You could go corny with something like “Explore the infinite possibilities of math”... but I think you’ll hook more by concentrating on the differences your class offers from traditional classes. It sounds like this might be the kid’s first exposure to a lot of these ideas and that’s exactly what you want? So maybe play it up to a specific group you’re targeting. Something like “Enjoy math but wish you could step past the formulas? Theoretical Mathematics 309 with Professor Finkelitis explores the truths behind the math you’re used to learning and encourages students to theorize and discuss areas that aren’t typically covered in school. No repeated formula memorization, no endless arithmetic, just solid discovery regarding the fundamentals of the basic language of our universe.” That last part might be laying it on a little thick, and you’d have to edit the rest for truth, but if I was thinking about taking pre-cal and saw Professor Finkelitis’s Theoretical Mathematics… I think I’d rather take that. You may want to throw something in there about preparing students for more advanced classes as well, kids in summer school are usually trying to get ahead, right? And the parents who are paying want to make sure they’re learning something that will be used later. Good luck with the class, can we get a syllabus? It’s been a looooong time.