Recent content by Singularity

Many people recommend Sean Carroll's lecture notes on GR as a great place to learn from. They can be found here http://arxiv.org/pdf/gr-qc/9712019v1

Hi, ok here is my 2 cents. Let's just take a normal n-dimensional vector space V to start with. Then a metric, in the differential geometry sense, is a symmetric non-degenerate bilinear form on V. If we define it by g say, then g eats up two vectors and spits out an element of the field over...

Hi all! I haven't posted here in some time, and I am in need of the expertise of you fine folks. I am busy doing some work on spin geometry. Now, as you guys know, spin structures exist on manifolds if their second Stiefel-Whitney class vanishes. This class is an element of the second...

Hi all, I don't know if this is the correct place to ask this, but I am looking for some tough linear algebra problems (though still accessible to bright 1st years) to give to my class for possible extra credit. Any problems, or sources would be appreciated. Thanks!

Haha...Landau is correct. In any event, I think you got the jist of how the charts work.

If I may be allowed to nitpick for a moment. In the original post, U is a subset of M, not an element of M. Apologies for being anal about this...it annoys my friends to no end as well!

Ok...I have decided to do the DIY thing and get some glass and see what I can conjure up. Now on to the next problem : Finding the stationary. I am assuming I can pick these up from a standard stationary outlet. Hopefully one doesn't have to have them specially ordered.

Thanks for the replies. $1000 is a bit much for my pocket. Guess I will have to stick with the regular stuff.

Hey guys, I have been watching some old numbers episodes and I saw they have this really cool translucent blackboard. Anyone know where I can buy one of those?

Homework Statement Show that there are only two possible categories with one object and two morphisms. Homework Equations None The Attempt at a Solution My thinking here is as follows : Let's say that the object in our category is A, and that the two morphisms are f and 1, where...

Hi all, I have figured out all the details of this problem. Thanks again.

Hi Hurkyl. Thanks for the reply. I realize that the concept of dual category already exists in the literature, and it has a different meaning to the one I am asking here. Clearly I am looking for a functor from C to Set (as stated in the first post I restrict myself to categories with sets of...

Hey PF gurus! I read that Cayley's theorem can be extended to categories, i.e. that any category with a set of morphisms can be represented as a category with sets as objects and functions as morphisms. I was looking at the construction and for some reason I don't fully understand how they...

I assume by the 20 greatest equations he means the 20 problems given by Hilbert in 1900.

Hello, didn't read everything, but here is one way of showing that 0v = 0 (Please pardon my lack of LaTeX skill). 0v = 0v + 0 = 0v + (0v + (-(0v))) = (0v + 0v) + (-(0v)) = (0+0)v + (-(0v)) = 0v + (-(0v)) = 0