[Edu-sig] still admiring J

[kirby urner]

On Fri, Mar 23, 2018 at 1:33 AM, Wes Turner <wes.turner at gmail.com> wrote:

>
> xarray.Dataset is n-dimensional
> https://xarray.pydata.org/en/stable/
>
> From a tweet a few days ago https://twitter.com/westurner/
> status/973058715149578240 :
>
>
​Excellent pointers!

I anticipate a steady stream of new math teachers (sort of like I was some
decades back, teaching high school level in Jersey City, first job outta
college),  and getting to where they're hungry to include more coding, and
need appropriately mathy topics.

Lots out there already, a steadily growing stash since the early days, of
Logo and OLPC (One Laptop per Child), SugarLabs...  The Learning to Code
movement (code.org etc.) is but the latest in a series of chapters.

BTW, one of my code school mentors just showed me this one:
http://www.codebymath.com/index.php/welcome/lesson_menu

My own contributions to this genre go back to what I called the "Numeracy
Series".  That's closer to when I first came across Python. I'd already
played with "quadrays" in Visual Foxpro.[0]

http://4dsolutions.net/ocn/numeracy0.html  (that's part 1 of 4, early 2000s)

I was into mixing Python with POV-Ray, the free ray-tracer, to get simple
geometric figures.

These days mathy high school level topics might include...

-----

*1*  Crypto: a gateway to group theory.  Since my day, we've added more to
the "fun reading" shelf, such as with Cryptonomicon (Stephenson, historical
science fiction) and The Theory that Would Not Die (i.e. Bayesianism) by
McGrayne.  As clear from the cover (https://flic.kr/p/22z1vAy) she's
covering a lot of the same territory: Bletchley Park, Alan Turing, enigma
machines.  You've got prime numbers, RSA, Elliptic Curves and hashlib SHA
stuff.  Introduce blockchain.  A great way to access recent history.

*2* Geometry: and in my case a genre of "mental geometry".  My topic is the
somewhat off-beat solid geometry of the geodesic dome dude (another movie
coming up [2]), and my modality is often Python.  One of the slides shows a
Tetrahedron class with our formula for its volume, a public sandbox at
REPL.IT. https://repl.it/@kurner/tetravolumes

I don't remember if I've already shared this link ( https://goo.gl/zoVYF1 )
to my slide deck (Google Slides) for a recent talk at Systems Science
building, Portland State [1].

That's probably still too off beat for most, whereas Fractals (dynamical
systems, strange attractors, Wolfram automata), if counted as "geometry"
(certainly visual) already have a strong following and both connect back to
deeper math.  I've done work around those topics too and attest to Python's
applicability.

*3*  Data Science: which is where the nD-array ("xray", "tensor") and
Linear Algebra come in, and Calculus (which they're learning anyway).  When
not connect Calc to Stats with a thicker pipeline right from the start?
So what if the Gaussian Distribution doesn't have a closed form integral or
whatever (https://goo.gl/9XyzN5 )?  Not an issue.  We just wanna make sense
of the curves in some lessons, and both the CDF (the integral) and
derivative of the PDF (normal curve) are worth talking about visually, and
coding in Python.[3]

-----

In sum:  if you're a math teacher chomping at the bit for something fresh,
and not already over-exploited by the test-maker economy (you still have a
free hand), then we have riches in:

Crypto (web browser TLS, eCommerce, Supermarket Math [4]);

Geometry, including off-beat whole-number volumed polyhedrons from New
England Transcendentalist literature (v 2.0);

Machine Learning / Data Science. All accessible to high schoolers.

Kirby

[0]  Quadrays are a weird coordinate system featuring a "caltrop" of basis
rays to tetrahedron corner points (1,0,0,0) (0,1,0,0) (0,0,1,0) (0,0,0,1)
from origin (0,0,0,0) -- but there's nothing "4D" in the sense of
non-visualizable hyper-dimensional, just ordinary space mapping, 1-to-1
with XYZ if you stick to the unique canonical representation.
http://mathforum.org/library/view/6236.html

[1]  http://worldgame.blogspot.com/2018/03/systems-science.html

[2]  https://youtu.be/oyLWPWydvyo

[3]  one of my Jupyter Notebooks about the bell curve:
https://github.com/4dsolutions/Python5/blob/master/BellCurve.ipynb

​
​[4]  http://wikieducator.org/Supermarket_Math
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