On Friday, March 23, 2018, kirby urner <kirby.ur...@gmail.com> wrote:
> > On Fri, Mar 23, 2018 at 1:33 AM, Wes Turner <wes.tur...@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. > "Show HN: An educational blockchain implementation in Python" https://news.ycombinator.com/item?id=15945490 https://github.com/julienr/ipynb_playground/blob/master/bitc oin/dumbcoin/dumbcoin.ipynb https://cryptography.io/en/latest/ recommends https://www.crypto101.io/ (PDF) https://github.com/pyca/cryptography/blob/master/src/cryptography/hazmat/ primitives/ciphers/algorithms.py https://en.wikipedia.org/wiki/Fermat%27s_little_theorem https://en.wikipedia.org/wiki/RSA_(cryptosystem) "How secure is 256 bit security?" by @3blue1brown https://youtu.be/S9JGmA5_unY https://en.wikipedia.org/wiki/EdDSA#Ed25519 > *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. > Fractals... Mandelbrot https://en.wikipedia.org/wiki/Chaos:_Making_a_New_Science IDK what's a good Python package for fractals? > > > *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] > http://docs.sympy.org/latest/modules/stats.html#sympy.stats.Normal http://docs.sympy.org/latest/modules/integrals/integrals.html > > > ----- > > > 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. > https://www.kaggle.com/learn <https://www.kaggle.com/learn/overview> https://jakevdp.github.io/PythonDataScienceHandbook/ https://developers.google.com/machine-learning/crash-course/ml-intro > 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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