<p>A reality check?</p>
<p>This is an interesting thread, but most students and parents should realize it is a ‘best of the best’ discussion. A student would need to be 3+ years ahead of a standard high school curriculum to undertake multi-variable calculus, linear algebra, and differential equations at a local college, much less a real analysis course, which is typically a third year (or fourth year) college course. That’s if you have access to a four-year college. Most high schools generally have restrictions about placing ahead in math. RA can be one of the ‘weed-out’ courses for math majors, unlikely to be mastered with a summer of self-study by many students.</p>
<p>UC attracts very talented students, but I would make an educated guess that there aren’t many high school students nationwide at this level. Of course, there aren’t many students nationwide that qualify for admissions to UC!</p>
<p>Anyone majoring in math at a top-tier school is good at math. There won’t be any weak students in your classes.</p>
<p>If you read CC enough, you would think scoring 800 on the math portion of the SAT, 800 on the SAT II Math 2C, and a 5 on the AP Calculus BC is common. It isn’t.</p>
<p>One last point - check carefully for the numbers of math majors at top-tier schools. The numbers are lower than you might expect.</p>