+1 for defining multiplication as a tensor product. I made it though more than 15 years of school before I learned that matrix multiplication is actually the tensor product (with broadcasting):
https://en.wikipedia.org/wiki/Tensor_product The Theano docs explain tensors and tensor broadcasting: http://deeplearning.net/software/theano/tutorial/broadcasting.html http://deeplearning.net/software/theano/library/tensor/basic.html#operator-support ( https://keras.io/#getting-started-30-seconds-to-keras does tensors with TensorFlow, Theano, CNTK, but not yet xtensor. ) The product (__mul__) operator (a binary operator) can be defined in lots of ways; both in Python and in mathematics: with linear algebra, we mean "scalar multiplication" (with standard broadcasting) https://en.wikipedia.org/wiki/Product_(mathematics)#Scalar_multiplication On Monday, September 4, 2017, Wes Turner <wes.tur...@gmail.com> wrote: > Re: dimensional analysis and units > > - pint does units: > https://github.com/hgrecco/pint > https://github.com/hgrecco/pint/blob/master/pint/default_en.txt > > - CSVW can handle units (with QUDT URIs) > - {CSV, JSON,} don't include support for datatypes or units > - ( Spreadsheet tools should handle units (and significant digits) just > as well as they handle columnar/series/range text formatting. > #LinkedReproducibility ) > > On Monday, September 4, 2017, Wes Turner <wes.tur...@gmail.com > <javascript:_e(%7B%7D,'cvml','wes.tur...@gmail.com');>> wrote: > >> >> >> On Monday, September 4, 2017, kirby urner <kirby.ur...@gmail.com> wrote: >> >>> PS: >>> >>> my recent exercises in teaching math with Python, ala Peter Farrell, is >>> sparking some heated debate on math-teach. >>> >>> http://mathforum.org/kb/thread.jspa?threadID=2876811 (especially in >>> recent days, early September 2017) >>> >>> Bob Hansen is trashing this writing as some of the worst pedagogy he's >>> ever seen. >>> >>> I'm trying to incorporate some of his feedback in my latest revisions. >>> >> >> Maybe a bit OT: >> >> I've wondered whether we could/should instead start mathematics education >> with bits as entropy (information theory first)?: >> >> - 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) >> >> >> - 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?) >> - CAS: SymPy, latex2sympy >> >> - Entropy >> - Independence of observations >> - Maximum Information >> >> ... >> >> class Shape >> class Quadrilateral >> class Rectangle >> class Square >> class Triangle >> class RightTriangle >> def perimiter >> def area >> def vertexes >> >> def scale >> def rotate >> >> class PlatonicSolid >> >> ... >> >> Are there computer science & mathematics curricula like this (that start >> with entropy)? >> >> >> >>> Our debates are reminiscent of some we've had here on this list in years >>> gone by. >>> >>> I've also been chronicling my progress in this related thread: >>> >>> http://mathforum.org/kb/thread.jspa?threadID=2877392 >>> >>> Kirby >>> >>> >>>
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