<p>I think there’s a middle ground between low-level linear algebra, differential equations, or multivariable calc at a local university and doing topological field theory research under a well-known professor. </p>
<p>I curious how taking upper division [real analysis, abstract algebra, etc.] math classes at a respected but not elite university compares to say USAMO qualification. There are a number of people I know like sbjdorlo’s kid who don’t focus on math competitions but take quite advanced math classes. At least in my opinion, taking the upper division math classes seems like a better use of time than learning whatever exotic inequalities and esoteric Euclidean geometry theorems that help on the AIME and USAMO.</p>