I'm teaching mathematics at a high school and I am offered the opportunity to get extra lessons, namely: I can provide an optional course about some topic of mathematics. The optional course will take two lessons (each 45 minutes) a week and last a whole semester.
The mathematical skills of the pupils will vary a lot: Usually, they will have covered one or two the three topics "vector geometry", "differentiation" or "integration". I myself am mostly interested in linear algebra and theoretical physics (quantum physics).
I'm having a hard time to come up with something interesting I know a lot about to teach them. Obviously, I can also read a bit about something not in my area, because I doubt I can show them any proper theoretical physics because a) it won't count as a maths course and b) not all of them know integration and none know complex numbers yet.
Does anyone have a suggestion what I could do? A friend suggested to do number theory but I'm not sure if that is appealing to high school pupils (I never cared for it) plus I still don't know anything about it.
//edit: It should also not be something that is taught in the standard curriculum, e.g. not complex numbers.