#### Comment Preferences

• ##### That part of integral calculus is overdone.(7+ / 0-)

In general, the existence of computers SHOULD have some influence on the teaching of math.  Thirty years ago it was important for a scientist or engineer to learn a wide range of integration techniques, or tricks.  Nowadays, not so much, because Mathematica or Maple can do the actual integral faster and more reliably.

But the important thing is to understand what the integral means, and the fundamental techniques (really, theoretical properties) such as substitution and integration by parts - and this much is accessible to high school students in half the industrialized world, from Russia to Singapore. It's hard to understand why in the US it's considered a big deal.

Silvio Levy

• ##### I find it particularly interesting(5+ / 0-)

That virtually all of mathematics was discovered and mastered long before there were computers.  The only thing I've heard of where computers helped create new mathematics was proving the four color conjecture.

The problem with computers in education is that they are used as a substitute for thinking, instead of a tool to help you think better.  IMO, creating a quadratic or cubic curve by finding the zeros, the local min/max, the inflection points, and then hand-plotting the curve on graph paper gives you far more mastery of the subject than letting Texas Instruments do your thinking for you.

Big Joe Helton: "I pay Plenty."
Chico Marx: "Well, then we're Plenty Tough."

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• ##### Computers have also shown us ...(3+ / 0-)
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that many hypotheses are most likely correct. For example, the Riemann Hypothesis and Goldbach's conjecture have been shown to be true for incredibly large numbers by computer, but have yet to be proven for any n.

So a lot of math nowadays is done is the caveat "Assuming the Riemann Hypothesis is true" and continuing from there. This also happened with the Taniyama–Shimura–Weil conjecture (a.k.a the Modularity Conjecture) which was then proven by Andrew Wiles as part of his proof of Fermat's Last Theorem.

Hopelessly pedantic since 1963.

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• ##### Ah, well, if hypergeometric functions are(5+ / 0-)

your shtick, then yes, Maple and Mathematica can do them all.  Speaking for myself, when I see that gobbledygook I go back to the blackboard.  While computers may be good at getting an answer, they are singularly bad at presenting it in a meaningful way.

Of course, then there are any number of integrals that don't admit usefully compact solutions.  We give them funny names and evaluate them numerically.  So that does matter.  But that is for a more advanced course than available in high school.

Justice deferred is justice denied. -MLK

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