Recent content by Mystic998

Actually, I can't really see a problem. So...am I really just that rusty? What's the answer supposed to be?

It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.

It seems like you're going about the problem correctly except that obviously the splitting field won't be as described if the quadratic is reducible. Other than that, unless I'm forgetting something (which would hardly be surprising), what you're saying is completely true.

In general. Well, for nonnegative integer exponents anyway.

The definition of the second partials is just the partial derivatives of the first partials. Why couldn't you just use the same method as before?

Well, it looks like you're trying to find the power series of ln(5 - x) by differentiating the series for 1/(5 - x) term by term. But ln(5 - x) is the integral of 1/(5 - x) (give or take a sign).

Oh, I meant for the intersection to be trivial. I'll think about what you said though.

I think changing the order of integration is the way to go. You'll get an x^3 term in the integral with respect to x. Then it's easy.

Homework Statement Show that G is isomorphic to the Galois group of an irreducible polynomial of degree d iff is has a subgroup H of index d such that \bigcap_{\sigma \in G} \sigma H \sigma^{-1} = {1} .Homework Equations The Attempt at a Solution I know that if G acts transitively as a...

I think you need to rethink your bounds on that one...

Without additional assumptions on m and n, the implications aren't true...

Bump before bed

Isn't your first question essentially, "Can you construct an integer multiple of a constructable angle?" Well...can you?

Homework Statement Let p(z) be a polynomial of degree n \geq 1. Show that \left\{z \in \mathbb{C} : \left|p(z)\right| > 1 \right\}[/tex] is connected with connectivity at most n+1. Homework Equations A region (connected, open set) considered as a set in the complex plane has finite...

Off the top of my head (that is, take this with a huge grain of salt), I think the approximating surface doesn't really matter in the answer, but the cone/cylinder might give the simplest (or maybe easiest to visualize) way to get to the answer.