So I'm appending some code I'm kicking around in anticipation of Pycon, call it "ambient Python for airports" (hello Brian Eno).
Given a specific sequence of math topics mostly motivates our pathway through Python (starting with using it as a calculator), we're likely: (a) to encounter generators early (e.g. for Fibonacci numbers), then (b) very simple classes, with emphasis on operator overloading. while of course (c) ordinary functions, like "def f(x): return x**2" will always be a part of it, along with those plotting libraries. I.E. this isn't a CS course where you do procedural programming for a year, before classes even get mentioned (such a methodic and detailed approach will be left to a college setting -- this is college prep). In a first pass, we provide the code below as scaffolding, explaining as we go, *not* requiring students to write it all from scratch (though some might -- plus there's room for improvement (see comments)). When learning a language (human or computer), you want to eyeball existing code, get used to the look in feel, e.g. in this case Python's trademark __rib__ syntax. So below is a good example of a class we'd encounter early in our high school math learning career. All it does is implement the four operations, plus the ordering operators (< , >, ==), among integers modulo M, with the modulus set at the class level. We want students to have interactive experiences like: >>> from chicago2 import M >>> M.modulus 7 >>> m2 = M(2) >>> m4 = M(4) >>> m2 * m4 m1 >>> m2 / m4 m4 >>> m4 ** 2 m2 >>> [m2 ** i for i in range(10)] [m1, m2, m4, m1, m2, m4, m1, m2, m4, m1] Note we don't get a nice division operation for every modulus, as there's not always a unique multiplicative inverse -- part of what we're learning about (group, ring and field -- a first pass, non-exhaustive). We're putting more emphasis on modulo arithmetic, as well as concepts of gcd, coprime, because we're aiming to encompass RSA the public key algorithm by senior year high school, ala Sarah Flannery's 'In Code' (a bestseller).** Kirby Primary reference: A. Bogomolny, Modular Arithmetic from Interactive Mathematics Miscellany and Puzzles http://www.cut-the-knot.org/blue/Modulo.shtml, Accessed 06 March 2008 Secondary reference: Urner, K. Vegetable Group Soup http://urnerk.webfactional.com/ocn/flash/group.html (apologies for the annoying machine noise) ** http://en.wikipedia.org/wiki/Sarah_Flannery #=== test code === class M: modulus = 7 def __init__(self, val): self.val = val % M.modulus # looking for mult. inverse (primitive brute force, # could use extended Euclid instead) for i in range(1, M.modulus): if (self.val * i) % M.modulus == 1: self.recip = i break def __repr__(self): return "%s mod %s" % (self.val, M.modulus) # note: all of these return M-type objects def __add__(self, other): return M(self.val + other.val) def __sub__(self, other): return self + (-other) def __mul__(self, other): return M(self.val * other.val) def __truediv__(self, other): return self * other**(-1) def __neg__(self): return M(-self.val) def __pow__(self, e): # note: m ** (-e) == (m ** (-1)) ** e if e < 0: base = self.recip else: base = self.val return M(pow(base, abs(e), self.modulus)) #======= ordering operators def __lt__(self, other): return self.val < other.val def __gt__(self, other): return self.val > other.val def __eq__(self, other): return self.val == other.val _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
