OK, you AP calculus students, here is your test this Friday.
Or it is a free-response question for
college credit. This was meaningful twelve
years ago when I worked as a substitute teacher (high school), which is a saga
in itself. You have to prove two
controversial theorems in complex variables, and one in statistics.
Ritvikmath, in this video, proves two of the least intuitive
theorems in mathematics (complex variables), the Morera Theorem and the LiouvilleTheorem (that a bounded everywhere-differentiable function remains a constant everywhere,
like Facebook). It probably does not
apply to quaternions. There is a related theorem in statistics of significance in fluid mechanics. (The spelling of the mathematician's name is different from the Kentucky city's.)
The math professor’s technique is simple: write the steps of
the proof on simple sheets of paper and use colored felt ink. You don’t need fancy cameras to make the
videos.
The Liouville (an odd spelling of a French mathematician’s
name) was a question in my Master’s Orals at the University of Kansas, I
believe on January 18, 1968, on an unusually mild winter day in Lawrence. I
stumbled through this theorem (its in the Chapter 7 of my DADT-III book) and
probably barely passed the orals. (Yup, “You
passed”. But “He’s going into the
service”.)
On campus, we used to talk about “all this useless math” that
gave people deferments from going into Vietnam combat. No matter, quaternions probably explain the
elementary particles of physics, and the entire Universe follows the laws of
mathematics and statistics to a tee. We wouldn’t have Facebook’s algorithms or
today’s Internet without it. We all
exist because statistics says we must at some point.
I gave a much better technical talk, on my Master’s Thesis
(Minimax Rational Function Approximation) at one of my first job interviews in
Princeton NJ in December 1969 just before getting out of the Army.
What “professionalism” means has changed so much since then.
Also, for a video about a physics exam, try this.
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