An intensely cool and nice prof, who probably knows more about DifferentialGeometry? than anyone on the planet. She also teaches Linear Algebra I and II, and Advanced Linear Algebra.
Ask her to demonstrate the hairy ball theorem to you sometime.
"Did you notice? You're backwards thinking."
"You know why I say this is clear? Because I saw it!"
"I want to send a soldier from this universe to that universe."
"I want to add a negative sign to make sure 1 is greater than zero."
"We reviewed covariant derivatives, which you probably never saw before."
"You put them together like a goat and a cabbage: they eat each other."
"The whole complicated thing can be written as this complicated thing."
"Let's say B is a boy... and this C is a girl. B wants any relationship it can find with C - Now, every step must be legal..."
"Here z can be anything! ::pauses and laughs:: ...meaning anything in the Real Numbers, of course. Not z to the chicken, z to the apple, you know?""
(after checking the solution to a group of linear equations) "That's cool!" ::wiggles and points to board with a smile:: "So you say then, 'that's cooool !!'"
"Meaning these leading entries run da da da."
"I don't know if you get it but that's fine." (points to head) "What is Professor Gu talking about?"
(in reaction to MicahSmukler's .sig:) "It should be: 'We must at any time be prepared to replace "points, lines and planes" with "Grassman manifolds."'"
"I can give you a formula very yuck! How you solve?"
"You all understand? I not saying something funny here?" ::blank looks from students:: "Aha. Yes." ::erases important concept and continues scribbling madly::
"You have an army with infinite soldiers, and you want them to turn around. You don't want to tell every soldier to turn around, that's too many! So you tell the commanders instead, those are like the basis vectors!" (BADLY paraphrased since it's been a while since I heard her say this...)
"Well, when I was in school, this is how I remembered what to guess for a solution...
When you take e^x, and beat it with a derivative, it doesn't change, because e^x is like the strong man, right?
When you take sin x and beat it with a derivative, well it, like it changes, see, kind of like the snake. *points to cos x*
Well, ln x is like the beaten child... it goes and hides under the table... *points to 1/x* "
Ha ha ha! You all laugh away the cancer!