A comprehensive approach would include alumni coming back to campus regularly as guest speakers, followed by long-term alumni mentoring, followed by shadowing and internships. Not just for those motivated to seek out the extracurricular opportunities, but as a normal part of education for every student.
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Love it! Hearing about what people are doing in their fields and how they are using the math is invaluable.
Well, then, here's a concrete example. http://www.stemeast.org