Hitting two targets: OO + group theory (pedagogy)

David C. Ullrich ullrich at math.okstate.edu
Sat Mar 3 16:15:51 CET 2001


On Fri, 02 Mar 2001 18:07:16 -0800, Kirby Urner
<urner at alumni.princeton.edu> wrote:

>
>============== OREGON CURRICULUM NETWORK =====================

Does the Oregon Curriculum Network have any official status, ie
any actual connection with the state of Oregon?

[...]
>
>OO + GROUP THEORY 
[...]
>Let's define our sandbox to be groups of relative primes less
>than a particular prime modulus n.  These are groups under 
>multiplication, where a*b is defined as (a*b) mod n. 

One comment would be that if we're talking about pedagogy and
curricula and things we probably want to get the terminology
straight. There's no such thing as a "relative prime" - you
meant "the positive integers less than n which are
relatively prime to n."

And more important there's no reason why the modulus n
should be prime! This gizmo is a group under multiplication
whether n is prime or not. (That's the point to specifying
we're talking about the integers relatively prime to n...)

Seems more interesting to me to start with a class
Group that includes stuff common to all groups, so
that a subclass can represent any group at all. If we're
going to implement what's above as part of a
"curriculum" then at least we should make it clear
that our sandbox is not "groups", it's a tiny part of
the category of all groups.



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