[Edu-sig] Computer science without all that "heavy math" stuff...?

[Kirby Urner]

I think a worthwhile CP4E trajectory is to phase more
Python into a standard math curriculum.  Learn math with
a computer language at your elbow.  CP4E does *not* mean
"CS for everybody".  And to learn some programming is not
to turn yourself into a professional programmer if that's
not where you want to go -- any more than learning some
biology and first aid skills commits you to becoming a
medical doctor.

Students entering the higher level U-type courses would
have more background in the relevant math/computer concepts.

Here's a pre-university math curriculum I posted to k12.ed.math
the other day, in which Python might feature:

===========

   Intro to Number Theory
     primes + composites
     gcd lcm
     totient
     mod operation

   Intro to Programming (Python)
     boolean algebra
     bases 2,8,16
     operator overriding -- class/object concepts
      -- build a fraction object, using above
     (adds/subtracts, multiplies/divides rationals)
     residue classes and more operator overriding
     initial group, ring, field discussion
     cryptology thread

   Sequences and series:
     sigma notation
     triangular and square numbers
     tetrahedral and cubic numbers etc.
     recursive definitions (e.g. Fibonacci)

   Functions:
     domain, range, function, inverse functions
     inverse as negation vs. reciprocation
       -- reinforce group, ring, field concepts
     Preview of trig and exponential functions
       cos,sin,tan,exp plus inverses
     linear functions and polynomials
     delta f(x)/delta x = slope, preview of derivative
     Polynomials and complex plane, fractals
     Build a polynomial object

   Pascal's Triangle:
     permutations and combinations (factorial notation)
     Gaussian distribution, averages, standard deviation
     binomial theorem -- link back to polynomials
     Bernoulli numbers

   Polygons and Polyhedra:
     trig functions (reinforce inverse functions)
     angle vs. size (shape vs. volume) -- rates of change
     rotational symmetry groups (phi - Fibonacci - Pascal's
                            Triangle)
        rotation matrices
     Fuller's concentric hierarchy
     CCP HCP BCC SCP (sphere packings - crystals)

   More advanced electives:

     More calculus:
         convergence
         infinite series
         approximations (Newton's and LaGuerre's Method)
         physics concepts (velocity, acceleration, energy, power)
     Spherical trig:
         cartography
         GPS
     Computer graphics:
         still (rendered) and dynamic
     Simulations and Modeling:
         modeling software, Forrester-type concepts,
         discussion of chaos/complexity mathematics

Narratives:

   Evolution of cryptography in tandem with computer
   machinery.  WWII, Enigma and Bletchley Park, the
   discovery of public key cryptography and the
   spread of new algorithms.  Gives an application for
   group and number theory.

   Evolution of computers and programming paradigms.
   Helps foster an understanding of the feedback loop
   between mathematics and computer science as related
   disciplines.

   Evolution of polynomials and finding their roots.
   Invention of negative and then complex numbers.
   Galois and Gauss's construction of the 17-gon.
   Explains expansion of the number system.

   Evolution of vector algebra concepts, including
   the invention of quaterions and Clifford algebra.
   Links algebra to geometry.

   Macro and microarchitecture:  geodesic domes, the virus
   and buckminsterfullerene (also quasicrystals).  Octet
   truss, Alexander Graham Bell and the FCC [means face-
   centered cubic lattice, not Federal Communications
   Comission].  Gives insight into spatial relationships,
   a basis for "mental geometry" (vs. mental arithmetic).

   Evolution of the calculus in a physics context, along
   with the story of supplying a logical framework for
   continuous (vs. discrete) mathematics.  Gives insight
   into mathematics as an evolving discipline.

Context:  http://www.mathforum.com/epigone/k12.ed.math/golspiglax
===========

Beyond this, I'm a big fan of field experience mixed with
coursework (a.k.a. work-study).  As the not-for-profit sector
gets higher tech, it gives para-professionals opportunities
to hone skills in more volunteer-like capacities, perhaps
apprenticing under those with more experience.  This is how
many have used their military experience, but I'm also
talking civilian sector opportunities -- e.g. learn some
IS skills in the Peace Corps, in Burundi.

Kirby