Some notes on:

Mathematics for the Digital Age and

Programming in Python, 2nd Edition

by Maria Litvin and Gary Litvin

===

I just got my evaluation copy of the 2nd edition and I've been

plowing through it eagerly.

For those just joining, I've been somewhat zealously proposing

we converge math and computer topics more successfully --

including pre-college. I've been internationally outspoken on

this per 4dsolutions.net/presentations

Now we finally have a slim, yet action-packed volume that's a

pretty good proof of concept I think, plus it comes with a small

test demographic @ Phillips / Andover, a world class school.

I'll just enumerate some of features I've been hoping for, and

am finding in this book:

0) a Rational number class w/ operator overloading

1) graphs (as in networks) relating to polyhedra

2) ASCII -> Unicode

3) a Madlib example

4) triangular numbers, link to OEIS **

5) polynomials

6) fibonacci numbers, phi

7) RSA (public key crypto)

Lots more is included of course, including a rather

deep foray into computer hardware and low level

language (8088 assembler), boolean truth

tables, strategy games, matrix multiplication (exercise

pg. 249).

** On-Line Encyclopedia of Integer Sequences

This text is like a kernel or seed in that it plants all the

"right stuff" for a larger tree of topics, branching off

from the many covered.

As a teacher, you're at liberty to expand coverage in

any number of directions.

Just to take one example:

<technical>

Let's go from triangular and square numbers, ala 'Gnomon'

by Midhat Gazale, to polyhedral numbers ala 'The Book

of Numbers' by Conway and Guy.

The number sequence 1, 12, 42, 92, 162... is especially

worthy (including of Python generator treatment). Type

that into OEIS and we get the cuboctahedral numbers,

aka icosahedral numbers:

http://www.research.att.com/~njas/sequences/A005901That these polyhedra go together is deep chemistry (literally),

plus you'll find segues to architecture and virology. Scroll

down to the links section and you'll find one to my site:

K. Urner, Microarchitecture of the Virus

Grunch.net/synergetics/virus.html

See also: 4dsolutions.net/ocn/numeracy0.html (includes

animated GIF showing the ball packing in question:

http://4dsolutions.net/ocn/graphics/cubanim.gif )

The Python generator might be:

def cubocta():

layer, total = 1, 1

n = 0

while True:

yield (layer, total)

n += 1

layer = 10 * n * n + 2

total += layer

Where "layer" will be 1, 12, 42, 92... and "total" will

be a running accumulation of that total number of

balls packed out from a nucleus, 1, 13, 55, 147...

See also: wikieducator.org/PYTHON_TUTORIALS#Generators

(crystal ball sequence)

</technical>

<lore>

When new x-ray diffraction techniques were disclosing

the icosahedral shape of the virus, scientists contacted

Buckminster Fuller, because he was Mr. Icosahedron

in those days (the geodesic dome guy).

He had this formula for 1, 12, 42, 92..., a mathematical

result H.S.M. "King of Infinite Space" Coxeter thought was

pretty brilliant (simple, elementary, easy to prove).

"Coxeter told Fuller how impressed he was with his formula

-- on the cubic close-packing of balls. And he later took

pleasure in proving it, noting in his diary one day in

September 1970: "I saw how to prove Bucky Fuller's

formula," and publishing it in a paper, "Polyhedral Numbers."

Of course more than anything, Coxeter fell in love with

Fuller's geodesic domes."

[from: Siobhan Roberts, King of Infinite Space (recent

bio of H.S.M. Coxeter, to whom Fuller dedicated his

magnum opus -- w/ permission -- citing pg. 71 of

'Regular Polytopes' deeper into his text) ]

< technical >

Here's my own proof, dunno how similar, and kinda

dense (f is the number of intervals along an edge, so

one less than the number of balls).

http://mybizmo.blogspot.com/2007/01/gnu-math-memo.html</technical>

Fuller's formula was published in the NY Herald Tribune in

connection with a virology conference @ Cold Spring

Harbor, but then a follow-up Scientific American article

on the same topic dropped all mention of Fuller, ostensibly

because Coxeter and others had by this time generalized

the viral micro-architecture using the related mathematical

work of Michael Goldberg.

I know Fuller was distraught about being cut out of the

narrative (I saw some of the archived correspondence),

though he had his posthumous comeuppance I suppose,

w/ the discovery of "buckminsterfullerene" (also icosahedral,

in the sense of five-fold rotationally symmetric).

"They show the same kind of structure as the domes

of Buckminster Fuller" Dr. [Robert] Horne, who took

the first photos, explained, "We went along working

out the mathematics of the viruses when somebody

told us about Fuller's book . . . We opened it and

there it was all worked out. It seems that both Fuller

and nature have picked out the most rigid geometry

they can find."

"Virus - A Triumph and a Photograph"

New York Herald Tribune. February 6, 1962.

(cited in B.G. DeVarco, Invisible Architecture: The

Nanoworld of Buckminster Fuller, 1997)

</lore>

Per my workshop @ Pycon / Chicago, I go with

these two axes: technical content vs. lore. A curve

of finite / constant bandwidth, like the opportunity

cost curve in economics, suggests we need to vary

the mix, going more for the lore in some contexts.

Dry-as-bones technical stuff is just as necessary

though, so we oscillate, go back and forth.

Kirby

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