[Edu-sig] re: Python Programming: An Introduction to
ComputerScience
Kirby Urner
urnerk at qwest.net
Sun Dec 14 14:38:33 EST 2003
> I think teaching math and programming is a very interesting idea ...
> proofs are just a kind of code walkthrough.
>
> Toby
> --
In my own case, I've thought less about proofs and more about using programs
to demonstrate what a proof means/says (i.e. what's asserted, before you
even prove it).
I understand Jeff's point that lots of kids dislike mathematics and bringing
more math into programming might be a sure way to kill it -- takes all the
fun out.
But he also sees the flip side of the equation, which is we have the
opportunity to take a somewhat unpopular subject (math) and enliven it with
a command line such as Python's.
An example I like is polynomials (usually a big topic in algebra). You get
to see that there's a kind of positional notation, as with decimal numbers,
where the positions correspond to 'degree' i.e. x**0, x**1, x**2 and so on.
So Poly([1,2,-3]) would be a way to instantiate 1 + 2*(x**1) - 3*(x**2).
Then using __call__, you can actually pass in some value for x, e.g.:
>>> p1 = Poly([1,2,-3])
>>> p1
1 + 2*(x**1) - 3*(x**2)
>>> p1(5)
-64
With this framework in place, we'd now like to define __add__, __sub__, and
__mul__ so that we might go:
>>> p2 = Poly([0,0,1])
>>> p1 + p2
1 + 2*(x**1) - 2*(x**2)
>>> p3 = p1 * p2
>>> p3
(x**2) + 2*(x**3) - 3*(x**4)
In coding the guts of polynomial addition and multiplication, you learn
quite a bit about programming, and polynomials, at the same time.
And it's remarkable how little Python code it takes to implement all of the
above.
And as I mentioned earlier, I think it really pays off to develop a Vector
class in Python, complete with operator overloading. I did this with 13
year olds in conjunction with POV-Ray. They remained open minded and
pleased with the topic, even though it was way above grade level, because it
was presented in a context that was interesting to them.
http://www.4dsolutions.net/ocn/pygeom.html is where I've archived materials
from this course (now complete).
Kirby
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