Happy Boxing Day, everyone.
We went through a phase in graduate school of writing poems and songs, usually based off existing ones. I think they’re worth preserving, though I do shake my head a bit when I read some of them. I’ve given credit (blame?) below, though I did leave them in their original first-name-only state; anything not ascribed is my own handiwork.
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.
The following was something I had buried in my real analysis notebook. Julie said I should share with the world because it’s funny to have such a bleak poem about something as innocuous as analysis. I’m not sure analysis is so innocuous. Anyway, this blog post is the first time it has seen the light of day.
Analytic Howl
(with groveling apology to Allen Ginsberg)
I have seen the best minds of my generation
Destroyed by madness, starving, hysterical
Driven to abstraction by the fragments of analysis
Crumbs dropped from the masters, fractions and dimensions
Sobolev wields a whip, clamoring for integration
Compute and work within epsilon for your bread.
Then Hardy, no comedian now, looms large above
The meek mathematician’s last grasp on sanity
Slips away and he weeps, tears and mucous and saliva
Mingling on the floor on which he lies.
Numerical and functional they merge
Blending together like gashes in a river
Unruly children convolve, they star, like some profanity eradicated
Regularize! the masses cry, and support the intertwining
The norm must be upheld, it keeps the rules from failing.
Signed measure takes your name and spits out
A number, a value for your life
Fubini and Tonelli weave too fast for the weeping eye to see
The integrals and functions dance a sickening
Do-si-do, shifting position, sometimes equal, sometimes less
We lose some life when we know it more.
[I should make the caveat that while I did not find analysis an easy course, I do not hold any grudge against it. I simply got going on this and I couldn’t stop. It was going to be my magnum opus until I realized I didn’t feel strongly enough about analysis to justify creating an entire rework of Howl, long, bleak, and depressing, about it.]