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<p>I’ve always thought of this as quite important. Numerous people don’t even do anything academic over the summer (especially if that requires self-motivation) and as a result find themselves pressed for time once they start on the math courses. Hell, one can even self-study an entire Caltech course over the summer if one wants to (the materials are all online and Apostol can be retrieved off a school library - or BitTorrent, for that matter)…</p>
<p>Mathematical problem solving is a skill that takes time to develop. Unfortunately, many people never have the opportunity to develop it until their freshman year in college - and by then - they’re so overrun with other commitments and classes such that it’s often difficult to put too much time into it.</p>