Before the feels fade and the high subside, I just want to document that I had a really great time in this year's MSP Region 10, 12 & BARMMM annual convention. I think it's the most fun conference I've attended, to date. I've been to a couple conferences in other MSP Regions, and conferences in math education but I think what makes this special is that most participants in this conference are my cohort. My peers who I used to only interact virtually I saw face-to-face. It was fun discussing math and everyone being enthusiastic about it. You could see collaborations forming after presentations. I don't think I will have a collaboration from it but it doesn't matter. This is me dipping my toes in the math ocean. I crave community and I got it. So many more things to reflect on but that will be reserved to my private journal. We gotta move forward, baby. No time to dwell.
The D-classes have a certain type of hierarchy. And to illustrate this, I'll give relevant properties of the rank of a transformation. The first property is that the rank of a product of two transformations is less than or equal to the minimum of the individual ranks. Let's flesh this out some more. Let's start with what I call the nobility in this hierarchy--the permutations. The noble class would like their wealth and power to stay within their class or family. How do they do that? The idea is to marry someone with the same social class as you are. It's a very common trope in movies and TV. So in the same way, for an "offspring" of a permutation to have the full rank still, both of its "parents" should be permutations. rank(ab)=n if and only if rank(a)=rank(b)=n As part of group theory, we study permutations. This is because a group is embedded in a permutation group by Cayley's theorem. In the finite case, every group of order n is isomorphi...
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