## The Unreasonable Effectiveness of Number TheoryThis book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of applications of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications. |

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### Contents

The Unreasonable Effectiveness of Number Theory in Physics Communication and Music | 1 |

The Reasonable and Unreasonable Effectiveness of Number Theory in Statistical Mechanics | 21 |

Number Theory and Dynamical Systems | 35 |

The Mathematics of Random Number Generators | 73 |

Cyclotomy and Cyclic Codes | 91 |

Number Theory in Computer Graphics | 105 |

### Common terms and phrases

add-with-carry additive continued fraction algebraic algorithm Amer analytic Arnol'd atomic Baxter chain code codes of length coefficients completely integrable computer graphics concert hall acoustics congruential constructed continued fraction coordinates cosets curve cyclic codes cyclic shift cyclotomic cosets dimension Diophantine Diophantine approximation discrete duadic codes dynamical systems editor Effectiveness of Number equation ergodic theory error-correcting codes even-like example exist Farey series Farey shift Farey tree Figure finite Fourier transform Freeman approximation function Galois sequences Gauss Gauss map GF(q half-Freeman Hamiltonian systems Hamming code Hard Hexagon model idempotent integer invariant circles iterates lagged-Fibonacci lattice points linear Marsaglia Math mathematics matrix mode-locking modulus motion multiplier number theory odd-like orbits partitions period permutations Phys polynomial prime problem properties quadratic residues quasicrystals random number rational rotation number seed values segment self-dual codes self-orthogonal square structure substitution rules symbolic dynamics Theorem tilings Unreasonable Effectiveness weight York