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<p>Like I’ve been saying: we already have this option. You want to really prove via a class that you have the wherewithal to handle a math grad program? Fine. Then take Math 204. Take Math 205. Take Math 222. Take Math 250. Why not? The prereqs for these courses are undergrad (upper division) math courses. Do well in those courses and you will present incontrovertibly strong proof that you have the ability to handle a top flight math graduate program, for after all, those are the courses that the current Berkeley math grad students take. </p>
<p>That option provides the further benefit of academic recovery. Who really cares if you performed poorly in Math 185 if you performed smashingly well in 205? Maybe you just didn’t understand 185, but you clearly recovered for 205.</p>
<p>The greatest advantage is that it allows people to major in math as an intellectual curiosity while still preserving the full range of career choices if they don’t actually intend to go to math grad school. Those people can simply choose not to take grad math courses.</p>