Math Department (Thesis/2012-13)

# Commuting Polynomials

## Under the direction of: Karl Zimmermann

It is well known that polynomials commute under addition and multiplication, but not (necessarily) under composition of functions. In fact, you may have to think for a while before finding an example of two distinct polynomials, $f(x) and g(x)$, for which $f\big(g(x)\big) = g\big(f(x)\big)$. For this topic, the goal is to find examples of commuting polynomials and to learn about the properties these polynomials satisfy.

For a one-term thesis, the only prerequisite is Math 199. For a two-term thesis, it would be helpful (but not essential) to have taken Math 330.

 Math Department web pages Created: 25 Apr 2003 Last modified: 30 Apr 2012 14:08:36 Comments to: math@union.edu