...

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

Bill Janssen wrote: 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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