[Edu-sig] some new open source Python writing (Jupyter Notebooks)

[Wes Turner]

On Monday, September 4, 2017, kirby urner <kirby.urner at gmail.com
<javascript:_e(%7B%7D,'cvml','kirby.urner at gmail.com');>> wrote:

>
>
>> Maybe a bit OT:
>>
>>
> OT:  "off topic" or "over the top"?  :-D
>

Off topic


>
> I've wondered whether we could/should instead start mathematics education
>> with bits as entropy (information theory first)?:
>>
>>
>
> That's an interesting suggestion.  When everything seems impenetrable /
> indecipherable, we're in a high entropy state.
>
> Like when you first get off the airplane in some alien culture and so much
> of what goes on seems an utter mystery.
>
> We're more like newborns.
>
> Then as we "learn the ropes" and start to "figure it out" there's a sense
> of Entropy decreasing.  It all makes more sense.
>
> To a point.  :-D
>
> Is the self-education process itself a struggle against our own mental
> entropy?
>

Comply!


>
> - base 2: 00, 01, 10, 11 (on our hands (2**?))
>> - counting
>> - ASCII (0-127)
>>   - how do we know the number represents an integer or a character? ...
>> Encoding, Types
>>   - The number zero is actually # (code point): ___
>> - Unicode
>> - class SpecialString(str)
>>
>>
>
> http://4dsolutions.net/ocn/mainoutline.html
>

This looks useful; thanks!

This doesn't even include the word entropy!:

"Mathematics for Computer Science"
https://ocw.mit.edu/courses/electrical-engineering-and-
computer-science/6-042j-mathematics-for-computer-
science-spring-2015/readings/MIT6_042JS15_textbook.pdf

https://en.wikipedia.org/wiki/List_of_important_publications_in_theoretical_
computer_science#.22A_mathematical_theory_of_communication.22

"A Mathematical Theory of Communication"
https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication

- [...]
- Entropy (Information Theory)
- "bit" *
- [...]

https://scholar.google.com/scholar?hl=en&q=+
"A+Mathematical+Theory+of+Communication"


>
>
>> - Binary and then floating point arithmetic
>>   - unary, binary operators
>>     - import operators: sorted(dir(operators))
>>   - left and right shift
>>   - multiplication as repeated addition
>>   - long division
>>     - floating point (error, BigFloat)
>>     - symbolic mathematics
>>       - MathJax, LaTeX (how to even type this?)
>>
>
> I really like how I can put LaTeX between dollar signs in a Jupyter
> Notebook and use it inline.
>

"A Primer on Using LaTeX in Jupyter Notebooks"
http://data-blog.udacity.com/posts/2016/10/latex-primer/

SymPy has some really convenient plotting functions for symbolic equations
and things:
http://docs.sympy.org/latest/modules/plotting.html#plot-window-controls


>
>       - CAS: SymPy, latex2sympy
>>
>
If only it were possible to latex2sympy all of the sad PDF-embedded inline
equations; to free them as (sensibly named) Python functions.
https://github.com/augustt198/latex2sympy


>> - Entropy
>>   - Independence of observations
>>   - Maximum Information
>>
>>
> Enlightenment!
>

TIL that even logistic regression is a maximum entropy model:
https://en.wikipedia.org/wiki/Principle_of_maximum_entropy#Maximum_entropy_models



>
> ...
>>
>> class Shape
>> class Quadrilateral
>> class Rectangle
>> class Square
>> class Triangle
>> class RightTriangle
>> def perimiter
>> def area
>> def vertexes
>>
>> def scale
>> def rotate
>>
>> class PlatonicSolid
>>
>>
> I started on a Polyhedrons notebook.  This is where I've invested a lot of
> time over the years.
>
> Bob and Wayne on math-teach say my use of Quadray Coordinates is not
> math.  Some kind of hocus pocus.
>
> I'm the only one in the world who seems to think they have a place, if
> only to stimulate our thinking about coordinate systems more generally.
>

The origin is: the center of the Earth. Estimate.

... React VR flips the Y axis (and exchanges pixels for meters):
https://facebook.github.io/react-vr/docs/3dcoordinates-and-transforms.html#content

That c OR v+c  question is complicated because *the space changes*; IDK how
that affects coordinates. Apparently, there's a gradient of affect on
photons around a black hole?


>
>
> ...
>>
>> Are there computer science & mathematics curricula like this (that start
>> with entropy)?
>>
>>
> In the sense that we all start out ignorant of what these curricula aim to
> signal, I think we all begin in a bath of noise.
>
> Thanks as always for intriguing input.
>
> I'm on a physics teacher list where they like to argue about Entropy and
> how best to teach about it.
>
> They're talking thermodynamics more than information theory, but that's
> all the more reason to look for these unifying concepts.
>

https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory

...

https://medium.com/the-physics-arxiv-blog/deeper-than-quantum-mechanics-david-deutschs-new-theory-of-reality-9b8281bc793a

"Constructor Theory of Information"
https://arxiv.org/abs/1405.5563

https://en.wikipedia.org/wiki/Constructor_theory

...

"Physicists want to rebuild quantum theory from scratch"
https://www.wired.com/story/physicists-want-to-rebuild-quantum-theory-from-scratch/




> Perhaps Hell is pure nonsense, separated from Heaven by the thinnest of
> veils, like a decrypting key.
>

https://en.wikipedia.org/wiki/Greek_underworld

https://en.wikipedia.org/wiki/Gehenna

Books went to Pergamum and then the Library of Alexandria:
https://en.wikipedia.org/wiki/Library_of_Pergamum

How many minutes of time out would've been appropriate for Alexander "the
great" (if any)? #EvidenceBased #OutcomeStudy


> Like the less redundancy in a channel, the purer the signal, the closer it
> comes to appearing random, if we're locked out of its meaning.
>
> Right?
>

https:// HPACK (from HTTP/2) is an interesting study / modern example of
Huffman coding:

https://http2.github.io/http2-spec/compression.html

https://en.wikipedia.org/wiki/HTTP/2#Genesis_in_and_later_differences_from_SPDY

https://github.com/python-hyper/hpack
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