Re: The logical structure of calculus, request for help.

In <d5o8eb$4i76@xxxxxxxxxxxxxxxxxxxx>, on 05/09/2005
at 12:59 PM, hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) said:

>Not necessarily. It is quite possible to teach mathematical logic
>through the restricted predicate calculus to most elementary school
>children in well under a year,

Not if the stools of education have a hand in it. That's what happened
to "New[1] Math".

>Add a short course in algebra, now easily proof designed, and you
>have what is needed to do rigorous calculus. In fact, it is my
>opinion that this would work much better than what is now done, where
>students are taught how to do what may be called "calculus
>calculations" without having the slightest idea of what a derivative
>and integral are.

The present approach is often based on the inference that since the
Word Calculus is derived from the Greek word for stone, the students
should be treated as stones. They often learn about as well as could
be expected from such an approach.

>Euclid's students had the ideas,

For the most part, but there were some issues of rigor and some
"theorems" that did not actually follow from Euclid's axioms and
postulates. Some of the ancient Greeks who followed him did better.

[1] That fact that the "educational" establishment called it that
should have been a warning sign as to how badly they
misunderstood it.

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Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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