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A Classroom Capsule is a short article that contains a new insight on a topic taught in the earlier years of undergraduate mathematics.
As calculus instructors, we often work with classes consisting largely of non-mathematics majors. As a result, we spend a great deal of time and effort constructing examples and projects that demonstrate the uses of calculus in fields other than mathematics. This is great, and as an ex-physicist I'm all for it. However, now I'm a mathematician, so I'd like to propose an alternative: why not develop projects based on advanced mathematics of the sort typically seen in graduate courses?"
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