Rational Numbers and Polynomials: The Complete Story

Susan Loepp
Department of Mathematics and Statistics, Williams College

Abstract: We will begin by briefly reviewing the technique of completing the rational numbers to obtain the reals. This will lead into the definition of a special distance function on polynomials, thus making it possible to define the completion of a set of polynomials. Examples of strange relationships between rather simple sets of polynomials and their completions will be discussed. Time permitting, we will discuss a few research results and/or open questions in the field.