[Edu-sig] Long Integer Fractions

[Kirby Urner]

Tim Peters wrote (in part):
>Even so, the subject matter is difficult at points and the 
>book makes no apologies for that, or for its refusal to
>"dummy it down".  Most of it remains college-level material.
>
>somebody-should-teach-uncle-don-how-to-use-a-computer<wink>-ly y'rs  - tim

OK, sounds like "Concrete Mathematics" (CM) is my next 
investment (along with more RAM for my wife -- she's
got some RAM-hog bookkeeping software that's really
bogging down).

No doubt CM is college level, but the point of a well-
designed curriculum is to "lower a ladder" consisting 
of "grades" or "rungs", such that by the time you get
to the tough stuff, it's within reach, i.e. you're
well prepared for it.  The metaphors of "steepness"
("stepness") apply:  learning curve, on-ramp, higher 
learning.

These days, it seems to me that the conventional math 
curriculum is too slanted _away_ from engineering. Is 
it a class thing?  Seems a lot of effete aristo-bluebloods 
who can't abide getting their hands dirty in anything 
like "machinery" (ooo, dirty) must have concocted the
current cafeteria plan: "like, would you like some more 
calculus with your pre-calculus?"

I have nothing (much) against calculus, but not if we 
divorce it from discrete math so completely that we 
can't do some delta-x alongside our dx, some SIGMA 
alongside or Riemann sums.  Why not some simple Python 
in grade 11 (age 16):

def mkderiv(domain,f,h):
    # function derivative builder (discrete)
    pairs = []
    for x in domain:  # for each member of domain...
        rvalue = (f(x+h)-f(x-h))/(2*h)
        pairs.append((x,rvalue)) # append tuple
    return pairs

I'd like to open doors to OOP, cryptology (links between 
RSA and prime numbers), spatial geometry (rotation 
matrices, vector ops), number theory (Fermat's "little 
theorem") even spherical trig, sooner rather than later.  
Not in some elective AP rivulet, but in the main stream.

Spending a whole year doing AP calculus, all that chain 
rule stuff, integrating by parts, seems way too much 
nuts and bolts specialization -- like, let's wait and 
see if you're really going to _use_ the calculus on 
the job (and _how_ will you use it?) and stop using 
this one neck of the woods as your "killing field" 
wherein to sort out "those with potential" from "those 
we feed pablum" in the math-sciences.  

That's a cruel design, plus seems increasingly unable 
to justify itself (the cost is way too high, given 
the "turn off" factor).  Personally, I'm for letting 
the kids victimized by this obsolete system having 
their revenge (no, I'm not speaking from personal 
bitterness, I did fine in AP calc and taught it for 
two years at the HS level).

thinking-it's-time-to-swing-the-wrecking-ball-ly yrs
Kirby