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Topic: Pure Mathematics Courses in High School?
Replies: 48   Last Post: Apr 17, 2009 6:44 PM

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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Pure Mathematics Courses in High School?
Posted: Mar 11, 2009 11:20 PM
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While I agree that "schoolish math" (also known as
"fish ladder math") as meted out in the grammar schools,
is rather far from the real deal, I don't think the
solution is "pure" anything, as over-specialization has
taken a real toll, and anything further towards "getting
a PhD in elementary school" (because precocious or
something) should not be considered an optimal design.

Pre-college, we definitely need to fix the math track,
which the engineering professions judge to be broken, given
their best technologies (e.g. computer languages) hardly
get a footprint. As taxpayers, not just business execs,
we have little patience for all this dilly-dallying, while
the rest of the world gears up for business.

So as I've many times mentioned, here in Portland there's
more interest in let's call it "dirty math" (if you're
thinking of Britney Spears, hold that thought **). What
we mean is we want to blend the disciplines far more,
especially in terms of geography. You'd be amazed how
many kids can't tell north from south, in this age of
Google Earth. Consider that a "minimum job interview",
to sit in front of some desk and point to the cardinal
directions. Can't do that? You don't know "the math".
A lot of other stipulations of this kind.

On another front, some of you have been asking about
A&B modules. These come from one of the core geometries
of the 21st century, by way of another bold entry,
Regular Polytopes and the MITE on pg. 71, our minimum
space-filler. You'll want to compose MITEs into a
space-filling disphenoid known as the Rite for example
(as distinct from the Bite and the Lite, all Sytes). If
this nomenclature is unfamiliar to you, that's because
you're not enrolled in Portland's "dirty math" courses,
brought to you by... your Silicon Forest.

http://controlroom.blogspot.com/2009/03/matrix-of-sytes.html

Anyway, I'm definitely all for keeping some calculus and
my Pythonic Math handout for Chicago, which I need to send
to the organizers next, does include 1st, 2nd and 3rd
derivative of this polynomial. Let me cut and paste some
of the code:

You'll need plaintext view if looking through web archive
and wanting to see indentation (of syntactic significance
in this non-curly-brace language):

def testme():
"""
>>> from stickworks import testme
Visual 2005-01-08
>>> testme()

See:
http://www.4dsolutions.net/ocn/graphics/cosines.png
"""

from math import cos

def f(x): return cos(x)

d = dgen(-5, 0.1)
axes(-5,1,0)
graph = xyplotter(d, f)

for i in xrange(100):
graph.next()

def testmemore():
"""
See:
http://www.4dsolutions.net/ocn/graphics/pycalculus.png
"""

def snakeywakey(x):
"""
Polynomial with x-axis crossings at 3,2,-3,-7, with scaler
to keep y-values under control (from a plotting point of view)
"""
return 0.01 * (x-3)*(x-2)*(x+3)*(x+7)

def deriv(f, h=1e-5):
"""
Generic df(x)/dx approximator (discrete h)
"""
def funk(x):
return (f(x+h)-f(x))/h
return funk


d1 = dgen(-8, 0.1)
d2 = dgen(-8, 0.1)
d3 = dgen(-8, 0.1)

axes(-8,5,3)

deriv_snakeywakey = deriv(snakeywakey)
second_deriv = deriv(deriv_snakeywakey)

graph1 = xyplotter(d1, snakeywakey)
graph2 = xyplotter(d2, deriv_snakeywakey)
graph3 = xyplotter(d3, second_deriv)

Edge.color = (1,0,0) # make snakeywakey red

for i in xrange(130):
graph1.next()

Edge.color = (0,1,0) # make derivative green

for i in xrange(130):
graph2.next()

Edge.color = (0,1,1) # make 2nd derivative cyan

for i in xrange(130):
graph3.next()

if __name__ == '__main__':
testme()

Anyway, back to work, gotta get that handout posted and
out the door (some port on my laptop).

