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BK

Berkeley : MSRI Mathematical Sciences Research Institute ; Providence : American Mathematical Society, [2015]

vii, 158 stran : ilustrace ; 22 cm

ISBN 978-0-8218-9416-3 (brožováno)

MSRI mathematical circles library ; 16

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Obsahuje bibliografii na stranách 157-158

001643901

Preface to the English Translation v // Introduction 1 // Lecture 1. The Statistics of Topology and Algebra 3 // §1. Hilbert’s Sixteenth Problem 4 // §2. The Statistics of Smooth Functions 20 // §3. Statistics and the Topology of Periodic Functions and Trigonometric Polynomials 35 // §4. Algebraic Geometry of Trigonometric Polynomials 46 // Editor’s notes 55 // Lecture 2. Combinatorial Complexity and Randomness 59 // §1. Binary Sequences 60 // §2. Graph of the Operation of Taking Differences 64 // §3. Logarithmic Functions and Their Complexity 69 // §4. Complexity and Randomness of Tables of Galois Fields 74 // Editor’s notes 79 // Lecture 3. Random Permutations and Young Diagrams of Their // Cycles 83 // §1. Statistics of Young Diagrams of Permutations of Small // Numbers of Objects 85 // §2. Experimentation with Random Permutations of Larger Numbers of Elements 92 // §3. Random Permutations of p2 Elements Generated by // Galois Fields 96 // §4. Statistics of Cycles of Fibonacci Automorphisms 97 // Editor’s notes 106 // Lecture 4. The Geometry of Frobenius Numbers for Additive // Semigroups 111 // §1. Sylvester’s Theorem and the Frobenius Numbers 112 // §2. Trees Blocked by Others in a Forest 115 // §3. The Geometry of Numbers 117 // §4. Upper Bound Estimate of the Frobenius Number 121 // §5. Average Values of the Frobenius Numbers 132 // §6. Proof of Sylvester’s Theorem 135 // §7. The Geometry of Continued Fractions of Frobenius Numbers 137 // §8. The Distribution of Points of an Additive Semigroup on the Segment Preceding the Frobenius Number 148 // Editor’s notes 154 // Bibliography 157