I'm currently studying the theory of Galois fields. And I have a question, what practical usage of this finite fields?
As stated in Wikipedia:
Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, coding theory and Quantum error correction.
And what the other usage? I heard it used extensively in the image processing and recognition.
Finite fields are extensively used in design of experiments, an active research area in statistics that began around 1920 with the work of Ronald Fisher. Fisher was a major pioneer in the theory of statistics and one of the three major founders of population genetics.
I've heard of the use of finite fields in scheduling tournaments. Problems in that area may be the same mathematical problems as some of those that occur in design of experiments.