totally agree! in high school, lots of things were vaguely defined. I remember, I didn't fully understand what "f o g" was until I was given the definition of a monoid. Also limits and derivations, once you get the proper definition, you can pretty easily derive all the formulas and theorems you use in high school. Also in high school, we mostly did calculations and simple deductions, but at university we were proving everything. Nice change of perspective.