I think that's a super idea. I'd like to design it and I'd like to take it. The ideas that underlie everything else. Like a whole university course devoted to A-level maths, but covering every simple underlying idea. We should start by trying to work out what the syllabus should be.

(one 16 lecture course on each topic, and we'll have three courses per term so that's 36 courses in total)

Off the top of my head we should have: groups, calculus, dimensional analysis, estimation, probability (inc bayes), relativity, quantum mechanics, electronics, programming, chemistry, evolution, evolutionary psychology, heuristics and biases, law, public speaking, creative writing, economics, logic, game theory, game-of-life, how-to-win-friends-and-influence people, history, cosmology, geography, atomic theory, molecular biology ...

All taught with immediate direct applications to actual things in the immediate environment and if you can't come up with simple examples that a child would find interesting and could understand then it doesn't make the cut.

Any more suggestions? If we get loads let's make a post on 'The ideal 4-year university course'.