Date of Submission

Fall 2012

Academic Program

Mathematics

Project Advisor 1

John Cullinan

Abstract/Artist's Statement

The objective of this project is to investigate how polynomials with rational coefficients and their iterates behave modulo p where p is a prime number. The project integrates Number Theory, Galois Theory, Dynamical Systems and Calculus Theory and it makes extensive use of programming. We state conjectures on how an iterated polynomial behaves modulo prime numbers and we explain most of this behavior by examining the role of the discriminant on the iterates of postcritically finite polynomials and the Galois group of the second iterate of these polynomials.

Distribution Options

Access restricted to On-Campus only

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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