On Sun, May 15, 2011 at 04:12, kirby urner <kirby.ur...@gmail.com> wrote: >> Groupoids, categories, rings (clock time), fields (modular >> arithmetic), vector spaces, and algebras require a bit more thought, >> but I am sure that they can be done.
I mentioned a few Lie Groups, but I omitted the name. Toposes, topologies, tilings, and fractals would be interesting to investigate, too. > That's perfect Ed. Good to hear for another die-hard "group > theory for children" dude, a vanishing breed perhaps. It's just a fancy name for symmetry. MC Frontalot: Why do mirrors reverse left and right, but not up and down? John Hodgeman: They're just lazy. They could if they felt like it. Yeah, so what's really going on with mirrors? MC Frontalot is a nerdcore hiphop artist, and John Hodgeman is the author of More Information than You Require. He was also the PC in the Mac ads, and is sometimes on The Daily Show. > My intended audience might actually be older people, including > so-called "retirement community" students who have grand kids > and want to have inter-generational topics. Many learned > BASIC as kids (the Bill Gates generation). > > Another group you can massage into a field are integers > multiplying modulo N, except not just any integers, only > N's totatives. Back to permworld and Guido's exceedingly > simple implementation of Euclid's Algorithm. > >>>> def gcd(a,b): > while b: > a , b = b, a % b > return a > >>>> gcd(12, 4) > 4 >>>> gcd(12, 5) > 1 >>>> totatives12 = [m for m in range(12) if gcd(m, 12) == 1 ] >>>> totatives12 > [1, 5, 7, 11] >>>> from random import choice > >>>> (choice(totatives12) * choice(totatives12)) % 12 > 11 >>>> (choice(totatives12) * choice(totatives12)) % 12 > 1 >>>> (choice(totatives12) * choice(totatives12)) % 12 > 5 > > Asserting closer (group property): > >>>> if (choice(totatives12) * choice(totatives12)) % 12 in totatives12: print >>>> (True) > > True >>>> if (choice(totatives12) * choice(totatives12)) % 12 in totatives12: print >>>> (True) > > True >>>> if (choice(totatives12) * choice(totatives12)) % 12 in totatives12: print >>>> (True) > > True > > If the target number is prime instead of composite (e.g. 23 > instead of 12), then you have field properties, not just group > properties i.e. + is closed as much as * is. > > You'll find me ranting on mathfuture how high schools bleep > over any opportunity to introduce "totative" or "totient" in > favor an an exclusive "factor tree" based approach to > gcd. That made more sense before RSA was in every > web browser. In a "how things work" curriculum, one > would wish for more computer literacy. > > http://groups.google.com/group/mathfuture/msg/11005d0c9dc9eba2 > (I've gotten more correspondence from Milo -- he wants to > make sure we all know that Turing at Bletchley Park did > *not* solve the German U-boat 5-rotor puzzle, doesn't like > how much credit Turing gets). > > I'd like want to use John Zelle's graphics.py in the module > where we draw some Wolfram checkerboard of black > and orange rectangles ala New Kind of Science (NKS). > We were doing that back in February 2007. > > http://mail.python.org/pipermail/edu-sig/2007-February/007736.html > > The new version gets Conway's Game of Life from the > same "turtle" (called a "tractor" in farmworld, but the > same idea, transferred to all-ASCII waves of grain). > Even Mandelbrot is rendered in ASCII "tractor art": > > http://mybizmo.blogspot.com/2011/05/lesson-planning.html > > These are ancient threads as far as edu-sig is concerned. > We've always been trendy around here. :) > >> Of course, in every case I am talking about extracting and presenting >> the fundamental ideas, and leaving proofs, notations, and all but the >> simplest calculations for later. >> > > Of course. I've got an older bunch but this isn't a course > about Group Theory, it's a course about learning to > program in the Python computer language, with a backdrop > of standard Computer Science courses (Euclid's Algorithm > chief among them, at least here on edu-sig). > > Kirby > _______________________________________________ > Edu-sig mailing list > Edu-sig@python.org > http://mail.python.org/mailman/listinfo/edu-sig > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://www.earthtreasury.org/ _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
