A perverse scheme of sheaves
chews on a stalk of stacks.
Is it etale or crystal?
We are all chained to a ringed
topos in Serres saga of gaga.
Perverse sheaves exist, but they are neither
perverse, nor sheaves. Stalks of sheaves exist,
stacks are sheafes taking values in categories,
stalk of stacks is a word creation,
a ringed topos is a topos equipped with a choice of ring.
"Gaga" refers to "Géometrie Algébrique et Géométrie Analytique"
= "Algebraic geometry and analytic geometry",
of Jean-Pierre Serre.
and Witten said
Remarks: Dieudonne wrote huge amount of mathematics
ranging over huge amount of math, Grothendieck
probably thought about math like nobody else before,
Fermat guessed and conjectured, sometimes wrong.
Pythagoras believed in natural numbers,
Hilbert conjectured or
posed lots of problems. And the phrase "Witten said ..."
is a golden phrase,
especially among string theorists.
Remarks. Cohomology is a bit strange at first,
like Gaga, Miley knows to pull some numbers..
Holy sheaves of schemes!
What stacks of etale crystals
did Grothendieck smoke
in Deligne's secret garden?
Poor Baki! Mon Dieu Donnee!
Remarks. Grothendieck was one of the most
creative mathematicians ever. Some of his creations
appear so strange at first that they appear to have been created
with crystal meth involved (for which however
there is no evidence). But there is crystalline cohomology and
etale cohomology... Pierre Deligne is a student of Grothendieck.
"Poor Baki" refers to Bourbaki (an anonymous group of Mathematicians)
Dieu Donnee to Jean Dieudonne, "Dieu" is "god" in
French so that Mon Dieu Donnee means "my Dieudonne"
or "my god,... ". The phrase "Deligne's secret garden" is
article of Luc Illusie who reports that Deligne loves gardening.
Remarks. The first four formulas
are all due to Euler and belong to
the most famous formulas in mathematics
Making Euler the number one mathematician
who ever lived.
Remark. ODE=Ordinary differential equation,
PDE=Partial differential equation,
KdV=Korteveg de Vries equation, QED=
Quod erad demonstrandum.
Remark: these are all open conjectures. Hilbert's tenth is still
open over the rationals, the Navier Stokes, Hodge, Birch Swinnerton-Dyer,
Riemann problems are Millenium problems. The
Goldbach conjecture and the question about even perfect numbers or
existence of prime twins or sexy primes are open too.
Goldbach refers to the German "Bach", meaning creek.
Remark: more like associations like Galois
Gauloise cigarettes or rimes.
It is naughty,
if one more fly
eats up my pie!
Remark: this identity is always considered
the most important identity in mathematics
as it combines 0,1,e,i, Pi.
Row Row Row Reduce
Redundant columns we produce
swap and scale the rows we must
subtracting rows is lust and frust
Remark: summarizes, what Row reduction is. Made for a review.
Of course, heavily leaning on
Row, Row, row your boat!.
Laplace, Row Reduce,
Patterns you can use!
Remark: summarizes all the methods which can be used to find
determinants. For a 21b review:
a e s
o i u
d t m
Mia Deo Sot
Tuo Dis Emo
Remark: to remember a rule for computing determinants of 3x3 matrices.
Found using computer search.
Song (part 2)
What does the matrix say?
Rotation goes woof,
Translation goes meow.
Reflections goes tweet,
and ShearKernel goes moo.
Image goes croak,
and the Row reduce goes toot.
Columns say quack
and Rows go blurb,
and Basis goes ow, ow, ow.
But there's one sound,
that no one knows ...
What does the Matrix say?
Remark: this was a modification
of the iconic
"What does the fox say?"
song by Ylvis..
O PDE !
"Oh PDE, Oh PDE, solved easily with Fouriee!
For heat use ee to the minus n2 tee.
For wave, pick coosine n of tee.
Oh PDE, Oh PDE, solved easilee with Fouriee!
With velocitee, sin n of tee you see.
Mix X and tee and you will have to pee ...
Oh PDE, Oh PDE, solved painfully with penalty.
Oh PDE, Oh PDE, solved easilee with Fouriee"!
A piano performance or part of
a slide show.
The melody starts like O Tannenbaum
a Christmas song which is based on a folk song from the area of Schlesien (now mostly Poland).
In that song, the evergreen fir tree is praised as "faithful", contrasting to other trees
associated to faithless lovers. This is fitting, as Fourier theory is an "evergreen".
In the wonderful month of Mai
Two rabbits went to play
A third rabbit saw the day
Then five and eight - yuhei!
In the wonderful month of June
Thirteen rabbits grew to 21 soon
They sang and jumped and had more sex
Now, they all have an Oedipus complex!
Remarks.See The song.
was part of a review for Math 21b.
The priest 1000000
holds a frog 100000
in his finger. 10000
The flower fears 1000
that the monkey 100
is bending 10
its stem. 1
This is a memnonic to learn the Egyptian number system.
See Lecture 2: around 10:30
Hip Hop Review (PDE's, Extremization, Chain rule, integration) 2017
PDE rich. You can't stuck with me, if you wanted to:
These expensive, these is rare Laplace, these is bloody heat
Hit the wave, I can get them both, I don't wanna choose
and I'm quick, cut a function off, so don't get comfortable, look!
I don't derive now, I make money moves.
If you'r a saddle, you get popped, you are maxim, you are opt.
Don't you Nabla around my way, you can't Lagrange around my block.
And I just checked my accounts, turns out, I'm max, I'm sad, I'm min.
I put my hand around my D, I bet your D, his D, her D.
I say I let the chain rule go, this hit is hot like a stove.
My regions glitter as gold, tell the order play her role.
I just drove along a curve, I just came up in a nerve.
I need to fill up my x, no I need to fill up my y.
I need to let everybody know that none of their shapes is safe.
I go to polar and break, only the r can relate.
I used to live one D, now it's a crib with a square.
Regions got charms, like butterfly farms.
Had to let the functions go, just in case those cos forgot.
I just run and switch around another integration bound.
See the Video: I'm Boss, I make body moves,
or the extended version.