<p>swarthmoredad,
My S was fortunate that he was able to take those courses at his public HS with his classmates rather than hauling to the local university (where RA was a 400 level class and, as you correctly stated, a weeder for many students) . Granted, not many schools offer those kinds of options. </p>
<p>S was not a fan of math competitions and only did those which were given to all the math students in his classes. Never broke 4 on the AIME and didn’t care. However, he was seriously involved in competition algorithmic programming, which did at least as much for his math skills and creative mathematical thinking as his programming. He has always been good at teaching himself, a skill that has served him very well in some endeavors and been his downfall in others. For math, it’s a good thing.</p>
<p>A number even more interesting to check is the number of folks who declare a math major vs. those who actually graduate with one. Attrition can be high, even at the top programs. An 800 math SAT, Math Level II a 5 on BC Calc may be uncommon, but it is not necessarily an indicator that one would do well as a math major, either. It’s a whole 'nuther ball game when one gets to RA. I haven’t seen a problem set of S’s involving actual numbers in a couple of years!</p>