Hi all,

I'm a grad student and just joined a mentoring program in which I will visit a group of advanced year ten high school students (around 16 years old) from a group of schools in the area. I don't quite know where they're at just yet. I assume they've done Euclidean geometry, analytic algebra are just getting used to differential calculus. I'm fairly free to do what I want with them short of cruel and unusual punishment (such as making them read Gilbarg and Trudinger). They meet weekly and I had in mind meeting them every two weeks and going through a shotgun summary of what maths is all about, with an eye for a historical development. Of course, I want it to be fun! I have a semseter, so that makes about 6 or 7 two hour meetings.

To make the question precise: What do the potential answerers believe should not be left out of such an introduction?

Thanks,

Mat