### Songs For Beginners: Pascal’s Triangle

(:={
):=}

**********************************
()

${0 \choose 0} = 1$

(),(a)

${1\choose0}=1, {1\choose1}=1$

(), (a) (b), (a.b)

${2 \choose 0} = 1, {2\choose 1} = 2, {2\choose 2} = 1$

(),(a)(b)(c),(b.c)(a.c)(a.b),(a.b.c)

${3\choose0}=1,{3\choose1}=3,{3\choose2}=3,{3\choose3}=1$

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X
|\
0+

()
(),(a)
(),(b),(a),(b.a)
(),(c),(b),(c.b),(a),(c.a),(b.a),(c.b.a)
***********************************
${n+1\choose k} = {n\choose k} +{n\choose k-1}$

#### 4 Comments

1. more in this vein:
exercises at random (12/03/09)

2. I don’t ‘get’ the first verse.

3. i’m replacing the usual “{”
and “}”… for ease of typing…
with “(” and “)” [and lightly
mocking myself with a little
“ain’t type fun” stab-at-humor;
it looks like a smily, see?!
;0
oh well.].

the symbol “:=”
means “equals by definition”.
the actual handwritten notes
occur in the context of
*more instances* of this
same symbol.

readers of the zines are (implicitly)
invited to guess what the heck
anybody would want to go and do anything
like put a colon in front of an equal sign for.

[
actually in practice, there’ll very likely be
somebody standing by that can hardly wait
to tell ’em. anyhow this has been the case
in the few instances that’ve taken place so far…

and it was very clearly the case here again.
thanks for asking (and now aren’t you sorry).
]

“lectures without words”.
the trick is to get stuff that *seems almost*
to explain itself. get ’em hooked…
get ’em *talking*…

4. vlorbik

“A good line drawing
has the minimum number
of lines still adequate
for recognition. It is,
in a sense, the best
for mathematical illustration
because it leaves the most
space for decorations to be
applied by the user.”

http://www.scribd.com/doc/14009839/George-K-Francis-A-Topological-Picture-Book-1988-213p-0387964266

• ## (Partial) Contents Page

Vlorbik On Math Ed ('07—'09)
(a good place to start!)