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Appropriate Level: Real analysis. The Question: Suppose is infinitely differentiable and that for each there is some for which the -th derivative of at equals 0. Must be a polynomial?
Appropriate Level: Abstract Algebra The Question: Recall that the cyclotomic polynomials are defined for so that . Is it true that every coefficient of every cyclotomic polynomial is either 0, 1, or -1?
Appropriate Level: Trigonometry The Story: I spent a summer in Chicago and early one morning I watched the sun rise over Lake Michigan (the lake is large enough that you cannot see across it, at least from Chicago). I stood … Continue reading