S’alright. It’s my sister’s book - she just lent it to me.
To elucidate my comments a bit: I’m of the opinion that Witten is somewhat overesteemed as a mathematical physicist. A huge portion of his purportedly mathematical work (including what he won the Fields medal for) boils down to handwaving about what math “should” look like (mostly to make the physics side pretty) and leaving the details for the poor slags in the trenches to work out.
Don’t get me wrong. The guy’s a genius no doubt, but he didn’t really do half of the math that has his name attatched to it.
Don’t forgot Riemann geometry! Well, ok, that only is really necessary for General Relativity, but I feel kind of sure that it will, in the end, be worked into M-theory.
Now, who wants to tell me the math requirements for quantum loop gravity? Do they even know what math to use yet?
http://www.superstringtheory.com/math/index.html
Beware. This could easily tie you up for a couple of weeks or so.
Just to give you an idea of how simple this stuff is here’s a summary of K theory from the above site.
[Homer Simpson] Mmmm… Crullers… [/Homer Simpson]
I’m also reading Greene’s book right now as well, about 50 pages into it. I’m not a math guy, and I find it accessible (so far). Some of the analogies are dumbed down a bit, but I don’t mind that; it helps to have real world analogies to some of the concepts. I have no doubt I’ll move on to his next book after this one, and I’ll follow up on the references herein to Kaku’s works.
best to all,
plynck
I found Greene’s elegant universe very well written and worth it for the chapter on General Relativity alone. A lot of his stuff on strings is a bit out of date AFAIK as the field is moving very quickly.
Riemannian geometry is a special case of differential geometry. In fact, it’s almost useless for GR since GR assumes a Lorentzian metric.
Last night, Mrs. E=mc² gave me a copy of Greene’s The Elegant Universe, so today I’ll be reading it, too.
I never offered my heartfelt appreciation to all of you who contributed to this thread, so I’ll do so now:
Thank you all, very, very much for taking the trouble to make your contributions.
I’m currently enjoying my way through The Elegant Universe, and look forward to reading all the other books that were recommended.
I’ll probably never understand M Theory, but I am certainly having a good time exploring it.
Thanks again.
I used to think I was good at math, but then I read some of these threads and realize I don’t even know what I don’t know. I get the impression that multivariable calculus is just a drop in the bucket of higher mathematics.
Pretty much. Linear algebra and group theory are both very accessible and will give you a good feel for what higher math is like, so if you’re curious, those are good places to start.
If you’re serious about it, get a copy of Penrose’s latest book The Road to Reality. He starts from the ‘beginning’ and aims to describe all the laws of physics, including string theory. Penrose doesn’t shy away from the mathematics, which is a point in the book’s favour, IMHO.
Heh. I had to take linear algebra for my computer science degree; it kicked my ass. It took me 3 tries to pass the damn thing. They really should call it vector algebra or spatial algebra or something.
I’ll second that, I’m about a third of the way through the book at present, it helps if you have a mathematical background, but he does give very concise descriptions of the mathematical methods.
“vector algebra” would focus on the vectors, which are really incidental.
“spatial algebra” would focus on the very limited case of R[sup]3[/sup] (maybe R[sup]n[/sup]).
The subject isn’t vectors or about space. It’s algebras of linear transformations.
To be fair, most introductory linear algebra courses–especially those in an engineering program–really are about vectors and matrices.
I’d say they’re about matrices, which form a (say it with me, now) “linear algebra”. Besides, if we want to rename courses according to what they talk about rather than the field they’re a simple case of, we should call the old high school course “single-variable polynomials over the real (and usually rational) numbers”.
Band name?
Perhaps not.