On Monday, October 2, 2017, kirby urner <kirby.ur...@gmail.com> wrote:
> > Given I'm spending 3-4 days a week with 5th & 6th graders, teaching them > Python, I'm looking for ways to sync with what Common Core says they should > be learning math-wise. > > They general strategy here is to look for topics already in the curriculum > and develop coding skills around those topics. > > Turns out that prime versus composite is important at that age, and the > classic algorithm used to teach that is the Sieve of Eratosthenes. Most > coders have written at least one of those. > > Since we're transitioning from block-based MIT Scratch with not much > keyboarding, to full-fledged lexical Python, I'm thinking to assess > facility with keyboarding (typing) by having them hand-enter a Sieve, and > running it to check for any syntax errors. > > While we're still doing natural and whole numbers it makes sense to look > at other number series as well, ones we can explore using very simple > Python. > > Triangular and square numbers, then polyhedral number sequences, such as > successive shells around a nucleus. 1, 12, 42, 92... > > http://oeis.org/A005901 (note link to my website under links) > https://github.com/4dsolutions/Python5/blob/master/STEM%20Mathematics. > ipynb > > Pascal's Triangle is an important hub for studying number sequences. It > even embeds the Fibonacci Numbers. > > This is a bit old, in terms of the pyramid app the views are written in. It preceeds pypa/warehouse. It has some number theory implementations in Python that I found on stack overflow; and a force-directed factor graph visualization with D3 and NetworkX. https://bitbucket.org/westurner/flowstat/src/tip/flow/numbers/primes.py https://bitbucket.org/westurner/flowstat/src/tip/flow/numbers/templates/number.jinja2 > These are the kinds of ideas I've been circling for some years. > http://4dsolutions.net/ocn/numeracy0.html > What does this apply to? Project Euler problems? > What's new is I'm getting more opportunities to test them in real world > classrooms. Coding with Kids is keeping me busy. > Here are some real world number theory libraries and applications: http://docs.sympy.org/latest/modules/ntheory.html - https://github.com/sympy/sympy/tree/master/sympy/ntheory/tests - https://github.com/sympy/sympy/tree/master/sympy/ntheory - https://github.com/sympy/sympy/blob/master/examples/beginner/basic.py http://doc.sagemath.org/html/en/constructions/number_theory.html - http://wstein.org/edu/2007/spring/ent/ent-html/node26.html http://dit.readthedocs.io/en/latest/measures/shannon.html Encryption is pretty fun, right? https://github.com/warner/python-ecdsa/blob/master/src/ecdsa/numbertheory.py https://github.com/pyca/cryptography/blob/master/src/cryptography/hazmat/primitives/hashes.py https://github.com/pyca/cryptography/blob/master/src/cryptography/hazmat/primitives/asymmetric/rsa.py Project Euler has lots of great number theory / CS exercises: https://en.wikipedia.org/wiki/Project_Euler https://projecteuler.net/archives PyPI: https://pypi.python.org/pypi/eulerlib Src: https://bitbucket.org/transmogrifier/eulerlib Docs: http://pythonhosted.org/eulerlib/eulerlib.html https://www.google.com/search?q=project+euler+solutions+github https://github.com/nayuki/Project-Euler-solutions/tree/master/python For generating the .py files for a given Project Euler problem, there are a number of utilities: https://pypi.python.org/pypi/EulerPy/ https://pypi.python.org/pypi/EasyEuler Rosalind.info has a bunch of great exercises, too; IDK how many are specifically Number Theory in the real-world bioinformatics domain: http://rosalind.info/problems/topics/ Formulating each problem as a unittest.TestCase'able thing is worth the time. > > With my adult students, I'm looking at what I call the "Five Dimensions of > Python" wherein they expand their awareness of the language, from keywords > (dimension 0) to 3rd party ecosystem (dimension 4). > > http://mybizmo.blogspot.com/2017/09/five-dimensions-of-python.html > (links to another Jupyter Notebook) > > I've finally figured out that Codesters (codesters.com) is about Python > 2.7, not Python 3.x. I've been confused on that score. > > Given cryptography is playing a more important role in everyday eCommerce, > it makes sense to beef up some of the Number and Group Theory aspects of > K-12. > > I've been arguing on math-teach that right when we introduce primes versus > composites, we should likewise introduce Fermat's primality test. > > http://mathforum.org/kb/message.jspa?messageID=10241002 > http://mathforum.org/kb/thread.jspa?threadID=2883906 > > Kirby > >
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