

Why teach math? - ColinWright
http://davidwees.com/comment/22516

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pfortuny
We teach math (I do) to instill on Engineers the concepts of derivative and
integral. That is all there is to "math" for an Engineer.

The fact that we teach "vector calculus" and "differential equations" is just
taking the above to the extreme and enabling them to understand the physical
problems they find.

At least, that is how I see it.

Which, as I see it, is what enabled Newton and Leibniz to understand the
physical world as they did. And Einstein, by the way. Just differentials and
integrals. No more. No less.

~~~
ColinWright
So no combinatorics? Graphs? Topology? Logic? Groups?

Just calculus.

~~~
pfortuny
Well, as I said, I teach to Engineers. I should have said
'Civil/Mechanical...'

They need discrete mathematics very seldom and (I should have said this as
well) I prefer their grasping the derivative well rather than being able to
understand graphs etc.

So, yes, I try to focus more on what you call 'just calculus' which, as I see
it, is what made modern physics possible.

Not that I despise Topology, Algebra or whatever (I am an Algebraic Geometer)
but (I insist, I teach to Civil/Mechanical Engineers) I understand they need
to know what a derivative is much more than graph theory, groups or Topology.

And not only Engineers but most people (apart from those, which are a
singularity, needing discrete mathematics) only need to know arithmetic and
the notion of relative increment and cumulative addition (derivative &
integral). Graphs etc. are cool but mostly useless in real _ordinary_ life.

I _love_ Bourbaki's Topology, Grothendieck's Scheme Theory and the like.
However, I tend not to inflict them on anyone who does not _require_ them.

"Just" calculus would make Newton, Leibniz, Gauss and Einstein smile (I am not
trying to be paternalistic, only realistic).

Edit: I have just read your profile. I understand you know much more about
discrete maths than I do (and obviously, its applications). However, it is
difficult to find a real need for discrete maths in people who shall mostly
deal with mechanical and electrical problems.

Of course, it would be rather different if I taught to CS undergrads. But
then, the question has many aspects. I dealt with my present environment.

