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May17-08, 04:18 AM
Sci Advisor
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P: 4,300
I'd be nice if you could get hold of the textbook he'll be using, so you can go through it in the same order. I can imagine that you would want to offer him some extra mathematical background. For example, if the textbook starts with mechanics, you could try to cover the material he'll be supposed to know now ([itex]F = m a \cos(\alpha)[/itex], and such) and when the class actually gets to that, try to learn him something about vectors and where the [itex]\cos(\alpha)[/itex] comes from. And for example, when the mathematics class starts to teach differentiation, you could go through it a little faster and also introduce the exponential function, logarithms, etc., such that you can show him e.g. applications in physics and give him some more challenging exercises while the rest of the class takes 3 weeks to learn the chain rule. From experience I know that for interested and above-average mathematics skilled students, this is certainly reasonable to do.

But of course, it depends on what he likes, what he is able to do. I don't have a long experience with this, so I don't know if keeping him challenged all the time will always stimulate him or might have the opposite effect and make him lose interest after a year or two. And of course, always pay attention that he learns relevant stuff such that he doesn't get confused with what's he supposed to know (e.g. don't teach him complex numbers until after the test on quadratic equations, where you are supposed to write down that [itex]x^2 + 1 = 0[/itex] has no solutions ).