So, I got back from Alaska. A … long time ago. Pictures will be forthcoming. After that, it was pretty much straight back to CMU. And back into the thick of things.
Theoretically, this semester was supposed to be easy. Four classes: Intro to Psychology, Special Topics in Thermal Physics, Probabilistic Simulations, and a graduate course in Discrete Mathematics.
Four courses. Nothing, compared to things I’ve done previously.
So, my prolonged silence might cause you to ask … what happened?
And what happened, for the most part, seems to be this. I agreed to TA a section of Calculus in 3D. That sucks up a large percentage of my time, grading and preparing. Discrete Mathematics, by the nature of the course, takes a -tremendous- amount of time. I basically spent a week thinking about 3 problems and didn’t get anywhere, only to get them all in the last two days before it was due. Those two by themselves seem to be the largest contributors, plus scads and scads of psych reading, which is driving me nuts.
But … so much math. Fascinating, exciting, beautiful math.
Some problems I’d like to discuss, when I have the time, would be …
Suppose you were to color the edges of a complete graph on n vertices with k many different colors. Let f(k) be the largest value such that you can color the complete graph on f(k) vertices with k colors – such that no three edges form a monochromatic triangle. The problem is to show that 
Similar setup, but in this case show that 
One problem I've been trying to write up, for a very long time (and my inability to complete it basically started this trend towards little to no writing), is calculating Graham's Number – one of the largest numbers ever put to practical use. It is big. So big you can't really comprehend it in terms of value. And yet … we can calculate it! And that, in my opinion, is very exciting.
Plus! Some interesting recursions, and some simulation tricks … We're doing some very interesting things in thermal I would love to share, but I'm struggling with the 'how', without teaching thermal physics from the ground up. I'm sure I will figure something out. But, in any case … interesting maths ahead.
