Kirk: And then the *best theorem in all geometry* Kirk: The first one you ever learned Kirk: The Segment Addition Postulate // student point's out it's a *postulate* Kirk: Yeah, it's a postulate Kirk: I guess it's not a theorem
\\After a somewhat frustrating day of proving Laurent's Theorem in Complex Analysis, Mr. Schwartz sent the following email: Schwartz: Here's a better version of the proof we (sorta) skipped today. Should make it more clear. http://goo.gl/hEKqqI
//Functions, first period. Descartes Law of Signs and Upper Bound of Roots Theorem. Rose has just used synthetic division with 5 on a polynomial and ended up with a nonzero remainder. Rose: Oh no! 5 is not a real root! But, class, you see, dividing by a number that is not a root is a lot like a break-up: You could just rush on blindly looking for the next opportunity, or you could slow down and consider the implications, and why everything went wrong... So what does anyone notice about the remainder? Noah Kim: Wait, Mr. Rose, is this related to your personal experience? //a little bit later, talking about graphs of polynomials in relation to roots Rose: But we know what graphs of polynomials look like! They're so continuous and smooth and predictable.... Noah Kim: Mr. Rose, you are still talking about math, right?
//Analysis 1A is discussing Rolle's Theorem Rose: Yeah, so, that's Rolle's Theorem. It probably doesn't seem very significant to you right now, but it actually plays a very large role... Class: *giggles* Rose: Oh my god.
Rose: It's also called the Sandwich Theorem, because y'know, you've got g and h making a sandwich around f, like it's cheese or ham or whatever you want to put in there... Student: You should serve it with polynomial soup!
Rose: Now we're going to learn about one of the most important theorems in calculus -- Rolle's Theorem. //teaches Rolle's Theorem //class starts talking about the most important theorem in calculus Student: Is Rolle's Theorem the most important? Rose: Who gives a crap about the stupid Rolle's Theorem?!