Date of Award
Summer 2020
Degree Type
Thesis
Department
Mathematics
First Advisor
Justin Brown
Abstract
We provide a brief but intuitive study on the subjects from which Galois Fields have emerged and split our study up into two categories: harmony and chaos. Specifically, we study finite fields with elements where is prime. Such a finite field can be defined through a logarithm table. The Harmony Section is where we provide three proofs about the overall symmetry and structure of the Galois Field as well as several observations about the order within a given table. In the Chaos Section we make two attempts to analyze the tables, the first by methods used by Vladimir Arnold as well as (what we believe is) an improvement of his method, the second by statistical analysis of the Galois Fields at , the highest prime value we were able to generate Galois Fields of size for.
Recommended Citation
Schaffner, Drew, "Harmony Amid Chaos" (2020). Pence-Boyce STEM Student Scholarship. 13.
https://digitalcommons.olivet.edu/pence_boyce/13
Included in
Algebra Commons, Algebraic Geometry Commons, Geometry and Topology Commons, Number Theory Commons, Other Mathematics Commons, Other Statistics and Probability Commons, Set Theory Commons, Statistical Theory Commons