[Edu-sig] Pythonic Alg 2, Trig/Func

[kirby urner]

Hi Kevin --

I've done a couple Saturday Academy courses that touch on various high
school and college level math topics using Python as a vehicle for
improving understanding.

Sequences and series is one of my starting points.  I do figurate then
polyhedral numbers to limber up and keep geometry in view, then start
getting into the convergent/divergent and chaotic behaviors of
sequences (segue to phi via Fibonaccis, fractals via Python's cmath).

If you had a Rational class handy, you could carry out a series
expansion for sine and cosine to get fully rational results, e.g.:

sine (x) == sigma (  ((-1)**n * x ** (2*n + 1))/fact(2*n + 1) )

http://upload.wikimedia.org/math/6/b/f/6bf16b97ce1b4c86ffa1ed55c3fdc25f.png

where fact is factorial and sigma is just sum([list]) of n members
(however far you want to go out).

I was just writing about this recently (about how little use we make
of automation to play with these series expansions for trig and log
functions -- but why not change that?):
http://mathforum.org/kb/message.jspa?messageID=4796483

Kirby


On 6/13/06, Kevin Driscoll <driscollkevin at gmail.com> wrote:
> Next year, I'm going to be drafted back into the Math department after
> a year of exclusively teaching CS.  It looks like I'll have a class of
> 11th graders in either Alg 2 or Trig/Functions.  They are kids not on
> the AP Calc track (possible 12th grade AP Stats candidates.)  I'd love
> to incorporate programming into the course.  A handful of the students
> will have been in a 10th grade CS class with me and could be helpers
> in getting the rest of the students up to speed.
>
> Has anyone on-list taught a class at this level with Python integration?
>
> Kevin