Dynamics, Statistics and Projective Geometry of Galois Fields

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

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English

02 December 2010

Mathematics & Sciences; 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))
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 153mm, Spine: 1mm
Weight: 150g
ISBN: 9780521692908
ISBN 10: 0521692903
Publication Date: 02 December 2010
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Paperback
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.

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