Dynamics, Statistics and Projective Geometry of Galois Fields

by V. I. Arnold

Overview

V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Product Details

ISBN-13:	9780521872003
Publisher:	Cambridge University Press
Publication date:	12/02/2010
Pages:	90
Product dimensions:	5.90(w) x 9.00(h) x 0.40(d)

About the Author

V. I. Arnold is Professor of Mathematics at the Université de Paris IX (Paris-Dauphine) and the Steklov Mathematical Institute in the Russian Academy of Sciences.

Table of Contents

Preface; 1. What is a Galois field?; 2. The organisation and tabulation of Galois fields; 3. Chaos and randomness in Galois field tables; 4. Equipartition of geometric progressions along a finite one-dimensional torus; 5. Adiabatic study of the distribution of geometric progressions of residues; 6. Projective structures generated by a Galois field; 7. Projective structures: example calculations; 8. Cubic field tables; Index.

Editorial Reviews

"Throughout, Arnold's characteristic style of writing and thinking are evident. Ideas, intuitions, and well-presented examples abound, joined in only a few places by formal proofs... students and working mathematicians will find it accessible, provoctive, and maybe even inspiring."
Rafe Jones, Mathematical Reviews

From the Publisher