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Experimental mathematics / V.I. Arnold ; translated by Dmitry Fuchs and Mark Saul.
Math/Physics/Astronomy Library QA9 .A7613 2015
Available
- Format:
- Book
- Author/Creator:
- Arnolʹd, V. I. (Vladimir Igorevich), 1937-2010.
- Series:
- MSRI mathematical circles library ; 16.
- MSRI mathematical circles library ; 16
- Standardized Title:
- Eksperimentalnoe nablyudenie matematicheskikh faktov. English
- Language:
- English
- Russian
- Subjects (All):
- Experimental mathematics.
- Geometry, Algebraic.
- Combinatorial analysis.
- Functions.
- Physical Description:
- vii, 158 pages ; 22 cm.
- Place of Publication:
- Berkeley, California : MSRI Mathematical Sciences Research Institute ; Providence. Rhode Island : American Mathematical Society, [2015]
- Language Note:
- Translated from the Russian.
- Contents:
- Lecture 1. The statistics of topology and algebra. Hilbert's sixteenth problem
- The statistics of smooth functions
- Statistics and the topology of periodic functions and trigonometric polynomials
- Algebraic geometry of trigonometric polynomials
- Lecture 2. Combinatorial complexity and randomness. binary sequences
- Graph of the operation of taking differences
- Logarithmic functions and their complexity
- Complexity and randomness of tables of Galois Fields
- Lecture 3. Random permutations and young diagrams of their cycles. Statistics of young diagrams of permutations of small number of objects
- Experimentation with random permutations of larger numbers of elements
- Random permutations of p² elements generated by Galois fields
- Statistics of cycles of Fibonacci automorphisms
- Lecture 4. The geometry of Frobenius numbers for additive semigroups. Sylvester's theorem and the Frobenius numbers
- Trees blocked by others in a forest
- The geometry of numbers
- Upper bound estimate of the Frobenius number
- Average values of the Frobenius numbers
- Proof of Sylvester's theorem
- The geometry of continued fractions of Frobenius numbers
- The distribution of points of an additive semigroup on the segment preceding the Frobenius number.
- Notes:
- Includes bibliographical references.
- ISBN:
- 9780821894163
- 0821894161
- OCLC:
- 904801193
- Publisher Number:
- 99968466329
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