<p>mathboy98, that brings up an interesting topic. How do you explain a non-math-person what abstract math is about? I have had my own problems explaining younger math majors what abstract algebra is in a non-intimidating way. I have tried using modular arithmetic to get to the idea of an algebraic structure, but maybe the vector space approach works better because students are already familiar with it. The problem is that our linear algebra course does not really go into the abstraction of a vector space. It feels more like a course on matrix arithmetic. Maybe use matrices as an example of a group or a ring? Or on an even lower level, the integers vs the rationals?</p>
<p>If you know a good way of explaining abstract algebra that makes students actually want to take it, please let me now :)</p>