ChapterZero

If you were ever wondering why H is used for entropy instead of say E, here’s one theory courtesy of Tom Carter’s lecture notes:

“The enthalpy is [often] written U. V is the volume, and Z is the partition function. P and Q are the position and momentum of a particle. R is the gas constant, and of course T is temperature. W is the number of ways of configuring our system (the number of states), and we have to keep X and Y in case we need more variables. Going back to the first half of the alphabet, A, F, and G are all different kinds of free energies (the last named for Gibbs). B is a virial coefficient or a magnetic field. I will be used as a symbol for information; J and L are angular momenta. K is Kelvin, which is the proper unit of T. M is magnetization, and N is a number, possibly Avogadro’s, and O is too easily confused with 0. This leaves S . . .” and H. In Spikes they also eliminate H (e.g., as the Hamiltonian). I, on the other hand, along with Shannon and others, prefer to honor Hartley. Thus, H for entropy . . .

When, after a few hours spent recuperating from the mental fatigue induced by a week of harrowing math finals, you find that you can’t keep the promise you made to yourself to have a math free weekend.

Moments like these– where I have the freedom to do something, anything else, yet find myself compelled to do math– help me to remember why I’m studying math, even though I don’t always like the courses I’m taking.

I’m so screwed: check out my Large Deviations final. I’m totally not prepared for this. I haven’t been doing much beyond going to class and attempting my best to follow the ideas and proofs in class.

That said, I have about no idea how to do problem 3: we talked about a large deviation principle for a single Ito process, but I’ve been unable to apply that so far. Problem 4 is a give-away problem, and I’m almost certain that my approach to 1a is the best given what we learnt in class, but I’m too shaky on the others.

Sooo freaking screwed! And I still have to study for my 106 final tomorrow: I have about half of the class notes left to review.

Ramon’s notes for the stochastic calculus and stochastic control course, ACM217, are complete! I’m going to be rereading them this summer, at the liesurely pace of a chapter per week, because I don’t feel comfortable with almost anything I did in class

At the same time, I’ll be going through Jacod and Protter and Grimmett and Stirzaker (this last because we used it as the text in ACM116, the probability course that I’ll have to take a qual on in August). There’s lot of other qual-related reading in my future: I’ll also be scanning Ablowitz and Fokas and Carrier Krook and Pearson and Jordan and Smith, and Verhulst, the texts for ACM101 (forget trying to read any of those), and Miller, which although not mentioned in class, seems like a bang-up introduction to asymptotic methods, the subject I’m most shaky on. For ACM106, my numerical methods course, I’ll be reading Trefethen and Bau and Strikwerda, and scanning some other numerical PDE notes/books for information on FEM, shock-tracking schemes, and other miscellany. Finally, for ACM104 and ACM105, the functional analysis and linear algebra courses, I’ll stick to the course notes (which are redactions of various texts) and maybe some outside reading on those things I still don’t quite grok (e.g. anything related to the spectrum of an operator).

Gonna be a busy busy summer.

Andrea Bocelli is one of those few musicians who, as far as I’m concerned, can do no wrong. I’ve heard three of his albums, and loved just about every song. Of course, he could probably sing a receipt at me, and I’d think it was beautiful.

A while back, I made myself a promise that whenever I get a new Bocelli album, I’ll memorize the lyrics to at least one of his songs (an Italian one)– it feels good to be able to sing a beautiful song in a language you can’t speak. Part of the attraction is probably that you’re able to focus on the sound of the words instead of the meaning. You approach each song as a purely mechanical puzzle– when do I pause, put a treble in my voice, …– all preconceptions aside, something harder to do when you understand the lyrics.

One of the songs I’m attempting on “Amore” is Canzoni Stonate. I’m trying it because the singing is slow enough that I can have a chance at enunciating some of the words correctly, and it’s a just-platonic-love song or a non-cheesy-romantic-love song, depending on how you choose to interpret it (check out the lyrics, original and translated).

The first one of his songs I memorized is Con te Partiro. Check it out on youtube (the lyrics are also there in Italian and English if you want to learn them):

Here’re two guys (no idea who they are) singing Canzoni Stonate. Not nearly as good as Bocelli’s version, but it’s a good song, and I couldn’t find one of him singing it.

Fredholm integral equations of the second kind are of the form

where the kernel and data are given, and the problem is to find . Sometimes solutions exist and are unique, but that’s not guaranteed.

But you don’t need to know anything about IEs to solve this problem:

Give it a try!

Bonus! solve this one:

I was surprised that it’s relatively easy to get this solution in a closed form. There’s a trick to it…

To my surprise, I don’t like Rufus Wainwright’s latest album. What the hell was he aiming for? Poses, Want One, and Want Two are so much more vital and real than this pastiche. Brilliant, cryptic lyrics as usual, but I can’t pick out one song that really stuck on me. Try again– you did it once with songs like ‘Grey Gardens’, ‘Go or go ahead’, etc. that tackle you to the floor at just the first listen– I’m sure you can get there again.

I did get Dashboard Confessional’s ‘Dusk and Summer’ at the same time, which is sort of a consolation, because that is a good album.

Update It’s growing on me

I found this surprising: the Sunnah (the words of Muhammad as written down by his companions the Sahaba, which have become the second source of Islam law after the Qu’ran) requires adult Muslims to remove their pubic and armpit hairs approximately at least once every 40 days. I find it strange that Muhammad thought about this: why?

I think the removal of the hair is supposed to make you ‘cleaner’ in the eyes of God. But that doesn’t make much sense if you believe God gave you that hair in the first place. Likewise with the debate surrounding the necessity of growing a beard: why the hair splitting? What could possibly be so important about a beard? A little further off, but still connected to the issue of cleanliness, is the debate about the necessity of circumcision. Look at some of those arguments: “the procedure isa removal of a part of the body that does not grow back, and it is done as an act of worship. This makes it obligatory, the same as the amputation of a thief’s hand.” Doesn’t that seem like some pretty twisted logic?

I’ve been considering switching to a straight edge razor for a while now. Partly because I think it may help with my pseudofolliculitis barbae but mostly for the sense of ritual and the opportunity to use my shaving brush and start using a shaving scuttle.

I’ve held off because if I make the switch, I’d like to play it smart from the start, and there is a large disparity between the information and the products available: what exactly constitutes the difference between the $20 razors and the $120 razor kits? Is the latter just the former with bells and whistles, or is the former the latter minus some crucial pieces? Does it matter whether the handle is plastic/bone/whatever? Between Razor Central– which seems to be a wonderful resource on using and caring for straight razors– and shaveblog, looks like I’ll soon be informed enough to decide on my plan of action.