(no subject)

[nibot]

I went to Ned's and grabbed a copy of the textbook for Math 114. It wasn't in the right place, but I had just recognized it by the cover.

Next to me a girl stood looking plaintively at the empty spot on the rack over the "114" label. She said, "Oh, last one I guess."

"Hmm, looks that way."

"Hey, how was lecture on Thursday? I missed it to go to another class."

"Don't tell me — Combinatorics?"

"Yeah, how'd you know? Anyway, I really like the professor.. I'm not sure which to take."

Seems that everyone's having that same difficulty in decision-making. Maybe the math department did this intentionally, to force us into the choice, and prevent each class from being overflowing. (-:

"You take the book," She said.

But then before I could find the words to express "I'm really only planning to borrow this book from the bookstore long enough to do the homework -- maybe we could share it, or I could borrow it, or ..." she was out the door, no Galois Theory by Ian Stewart in hand...

so sad.

Anyway, the ironic thing is that the most interesting problem on the galois theory homework is a combinatorial problem (#11, for those of you in the the TV audience). otherwise, I just can't get too excited by "equations in radicals." I never did like them. I'm happy that polynomials have roots over the complex numbers and that they can be found by numerical means if not by closed-form equations, and I'm happy that there are polynomials over finite fields and that they make field extensions and the like. But solutions in the real numbers -- they're neither here nor there.. I just don't care so much. I never did like number theory so much, either, for similar reasons -- it seems like lots of special features and no sweeping theory.

I checked out Howard Georgi's Lie Algebras in Particle Physics again, but the copy in the library here is old. The exposition and the typesetting (on a typewriter!) are equally atrocious. I know the newer edition is vastly better (it was in the CERN library).. I'm looking for a copy. Also Jing-Song Huang's Lectures on Representation Theory. Somehow all this theoretical physics stuff is suddenly making sense, what with bosons and fermions and everything, and now it's time to catch up on representation theory. I've discovered that there's actually a lot of good stuff out there on usenet, specifically in the moderated newsgroup sci.physics.research. The group sci.physics, on the other hand, is just full of crackpots. I also just discovered the ArΧive.

A representation of a group G is a homomorphism π between the group elements and linear transformations (matricies!) over some vector space V. A representation can be decomposed into a direct sum of 'irreducible' representations if there is a subspace of V that is closed ('invariant') under the linear operations of the representation. How, in general, do you find such an invariant subspace? It has something to do with simultaneous eigenvectors and diagonalization. (A matrix is diagonalizable if it has a basis of eigenvectors, but what is the requirement for a matrix to be block diagonalizable? it's similar, I think. I did it for set of one matricies by finding a simultaneous eigenvector v, which necessarily produces a one-dimensional invariant subspace. Then the set of all vectors w perpendicular to v is also an invariant subspace, one that I hadn't noticed originally. I wrote down two vectors that spanned this second space, and then the matrix holding all three vectors turned out to block-diagonalize each matrix from the representation. Alas, my linear algebra book is in Orange County.)

Anyway, there's this professor at UC Riverside (oddly enough) named John Baez who produces an unbelievable amount of easily-digested expository writing on mathematical physics. Check out his site, and/or search for his name in google groups. In addition to the theoretical physics stuff, here's a semi-political note I just found on his site: "Recently the University of California has begun a serious struggle with Reed Elsevier, the worst of the big science presses. Right now, 1/6 of the entire U.C. library budget is spent on Elsevier's "Science Direct Online", a bundle of online journals. The state of California is broke, but Elsevier wanted a 37% increase in the fee paid for Science Direct Online, phased in over the next 5 years." Man.

I was wondering recently how many students would consider donating their textbooks to the library when they're done with them. At first, of course, there's a financial sacrifice, but once the library has a good collection of textbooks, then there's a great benefit. But then, considering how poorly most people treat their books, and how expensive it would be for the library to be dealing with all these textbooks, I came to the conclusion that the bookstore / exchange is a reasonable solution. Still, they have not a single copy of the latest edition of Galois Theory.

Comments

[yodasan.livejournal.com]

She was probably disappointed you didn't ask her out for coffee.

[(Anonymous)]

It's not surprising that the library doesn't have the latest edition of Galois theory, as it just came out this year. The last edition is better anyway -- the solutions by radical stuff is just peripheral -- left until the end -- while the theory is emphasized more.

Anyway, the library's main purpose isn't to supply undergraduates with textbooks, but to supply monographs and research for the people engaged in research at this research university.

Lots of people in Math are trying to figure out ways to circumvent companies like Elsevier (on a mass scale). It'd be nice if that could actually happen.

[nibot.livejournal.com]

Yeah, I realize it's not the library's purpose to supply students with textbooks, but I think it would be nice if there were at least one copy on reserve, and I'd be willing to help that happen. I was mostly just musing on whether the University could get involved in the textbook allocation problem, as yet another solution to the bookstores-take-25%-cut problem, and concluded that they probably couldn't/shouldn't.

Circumventing Elsevier

[(Anonymous)]

People are trying in Computer Science. The editorial boards of two journals in computer science have resigned, and are trying to form essentially the same journals elsewhere. Elsevier, of course, wants to keep the old journals going...we'll see how this works out.

Re: Circumventing Elsevier

[nibot.livejournal.com]

wow, so many anonymous posts lately. who are you guys?

[anemone.livejournal.com]

The one about journal boards resigning was me.

[janviere.livejournal.com]

She was cute, wasn't she? :)

[eigenvalue.livejournal.com]

"but what is the requirement for a matrix to be block diagonalizable?"

jordan canonical form? the requirement for a matrix to have a jordan form is for its characteristic polynomial to split as a product of linear factors.

free science

[ocexile.livejournal.com]

If you're interested in the battle to free scientists and their work from the clutches of Reed Elsevier, then check out the new Public Library of Science. Not only is PLOS less expensive to use, it also allows scientists the right to reprint their own work. It's both great and sad that such a move is considered revolutionary these days.

While this saga has flown beneath the radar of public consciousness, news media from the Chronicle of Higher Education (http://chronicle.com/free/2002/12/2002121801t.htm) to al-Jazeera (http://english.aljazeera.net/NR/exeres/19A212E2-21E9-42C5-976C-DA5CA2600618.htm) have picked up the story.

[roxymartini.livejournal.com]

sharing a math book with another girl?
Such scandal.