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Answer this question: What kind of math specifically are you intersted in? If you cannot answer that question, then forget about research. Even that aside, one must also take into account the different emphases in different summer programs. Places like SUMaC do Algebraic Topology, and other places do number theory and such. Whatever you choose to do, don't take multivar calc. Too many students take it, and its weak. If you ever want to be a mathematician then you will do yourself a favour and not take that junk.
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