Recent content by styler

there is a thread on this a little bit further down in this forum.

No its not bad at al...just was a linking word more than a value judgement implying word. Butfor the sake of a 'course" of abstract algebra that statement if noit trivial would be considered at least assumed and fundamnetal. Anyway the point is a coset is a useful object and therefore...

I don't understand. Are you taking an abstract alegbra course in which you aren't assumed to know basic set theory? Or is this just a case of "you wanted to see it yourself"? The reason why there is a partiton is because it makes an equivalence relation. An existence is null issue.

Is what i wrote clear or do you need me to write the equations?

well an REU can be an eye opener and its always good for your application.

I disdgaree. I think the idea is that the range of the independet variable is determined in advance and that it defines the domain of the depenent varible so it makes sense to begin thinking in terms of realtions/functions. there is of course the philosophical matter of bringing up the issue...

Cool. Does it include discussion of representations of S0(4,2) ~ S0(2,1) X S0(4)? I believe the related work of Demeyer, Vanden Berge and Fack is collected in a book of papaers presented at the 15th internatrional Coloquim on Group Theoretical Methods in Physcis.

well in that case look up some of the following things: "spectrum of the laplacian" "einstein metrics" "ricci flow" "comparison geometry" How much mathematical background do you have? You will have trouble learning diff geom basics unless you have a solid grip on algebra. In...

The idea is that central force problems have a deeepr symmetry than SO3. The LRL vector shows that this is so. It was noted that since it commuted with the hamiltonian (possion brackets there i guess, classically) there was a larger symmetry algebra and another conserved quantity. Though...

All i meant by the quote about Qm and hilbert spaces was that it wasn't fair to say geroch was about categories cause it had some categorica stuff in itit just as you wouldn't say griffiths was a functional analysis book just cause it has a chapter on it. I misunderstood you i thought you...

Actually an enormous number of PURELY mathematical questions have come from studying physical problems and even applications of exisiting mathematics to physical problems. In the case you mention general relativity does actually lead to an interesting set of problems of a purely mathematical...

Yes, the idea is that y is dependent upon x or that we watch how y changes when we change x. Or we think y depends on x in some way (given by an equation) as we allow x to vary over some set of numbers We think of x as independent (like it takes on a certain set of values that we choose, not...

Without fancy language showing how general Stokes thm is the simplest answer to your question is that cosine (0) = 1. The angle whose cosine we need is that between the normal to the surface and the third coordinate. But these are identical in two dimensions for an orientable surface.

that it is symmtric is pretty clear: if r is congruent to s then we have s = rh so that r = sh inv but clearly h inv is in H (its a(sub) group) so s is congruent to r Reflexivity is easy too: r = re (e is identity of H) so r is self congruent Transitivity takes a tiny bit...

Its just because cosets are equivalence classes for the congruence defined by: s is congruent to r if r = hs for some h in H. Here obviosuly H is a subgroup of the group G in mind. (so that we can make sH with elements s and h in H)