Wikipedia is good (as usual) on the binomial theorem; part of today’s lecture will overlap parts of this. Ideally, one would already have the “natural number exponent” case completely under control before exhibiting Newton’s mighty generalization. And yet calculus students have typically never studied this incredibly basic topic; somehow this has been shunted off to the Statistics arm of the curriculum (where, ideally, it becomes part of Exhibit A in the—necessarily handwavy—”Central Limit Theorem” [roughly, “everybody tries to be Normal”; to be any less rough I have to tell you about Pascal’s Triangle, Binomial Coefficients, Bernoulli Trials and stuff like that—the Binomial Theorem (“easy” form)]; this work is typically omitted and its results handled by “technology” rather than student understanding).
June 1, 2009 at 9:20 pm
somehow i got through the whole lecture
without mentioning the binomial theorem.
i did two totally different topics instead.
the rest of the remarks still apply of course.
wednesday’s “wrap up” lecture, then.