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Topic: GNU Math = CS + Math
Replies: 2   Last Post: Sep 20, 2017 12:54 PM

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kirby urner

Posts: 3,482
Registered: 11/29/05
GNU Math = CS + Math
Posted: Sep 19, 2017 3:09 PM
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Rhymes with "New Math"...

I think we all know the pun by now: GNU stands for GNU is Not Unix.

However in being recursively defined, it's also an allusion to Lambda
Calculus.

GNU came along around Gen 2.0 of the C-STEM Epoch, which Epoch started
around PLATO (1960) and rolled through at least two revolutions: PC
(personal computer) and Liberation (free / open source).

Liberation was a long fought battle pitting the likes of GNU / Linux
against SCO. I'm sure some here remember those years, followed by Browser
Wars...

Where C-STEM starts hybridizing with the contemporary public schools math
sequence is around the Fundamental Theorem of Arithmetic, that every
integer has a unique prime factorization.

I'm going with Conway's suggestion that we throw in -1 as a factor along
with 1, go ahead and call the former prime if you like.

A prime has only itself and 1 as a factor, and -1 if negative. 1 itself is
not prime.

When we say factors, we may include or omit the 1 (identity element)
depending on context.

factors(42)
(1, 2, 3, 7)
factors(100)
(1, 2, 2, 5, 5)
factors(-12)
(1, -1, 2, 2, 3)

When students are ready to write code, in whatever language, to deliver
these unique prime factorizations, that's when CS starts to meet Algebra.
The Sieve of Eratosthenes, Trial By Division, Euclid's Algorithm, start
phasing in here, as things to code.

Yes, we're still doing arithmetic, using the four basic operators plus
modulo (%), but we're also introducing functions, the composition of which
will be our basis for getting work done.

Algebra has much to do with controlling the components of a function, one
might say inputs, arguments or parameters. The specifics are often fixed
with constants, as in:

A sin (Bx + C) + D

the paradigm oscillator. Only x is considered the dependent variable at
the end of the day, as A, B, C, D are used to construct a special case
function.

Polynomials are the same way. The coefficients fix the function, and then
x or t do the heavy lifting.

A*x**3 + B*x**2 + C*x + ... we have notation for arbitrarily long lists.

CS is good at this: providing an executable language wherein functions
have the ability to construct other functions.

CS profs further along in the pipeline will be grateful if we start writing
functions that build functions earlier.

C-STEM has a bright future.

Kirby



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