Mathematically speaking, it’s been a quiet week.
I hope to put out a summary of multi-collinearity this Monday… but, if necessary, I already have a different post written – a sketchy introduction to group theory. Finishing it off last weekend didn’t leave much time for other mathematics.
I did pick up chemical reactions again… namely, finding mechanisms – sequences of elementary reactions – that explain observed reaction rates… specifically, the dependence of rates on composition. It’s beginning to make sense, now that I’ve looked at it after a long layoff.
I also spent a little while looking through my books on spectrum analysis (that is, frequency domain analysis of time series). For this, I feel like one of the mythical 3 blind men trying to understand an elephant. I like having more than one way to come at something, but for spectrum analysis, there seem to be too many different ways of approaching it. (I know, first understand one, or maybe two together, and then move on to more.)
A 2nd book by Vladimir I. Arnold came in: “catastrophe theory”. The back of the book says that it “…provides a concise, non-mathematical review of the less controversial results in catastrophe theory.”
I beg to differ. One might call it “non-rigorous” but it is hardly nonmathematical.
The most significant thing I got out of it was: “On odd-dimensional manifolds there can be no symplectic structures, but instead there are contact structures.”
The point is that symplectic structures can only be defined on even-dimensional spaces – I knew that… the prototype is the even-dimensional phase space of Hamiltonian mechanics. And I have heard of contact structures… without realizing that there was any relationship. At this point, that’s about all I know.
So let me go learn some more about something.