# The Quadratic Equation and Why Secondary Ed Students Should Take Abstract Algebra

## Andrew Coppola

### Department of Mathematics

### University of Illinois at Chicago

Partly as a motivating framework, partly propaganda from a practicing
logician, we will discuss the importance of axiomatic systems in the upper
level courses and their particular relevance to students in secondary
education. On a simple level, the axiomatic definitions of algebra give a
framework to compare and contrast differences between objects like the
integers and rationals. But they also explain some often confounding
questions, like why can't we divide by zero? A nuanced understanding of
number systems can only come from considering their salient features.