Dynamics, Statistics and Projective Geometry of Galois Fields

V. I. Arnold (Université de Paris IX (Paris-Dauphine))

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English

Cambridge University Press
02 December 2010

Number theory; Geometry; Non-linear science

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.

By: V. I. Arnold (Université de Paris IX (Paris-Dauphine))
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 155mm, Spine: 10mm
Weight: 270g
ISBN: 9780521872003
ISBN 10: 0521872006
Pages: 90
Publication Date: 02 December 2010
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Dynamics, Statistics and Projective Geometry of Galois Fields

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