Kirby

** Silicon Forest execs may be good at marketing. As
CMO for CSN, I'm not above making mathematics seem like
something more interesting to a broader audience:

http://controlroom.blogspot.com/2008/04/meeting-math.html
http://controlroom.blogspot.com/2008/08/back-to-basics.html


Date Subject Author
3/7/09
Read Pure Mathematics Courses in High School?
Jonathan Groves
3/7/09
Read Re: Pure Mathematics Courses in High School?
Maria Droujkova
3/8/09
Read Re: Pure Mathematics Courses in High School?
Bishop, Wayne
3/9/09
Read Re: Pure Mathematics Courses in High School?
GS Chandy
3/9/09
Read Re: Pure Mathematics Courses in High School?
Pam
3/9/09
Read Re: Pure Mathematics Courses in High School?
Bill Marsh
3/9/09
Read Re: {SPAM?} Re: Pure Mathematics Courses in High School?
Greg Goodknight
3/9/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/9/09
Read Re: Pure Mathematics Courses in High School?
Maria Droujkova
3/9/09
Read Re: Pure Mathematics Courses in High School?
Jonathan Groves
3/9/09
Read Re: Pure Mathematics Courses in High School?
Milo Gardner
3/10/09
Read Re: Pure Mathematics Courses in High School?
GS Chandy
3/10/09
Read Re: Pure Mathematics Courses in High School?
Haim
3/10/09
Read Re: Pure Mathematics Courses in High School?
Bill Marsh
3/10/09
Read Re: Pure Mathematics Courses in High School?
Bishop, Wayne
3/10/09
Read Re: Pure Mathematics Courses in High School?
Milo Gardner
3/10/09
Read Re: Pure Mathematics Courses in High School?
Haim
3/11/09
Read Re: Pure Mathematics Courses in High School?
Bill Marsh
3/11/09
Read Re: Pure Mathematics Courses in High School?
Bishop, Wayne
3/11/09
Read Re: Pure Mathematics Courses in High School?
Maria Droujkova
3/11/09
Read Re: Pure Mathematics Courses in High School?
Bill Marsh
3/11/09
Read Re: Pure Mathematics Courses in High School?
Jonathan Groves
3/11/09
Read Re: Pure Mathematics Courses in High School?
Adrian
3/13/09
Read Re: Pure Mathematics Courses in High School?
Bishop, Wayne
3/11/09
Read Re: Pure Mathematics Courses in High School?
Haim
3/11/09
Read Re: Pure Mathematics Courses in High School?
Milo Gardner
3/11/09
Read Re: Pure Mathematics Courses in High School?
Kirby Urner
3/12/09
Read Re: Pure Mathematics Courses in High School?
Maria Droujkova
3/12/09
Read Re: Pure Mathematics Courses in High School?
Bill Marsh
3/12/09
Read Re: Pure Mathematics Courses in High School?
Louis Talman
3/13/09
Read Re: Pure Mathematics Courses in High School?
Bishop, Wayne
3/12/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/12/09
Read Re: Pure Mathematics Courses in High School?
Adrian
3/12/09
Read Re: Pure Mathematics Courses in High School?
Bill Marsh
3/12/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/17/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/12/09
Read Re: Pure Mathematics Courses in High School?
Kirby Urner
3/13/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/14/09
Read Re: Pure Mathematics Courses in High School?
Adrian
3/17/09
Read Re: Pure Mathematics Courses in High School?
Kirby Urner
3/24/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/24/09
Read Re: Pure Mathematics Courses in High School?
Adrian
3/25/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/25/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
3/25/09
Read Re: Pure Mathematics Courses in High School?
Adrian
4/15/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
4/17/09
Read Re: Pure Mathematics Courses in High School?
Sue VanHattum
4/17/09
Read Re: Pure Mathematics Courses in High School?
Dave L. Renfro
4/17/09
Read Re: Pure Mathematics Courses in High School?
Adrian

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