2008/12/10 michel paul <[EMAIL PROTECTED]>: << SNIP >>
> There is a big contrast between doing math the traditional way, solving > equations by manipulating symbols in some boolean assertion to isolate a > variable, vs. thinking computationally - creating sets of functions to model > concepts. Introducing this stuff eventually requires rethinking the whole > curriculum. But one step at a time. > > - Michel Yes Michel, but let's remember "schoolish math" isn't necessarily what the pros are doing to earn a living, with Mathematica, MathCad or whatever. Lots of degree holders in mathdom spend half their time talking to coders with humanities degrees like me, explaining what outputs from what inputs, in terms of algorithms per Knuth, i.e. the stuff you learn in K-12 isn't "computer poor" because of anything to do with real world mathematics in practice. The way I might do it in Portland (write ups in blogs) is take what we'd consider an advanced, college level theorem, such as Fermat's Little (not Last), and use Python to verify what it asserts, not the same thing as proving. What I say often @ Math Forum is something like: before you prove a theorem, you need to know what it means, i.e. you need to care. Having field applications helps motivate caring. We might not ever get to the proof in this class (heresy!) as these are underclassmen looking to understand RSA, haven't chosen to become mathematicians. What's so cool about Python is pow(2, 22, 23) is so easy to write and explain (no import required), whereas on a calculator you get digit overflow most the time, because of the overly small LCDs, hamster-brained programs (not open source). Per my Chicago talk, OSCONs before it, Texas Instruments is our only real competition in this picture in a business case sense, though "fear of snakes" (per 'Snakes on a Plane') is probably the biggest psychological barrier. North Americans are especially superstitious about snakes, owing to their making Eve do something bad in the Bible (what was it again?). Ruby has an edge in that sense (less charged) -- but then we have a Flying Circus, which helps a lot. We basically invite kids to "fill in the form": pow(2, prime - 1, prime) and verify that they always get 1 for an answer. Then comes the tricky part: does that mean that if pow(2, n-1, n) returns 1, that n must be prime? Having verified it's true for like a gazillion primes, the overly casual thinker might say "sure!". But of course this is a logical pitfall. "if a then b" does not support "b therefore a". That's where we talk about Carmichael numbers, look them up on the web (OEIS). Fermat's Little is a special case of Euler's more general one about totients (lots of fun Python), in turn critical for getting RSA to work (per Knuth). All before college, looks good on your application (that you went to this cutting edge Quaker school or whatever). Kirby 4D _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
