Dynamics, Statistics and Projective Geometry of Galois Fields

Erscheinungsjahr 2010
ISBN: 978-0-521-69290-8
Verlag: Cambridge University Press

Buch, Englisch, 90 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 148 g

• Written by one of the greatest mathematicians of our age
• Provides a general overview suitable for mathematicians at all levels
• Examples and explanations may be used in all applications of Galois field theory
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.

Autoren/Hrsg.

Arnold, V. I.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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.

Über Autor(innen)

Arnold, V. I.
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.