Kirby Urner wrote: [snip - deleted stuff about numerical integration]
So my general question is, as usual: wouldn't this be an interesting and intelligent way to teach math? You get concepts, and you get programming skills, and you start to think about analyzing and fine tuning algorithms. Plus you grow to appreciate the power of the calculus, which gives us close formed expressions so often -- a way to avoid fast for-loops entirely.
Kirby
I think it would be ... were it not for the following "facts":
1) subjects are taught in a compartimentalised way, leading to easy testing/grading ...
you don't teach introductory numerical analysis at the same time as you teach introductory computer programming at the same time as you teach introductory calculus at the same time as ....
(exception: many learn most of the useful math stuff in their physics class first, at least in North America.)
2) A mathematical limit is not the same as a small but finite numerical precision. Mathematicians would probably cringe at the thought of teaching about using these two side-by-side in the same course.
Of course, if one has the freedom to be able to cover many "unrelated" topics to the same group of students, one can get away with it. However, I don't know of many places in North American Universities when you can do such a thing (One exception might be the University of British Columbia where they introduced a general 1st year science course covering biology/math/physics/chemistry.)
However, I wish one could try it. (In fact, I'd love to be given that opportunity one day!).
André
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