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Topic: Square root of six
Replies: 21   Last Post: Aug 31, 2012 12:47 PM

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Robert Hansen

Posts: 8,434
From: Florida
Registered: 6/22/09
Re: Square root of six
Posted: Aug 28, 2012 12:41 PM
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Kirby, just a couple of weeks ago, on your advice, we checked out Beverly Hills High. They barely even had a digital offering at all and by no means did they offer (what they barely even had) in place of math. Since you will not offer accurate examples of this Math/CS thing then I will.

Here is something interesting. That Python Math course offered at Phillips. You either get CS credit or Math credit, but not both.

"COMP-470, Introduction to Discrete Mathematics and Programming
Five class periods. This course blends a study of programming (using the Python programming language) with mathematics relevant to computer science. Students learn how to design simple algorithms and write and test short programs in Python. The course covers Python syntax and style, as well as data types, conditional statements, iterations (loops), and recursion. Selected mathematical topics include sets, number systems, Boolean algebra, counting, and probability. A student in this course is eligible for credit in either mathematics or computer science. A student who wishes to receive mathematics credit should sign up for MATH-470; a student who wishes to receive computer science credit should sign up for COMP-470. Prerequisite: MATH-340 or permission of the department."

And you must complete math through pre-calculus (or get permission from the department) to take XXXX-470.

I think they have the formula just about right with regards to CS/Math. Replace calculus with CS, for some students.

But this is if you are talking about classical programming which was math based.

Creating applications like Facebook is neither mathy nor classical. I hate to break this to you like this, but the craft of writing software left its math origins decades ago. Saying that writing software is mathy is like saying that playing music is mathy. They all share a similar and energizing craftiness, but only math is mathy.

Bob Hansen



On Aug 28, 2012, at 11:52 AM, kirby urner <kirby.urner@gmail.com> wrote:

> Yes, I'm all in favor of roots and root finding. Raising to powers is
> an important concept. I'm also a big believer in "infinite series"
> i.e. the sums and sequences portion of precalc, where you're both
> converging and/or your partial sums are converging... I'm a big fan of
> that stuff.
>
> However, I think it's very important that we get away from numbers,
> meaning anything in the N, Z, Q, R, C pool, and focus on other objects
> that many also be multiplied, such as permutations.
>
> A permutation, in this namespace, is like a mapping of the letters A
> to Z unto themselves, such that each letter is paired with another (or
> itself). The identity permutation points every letter to itself.
>
> When you multiply two permutations, you get the one that does the work
> of both, e.g. if A -> R in the first and R -> K in the next, then
> their product goes from A to K in one step.
>
> These kinds of object are somewhat tedious to work with by hand and
> students rapidly get carpel tunnel or throw fits in frustration,
> twirling and foaming on the floor, as if possessed by demons.
>
> We don't get that behavior with bright talking screens are enlisted,
> and when we let computers do the guts of the operations. We program
> though, which means we take control, have insight. Programming your
> permutations, teaching them how to "multiply" is not just "for
> programmers" (the way they say in Florida), it's for anyone learning
> math, as this is group theory / abstract algebra, right at the core of
> the disciplines.
>
> So the nth root of a permutation: that makes sense. We can do "power
> tables" which show how often permutations cycle, when multiplied by
> themselves.
>
> There's this thing about using the GCD (greatest common divisor
> algorithm) to get the totatives of a number, those positive numbers <
> N with no factors in common with N. If you multiply totatives modulo
> N, you get a group. You are also laying some stepping stones for
> understanding cryptography, RSA in particular, within reach by senior
> year. This is the digital math track I talk about, used in the better
> schools with state of the art STEM curricula.
>
> There's a gap between schools with digital savvy and real STEM, and
> lower quality laggard schools that don't have such quality curricula.
> The USA is for the most part far behind, but here and there has some
> pockets of excellence. We can't really break it down by race though,
> as the better STEM schools are not furnishing us with exactly those
> kinds of statistics. They're not even really "schools" in many cases,
> just learning environments in cyberspace with no zip code, so more
> like Facebook (a socially engineered meeting space).
>
> Kirby




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