Recent content by sparkster

I'm trying to teach myself some algorithm complexity and I've run into a problem. I'm starting to understand about O and o notation and big theta notation. I've run into notations like O(n^2 M(n)). Does this mean that the complexity is n^2 times whatever M(n) means? (Natural next question) what...

Since the product of two manifolds is a manifold, the torus which is just S1 x S1 is a manifold. But any point has neighborhoods that are contractible, while the whole torus isn't.

Are the vectors sequences that are eventually zero?

Right, e^2x. Thanks for catching that.

Could you use it if you made a substitution? If you had to integrate 1/ex2+2ex+1 you'd want to substitute u=ex then use partial fractions.

What if your space is X=S^2? Wouldn't your homotopy travel outside X?

In what sense do you mean equals? Diffeomorphic? I would think do. The disjoint union of two manifold is a manifold, right? But any neighborhood has only one connected component but the whole manifold has two. ETA: Assuming both pieces are of the same dimension.

I'm teaching a junior level geometry course this summer (I'm a math grad student). The title of the course is simply "Topics in Geometry" with no other description in the catalog. I've asked the DUS and he says the content is pretty much left to the individual teacher. But I'm having trouble...

Can you elaborate? As x goes to 0, -2ln(x)-1/x gives the indeterminate oo-oo. I don't see how to manipulate it to get -oo. I already know the left side derivative is 0. I just need to show the right side is also 0.

Let g(x)=e^{-\frac{1}{x}} for x > 0 and g(x)=9 for x \le 0. I want to prove that derivatives of all orders exist. Now I know that the only possible problem is at 0. The limit of the difference quotient from the left is obviously going to be 0. The limit from the right is going to be...

So let f be analytic in the open unit disk and continuous on the closed unit disk. Also, |f(z)|=1 for |z|=1, all zeros are simple zeros at 0, and f'(0)=-1/2. I need to find f. I've tried using the cauchy integral formula for f' but that's not getting me anywhere. Can anyone point me in...

I think I'll just some time in the library next week looking.

They're rigged so that they agree with the classical definitions. At the end of the wikipedia article they give a link to an online book. I've seen the book and they prove it via spectral sequences. I don't understand spectral sequences yet, so I was looking for an easier proof. Knudson's...

The classical definitions of K_0, K_1, and K_2 for a ring R are K_0(R)= Grothendieck completion of the set of isomorphism classes of finitely generated projective R-modules. K_1(R)=GL(R)/E(R)=[GL(R)]^{ab} For K_2, Milnor used the Steinburg St(R) group which maps onto E(R) and defined K_2(R)...

I'm asking about uniform convergence. ETA: But the function would be uniformly continuous, giving me delta that works for all x in the interval. Thanks.