## Five more golden rules: knots, codes, chaos, and other great theories of 20th century mathematics"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. |

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### Contents

What Is a Dynamical System? In the Long Run Stability | 95 |

Control Theory | 101 |

Linear Stability Analysis Whats Best? The Pontryagin Mini | 3 |

Copyright | |

4 other sections not shown

### Common terms and phrases

Alexander polynomial behavior bifurcation boundary called cell center manifold Center Manifold Theorem channel chaotic closed curve code words colors completely reachable complex plane compute control inputs crossing number crossing point defined denotes digits dimension domain of attraction dynamical system eigenvalues element energy entropy equation equilibrium point error example fractal functional analysis geometric given Hilbert space imaginary axis infinite-dimensional information theory initial inner product integer Julia set Kalman filter knot diagram knot invariant knot theory look Lyapunov exponent mathematical mathematicians matrix measure motion move noise nonlinear norm Note observable operator optimal origin parameters periodic orbits perturbation positive problem quantity random real numbers Reidemeister Reidemeister moves result scalar sequence Shannon's shown in Figure shows simple solution stable strange attractor subspace Suppose symbols Theorem trajectory trefoil knot turns unknot unstable vector field vector field v(x vector space zero