<p>And that IMO gold medalist ended up regretting it, as far as I know :-).</p>
<p>The professors generally will let you do what you want (modulo some discouragement if you are setting yourself up for obvious trouble), but the most successful math students at Caltech, even those who know a fair bit coming in, tend to pace themselves and try to learn deeply as opposed to trying to skip as much as they can. It is generally much better to be the best student in math 109 than to struggle to catch up things you’re missing in 151, so it would certainly be a good idea to make sure you can do every problem set in the former class cold.</p>