how does the university system absorb math students with such massively different backgrounds?
I've recently been made aware of the Art of Problem Solving curriculum. I did a deep dive on it because I have some friends who are locally enrolling their kids and I recall wondering about math competitions in high school but I didn't pursue it.
I had a totally conventional U.S. math education, having done AP Calculus senior year in high school. I remember it being pretty challenging.
Dipping into this olympiad/competition stuff is really melting my brain - not just because the problems are absurd but because this supposedly parallel curriculum, that's supposed to be an enhanced superset of the regular curriculum, is actually completely and totally different.
What I don't understand is how this asymmetry can really exist. The 18 year old who just finished AoPS Precalculus and the 18 year old who just scored a 3 on AP Precalculus are different species. Is this what olympiad kids are? The level of difficulty, the integration of esoteric theory and advanced proof techniques in the AoPS curriculum seems to create a totally unrecoverable gap. I just had no idea how massive the difference was. It seems impossible that a university math department could cater to both individuals without wholly separating them. If they both pursued a math degree don't understand how they could ever converge on the same curriculum.