• The Lyapunov Exponents
• Chaos among the Planets
• The Correlation Dimension
• Gold Bugs and Efficient Markets
• Domains of Attraction
• A Mountain Is Not a Cone and a Cloud Is Not a Sphere
• Computing the Fractal Dimension
• The Fractal Dimension of a River Basin
• Bach and Fractal Music
• Fractals and Domains of Attraction
• Chapter 3 The Kalman Filter: Control Theory (p. 101)
• Looking for Life
• Can You Get There from Here?
• The Problem of Reachability
• The Problem of Observation
• Complete Observability
• Duality
• A Nonlinear Interlude
• Sharks and Minnows
• Linear Stability Analysis
• What's Best?
• The Pontryagin Minimum Principle
• Feedback Control and Dynamic Programming
• The Minimum Principle versus Dynamic Programming
• Getting the Best of It
• State Estimation
• The Kalman Filter
• Duality--Yet Again
• Chapter 4 The Hahn-Banach Theorem: Functional Analysis (p. 155)
• The Big Picture
• Problems at Infinity
• The Tale of Two Coffee Houses
• Spaces and Functionals
• Minimum Distances and Maximum Profits
• The Other Side of a Space
• But Does It Exist?
• Big-Time Operators
• Quantum Mechanics and Functional Analysis
• The Importance of Being Nonlinear
• Chapter 5 The Shannon Coding Theorem: Information Theory (p. 207)
• Communication, Information, and Life
• Making Codes
• Huffing and Puffing and Squeezing the Message Down
• Symbols, Signals, and Noise
• If It Ain't Broken, Fix It Anyway
• The Information of the Genes
• Randomness, Information, and Computation
• Zipf Up That Lip
• Appendix Derivation of the Power Law Form of Zipf's Law
• References (p. 255)
• Index (p. 263)

Reviews provided by Syndetics

Publishers Weekly Review

The success of Paradigms Lost, Casti's 1989 survey of science's most compelling questions, made this successor and its title nearly inevitable. Unfortunately, the new book fails both as a complement and as a contrast to the earlier work. Like its predecessor, it transforms multifaceted scientific inquiry into the motif of an adversarial courtroom battle--a device that, though useful for framing the discussion and possessed of some entertainment value, inevitably produces a distorted picture of the evolution of scientific thought. Scientific progress is continually punctuated by breakthroughs that vault new areas of inquiry into the foreground and relegate others to the background realm of apparently resolved questions. Because of these shifts in scientific thought, not all the topics important in 1989 merit the same level of attention in 2000--and yet Casti insists on revisiting them. As a result, although he devotes a dull chapter to recapitulating old arguments about artificial intelligence, for example, he admits in those pages that "nothing of eyebrow-raising substance has really changed in the AI debate since the mid-1980s." The book's strongest chapter is its last, which discusses the peculiarities of the quantum mechanical world. Casti's fascinating discussion of new insights into the wave-particle duality of matter and energy might make readers wish he had written a book about new paradigms for a new millennium instead of this sometimes contrived and oft-contorted sequel. Illustrations. (Mar.) FYI: Also in March, Wiley will release the second volume of Casti's survey of math in the last century, Five More Golden Rules: Gordian Knots, Secret Codes, and the Importance of Being Nonlinear--More Great Theories of 20th-Century Mathematics, with illustrations ($27.95 256p ISBN 0-471-32233-4). (c) Copyright PWxyz, LLC. All rights reserved

Author notes provided by Syndetics

John L. Casti, Ph.D., is a professor at the Santa Fe Institute and the Technical University of Vienna.