Applications of Finite Sets
Texas A&M Mathematics Masters Program
Final Oral Exam
Jeremy Knight

In many mathematical applications, it is valuable to consider finite sets to control outcomes, allow approximation, and provide valuable structure to processes and algorithms.  The goal of this presentation is to explore the impact of finite structures in the study and application of cryptography, partial differential equations (PDEs) and statistics. 

We will begin by examining the important role that finite fields have in the Advanced Encryption Standard (AES): Rijndael, and error-correcting codes.  In the application of PDEs, we often seek a numerical solution through the use of finite approximations when analytic solutions are not available.  The field of Differential Galois Theory also employs the use of finite fields extensively.  Finally, we will see the application of finite groups in the construction of statistical studies using  factorial designs.

Presentation Links:

MATLAB files:

  • binxor.m - XOR of two binary strings
  • binmult.m - multiplies two binary strings
  • bindiv.m - divides two binary strings
  • bin2poly.m - converts a binary number to its corresponding polynomial
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