CLASS: Saturday Academy: Pythonic Mathematics LOCATION: Portland State University, Neuberger Hall TIME: 10 AM - 12:30 PM While I'm at it, and while the memories are still fresh, I'll chronicle what happened in class yesterday. First, parking was difficult. PSU has two parking structures but I picked the wrong one, and wasted 15 minutes finding it was full, plus got caught going the wrong way in a narrow driveway and so on. Finally found meter parking with but minutes to spare. Broadway door to Neuberger was locked, had to go around. Elevator. Math computer lab. On time, believe it or not. Student peers, being dropped off by their parents, had similar problems, but all arrived, to find fractals being projected out of video.google.com, followed by a short explanation of same, with emphasis on the simplicity of the rule behind Mandelbrot's set: z = z*z + c. One of the fractal students took that on in IDLE later, preassigning c, setting z at 0+0j, and running forward, time and again, each time with a different c. Then I showed Warriors of the Net, which got quite a few laughs, but also respect for its close dissection of TCP/IP. Router, router switch, proxy server, firewall, ports... all in the form of an easy-to-parse cartoon. After it was over, I switched off the projector (means house lights down, as the infrared remote can't cut through flouresence), rolled up the screen, and discussed the difference between two flavors of IP: TCP versus UDP. I also talked about SMTP, FTP, NNTP and HTTP as examples of port-associated services. We dissected a packet, in theory at least. Then I forget the exact transition, but my next topic involved my longstanding augmentation of spatial geometry with a Fuller hierarchy based, sphere packing approach. That led us to Encyclopedia of Integer Sequences, with the link being cuboctahedral numbers (this probably makes little sense if you haven't gone through my orientation, or one like it). Then it was dive into IDLE, import sys and sys.path.append('long string into My Documents') and a snack break. The rest of the class was spent by Pythonic Maths students exploring topics of their own choosing, picking from the list below (this is a verbatim transcript of what I typed out in IDLE during the break, and projected): """ Kirby Urner Projects: ==== Number sequences: triangular, square, cuboctahedral numbers Write short functions (or generators to be fancy) that return sequences, such as the triangular numbers: 0, 1, 3, 6, 10... ==== Rational Number class: start work on a rational number with a numerator and denominator, that will add and multipy fractions e.g.:
myrat = Rat(2,3) myrat (2/3) myrat * myrat (4,9)
=== Fractal Geometry. Compile bookmarks for "Argand Diagram" and "multiplying complex numbers". Figure out how to implement z = z**2 + c in Python, where z starts as (0,0) and c can be any complex number. === Volunteer to help with someone with any of these. """ Most of the peers chose the number sequences, as this was the easiest on ramp to beginning Python (writing a few functions, getting the hang of the editor versus shell experience, import and reload). Here's sort of what their polys.py would look like by the end of the day (they just copied the generator, while a talked about what they were good for, and tri was our first example, jumping off from the aforementioned Encyclopedia). def tri(n): return n * (n + 1) / 2 def square(n): pass # most of 'em had a working version def cubocta(n): """ 1,12,42,92,162... """ if n == 0: return 1 else: return 10 * n * n + 2 def fib(a,b): while True: yield a a,b = b,a+b One advanced student started whipping out Rational Number code, consulting the internet, fingers flying. I showed him Guido's GCD around the time he was wrestling the prime factors, trying to think how to reduce after two rationals __add__. And one fractals-loving guy dove into z = z*z + c, as recounted above (I drew and Argand Diagram and suggested he develop a visual sense of how two complexes multiply -- a self-study topic). I'd do lower voiced lectures with a corner, rove between stations. But the main thing was to get students alone with the snake, working their charms. This is more likely to lead to home experimentation, i.e. there's no sense that a teacher must be present. Learn on your own, teach yourself. That's not a burden, but a freedom and a right. Then parents started showing up, some clearly already pleased with the results of session one. One parent expressed gratitude that the high tech sector is behind an education initiative for this age group. Twenty three years and counting. I'm a latecomer of course, and a proud standard bearer already. Per thread here, I encouraged kids to email their .py files to themselves over a web account, so even if the local hard drives got wiped (as sometimes happens in computer labs), we'd be set to go forward. I told one parent my parking woes and she advised me of the two garage situation, plus hoped I'd in future take full advantage of PSU faculty parking privileges. Kirby