I think that’s about enough of the representation theory of the symmetric groups for now. There’s a lot more to say, but we’ve been at this for months and I’m itching for something new.
I’m thinking next up is some differential geometry, although I’ll have to take a little side trip to cover some basic differential equations before too long. I am still looking for a good reference that gets straight to the basic existence and uniqueness theorems of differential equations. If anyone has any suggestions, I’m all ears.
You might be expecting another “Sunday Sample” here today, as there have been for the last 187 weeks, but not today. And you’ll find that they don’t even exist here anymore!
What happened? They’ve all been moved (along with this week’s installment) to drmathochist.wordpress.com, which will be my place for more personal posts. I’ll also relax the filter there, so Dr. Friedman can quit complaining about self-censorship (and I can post Cee Lo Green’s new track!)
At the same time, I’ve just opened up The Unapologetic Programmer for my more computer-programming related posts. It’ll be much less organized than here, I’m sure, but I know there’s a bunch of people into that sort of thing here.
WordPress seems to have messed with again, and fouled it all up. Dozens of perfectly well-formed expressions are throwing errors, including $ latex \sigma$. Since writing lowercase sigmas is pretty much essential for the current topics, I’m just not going to write until they fix their mess.
And if anyone from WordPress reads this: one of the major I encouraged people to start math, physics, and computer science oriented weblogs on WordPress’ platform is exactly its support for LaTeX. It really annoys me to no end that you keep screwing with it and breaking it in pretty severe ways.
I know I’ve been really lazy about my blogroll, and I should get around to that sometime. But there’s a new one I have to point out right away:
The Language of Bad Physics (as noted in the comments, now on WordPress at this address). Like Frank Costanza on Festivus, she’s got a lot of problems with you people (physics writers) and how mathematical terms get mangled and confounded in the physics literature. It’s one big Airing of Grievances, and you’d do well to listen up. My only complaint is that it’s one of those horrid, ugly Blogspot pages and not a nice -enabled WordPress page. But maybe it’s early enough to get her to switch
At least it won’t be hard to find it tomorrow morning.
Last May we started talking about linear algebra, with a little aside into complex numbers and another into power series along the way. Before that all, long long ago, we were talking about single variable calculus. Specifically, we were studying functions which took a real number in and gave a real number back out, and the two main aspects to this study: differentiation and integration.
The first part studied how a function changed as its input varied near a fixed point by coming up with the best linear approximation of the function near that point. Now that we’ve got an understanding of linear functions between higher-dimensional real vector spaces, we can work towards extending this idea of differential calculus into multivariable functions.
The second part studied how to “add up” a continuously-varying collection of values, each with its own (infinitesimal) weight. Again, our new understanding of higher-dimensional analogues of linear spaces and functions will help us find the right way to generalize the integral calculus.
I’m trying to get access to some of my references again, since I no longer have even as much of a mathematical library down the hall as Western Kentucky University provided. So I’ll pick up when I can.
As a much-anticipated visit approaches, my apartment is asymptotically approaching neatness. My former students’ comprehension of the word “asymptotically”, however, remains constant.
And this morning I received the proofs to a paper that was accepted for publication two years ago: “Functors Extending the Kauffman Bracket”. So yeah, I get out with it finally appearing in print, but in the meantime my career is shot.
This week’s been hectic, what with interviews (which I can’t talk about but I think went okay) and driving back to Kentucky. And now I’m about to spend two weeks up at Mammoth Cave. I should have some internet access, so I’ll try to keep up with lower-content features, but real mathy stuff is off the table for a while. You can always follow my twitter stream to keep tabs, and find links to pictures I take underground, assuming that the wireless at Hamilton Valley really works. But of course, the best laid plans of mice and men…