Preface to the English Translation
Introduction
Lecture 1. The Statistics of Topology and Algebra
1. Hilbert's Sixteenth Problem
2. The Statistics of Smooth Functions
3. Statistics and the Topology of Periodic Functions and Trigonometric Polynomials
4. Algebraic Geometry of Trigonometric Polynomials
Editor's notes
Lecture 2. Combinatorial Complexity and Randomness
1. Binary Sequences
2. Graph of the Operation of Taking Differences
3. Logarithmic Functions and Their Complexity
4. Complexity and Randomness of Tables of Galois Fields
Editor's notes
Lecture 3. Random Permutations and Young Diagrams of Their Cycles
1. Statistics of Young Diagrams of Permutations of Small Numbers of Objects
2. Experimentation with Random Permutations of Larger Numbers of Elements
3. Random Permutations of p2 Elements Generated by Galois Fields
4. Statistics of Cycles of Fibonacci Automorphisms
Editor's notes
Lecture 4. The Geometry of Frobenius Numbers for Additive Semigroups
1. Sylvester's Theorem and the Frobenius Numbers
2. Trees Blocked by Others in a Forest
3. The Geometry of Numbers
4. Upper Bound Estimate of the Frobenius Number
5. Average Yalues of the Frobenius Numbers
6. Proof of Sylvester's Theorem
7. The Geometry of Continued Fractions of Frobenius Numbers
8. The Distribution of Points of an Additive Semigroup on the Segment Preceding the Frobenius Number
Editor's notes
Bibliography
