Wonderful World
(with apologies to Sam Cooke)
Don't know much about topology
Don't know much Galois theory
Don't know much about Folland's book
Don't know how the complex plane should look
But I do know that I love math
And I know that if it loved me back
What a wonderful world this would be.
Don't know much about PDEs
Don't know much about set theory
Don't know much about Lie algebra
Don't know what a slide rule is for
But I do know one and one is two
And if my own claims were just as true
What a wonderful world this would be.
The Wiener Covering Lemma jingle:
Oh, I wish I were a covering by Wiener
To bound the size of measurable E
With a subset that is disjoint times a constant
Depending on dimensionality!
Homotopy
(to the tune of "Oklahoma", by Phil with help from the usual
lunch crowd)
HOOOOHHHHHHHH
motopy, where the curves deform continuously
and it's trivial
in spaces who
are called "connected simple-y"!
(incidentally, Maig and I were looking to fix the rhyme with "trivial" and the rhyming dictionary gave us "lord of misrule", which is just really cool)
Somewhere into a Spectrum
(to the tune of "Somewhere over the Rainbow", by Julie with my
willing but not very able help. it doesn't scan very well but it
was written in a very short amount of time.)
Somewhere into a spectrum
Saunders lives
Samuel waits with omega
For your map in from X
And when the cohomology
Is found with coefficients G
It's the same as classes, you see,
When you find homotopy.
Some explanation: Saunders and Samuel are Mac Lane and Eilenberg, respectively. If K(G,n) is an Eilenberg-Mac Lane space (the K(G,n)'s form an omega-spectrum, by the way), with G an abelian group and X a CW complex, n>0, then there is a natural bijection from the set of homotopy classes of maps X-->K(G,n) to the nth cohomology of X with coefficients in G. That is to what the song refers.
Twenty-Three Digits of Pi
(A Shakespearean rant by me and Phil)
Now I have a grand insolence
To martyr fools who prate conceits
Developed, blindly stewarded, and by our grooming,
Made subtle in measure.