Sharing an e surprise with kids after a question from Sam Shah and a comment from Steven Strogatz yesterday: https://mikesmathpage.wordpress.com/2019/03/02/sharing-an-e-surprise-with-kids/ … #math #mathchat cc: @samjshah @stevenstrogatz
Surely nothing *should* be less dull and less soul-crushing than a second course in algebra, for algebra is vast and marvelous. I can't help thinking that the right approach, especially with young kids, is to exhibit the marvels in countless concrete examples, and stand back.
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One phenomenon of extraordinary depth and power with which a second course in algebra ought to deal is the intimate analogy between polynomials and integers (and between rational functions and fractions.) How about Bezout's theorem for polynomials? How about Pade approximants?
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So many wonders to choose from! And, again, one has the great past masters to look to -- both for broad-strokes direction, and for tactical brilliancies in pedagogical execution. Read Euler, read Euler, he is the master of us all!
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