[Numpy-discussion] [Python-3000] PEP 31XX: A Type Hierarchy for Numbers (and other algebraic entities)
David Goldsmith
David.L.Goldsmith@noaa....
Fri Apr 27 13:25:15 CDT 2007
Bill Janssen wrote:
>> Jeffrey, is there any way you can drop the top of the tree and going
>> straight from Number to Complex -> Real -> Rational -> Integer? These
>> are the things that everyone with high school math will know.
>>
>
> I think knowledge of the concepts of group, ring, and field is
> supposed to be standard knowledge for any high-school senior -- isn't
> this what the "new math" was all about?.
Nah, AFAIK, not really. Of course, for those who remember Tom Lehrer,
New Math was about learning that one could base number representation on
bases other than 10 (even more fundamental to CS, no?), but I think it
was rather more about broadening the standard curriculum to include more
than just arithmetic drill, i.e., to more prominently include things
like problem solving skills, (somewhat) more abstraction, etc. Along
the latter lines, I do remember learning (and tutoring), by name, things
like the symmetric, reflexive, transitive, associative, commutative, and
distributive properties, but I didn't hear/see the words group, ring, or
field (in a math context) 'til I got to college and was formally
introduced to the subject of Linear Algebra (and lest you think my HS
math curriculum was deficient and/or non-standard, I don't want to go in
that direction, but trust me, it was more than sufficient and it was
non-standard, but in the positive direction, not in the negative, and I
graduated 1st in my class in math). As far as the scientific
disciplines which one might reasonably expect a college major therein to
have at least a "nodding acquaintance" w/ the classes of Abstract
Algebra, certainly Math (and hopefully Appl. Math and Stats), probably
Physics, perhaps Chemistry, CS if you say so, but even Engineering I'd
say you're beginning to tread in uncertain territory, and Biology, etc.,
unless taken with a large dose of formal mathematics, fuhget-about-it.
DG
> But they're pretty
> fundamental to computer science; anyone trying to do serious work in
> the field (that is, anyone with a reason to read the PEP) should have
> a nodding acquaintance with them.
>
> Bill
>
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