I don’t think there are any undergrads on this forum who have transferred from one school to the other, so I doubt if anyone can really know the answer to your question. From my research, though, it seems that both schools will give you all the really good research you want, but Caltech’s may be a little more cutting-edge and/or well-funded, and Mudd’s may let you do a little more responsible stuff because you aren’t competing with grad students.</p>
<p>Bottom line, both will give you great research. If you REALLY want to know the difference between the two, you could check out the public pages of the various profs and see if anyone is working on the thing that is most interesting to you, and then contact that prof.</p>
<p>Mathematics research requiring funding? I don’t think so I mean, if you want to get paid, then you might have to apply to outside programs in the summers. But really many mathematicians don’t even use computers much at all. Pencil and paper. </p>
<p>I wouldn’t worry too much about math research. There are many fields of mathematics where exposure to a university for several years is necessary before meaningful research can generally be touched upon. One can of course try some hard problems in discrete math, combinatorics, graph theory and such, but there’s something important to be said of working on the more standard mathematics material in more depth instead of trying to do something original in at least pure mathematics. In fact, learning the material from standard classes well and thinking about it actually matters a lot in mathematics, whereas in some fields, people ignore class in favor of outside products as a trend.</p>
<p>The main thing you want to think about in terms of math is whose ideas you want to absorb. If you have strong preferences on that, then you may want to choose a school based on which folks you want to learn from. Your resources for mathematics are books and people.</p>
<p>Depending on the type of CS work you want to do, funding needn’t be a problem there either. I can’t comment as much on this though. I imagine again, it depends on who you want to be talking to, and how much you think they will actually help you advance your way of thinking.</p>
<p>You can and probably ought to have applied to MIT as a Junior. Although not highly recommended (maximum hs prep is preferred), there are universities who take in very qualified juniors, granted that they have exhausted their course offerings at school (this would usually but not necessarily be in the case of high schoolers who had been home-schooled previously as their education).</p>
I mean, if you want to get paid, then you might have to apply to outside programs in the summers. But really many mathematicians don’t even use computers much at all. Pencil and paper. </p>