Recent content by mrbohn1

Sorry...I'm not sure what you mean. Is <2,0,3> a point? Are you being asked what planes this point lies on?

I have a .djvu version. PM me if you want it (it is 3.3MB).

If I were to give an opinion on which one were more "fundamental", then I'd say the linear algebra one. And that would certainly be the more useful subject to know (depending of course on what you intend to go on and do). Methods of solving differential equations tend to be just that: a...

I'm not sure that I completely understand the question. If you fix an x coordinate, then the resulting points form a plane parallel to the yz-plane. Simlarly if you fix a y coordinate, the resulting plane is parallel to the xz-plane, etc. Does this help?

Their Lie algebras are isomorphic, and they are locally isomorphic...but D H is right - they aren't isomorphic!

That's exactly right. And you'll go far in mathematics with such a healthily skeptical outlook!

Well...there are 13 C 5 ways of choosing 5 cards from a given suit. As there are 4 suits, there are 4*(13 C 5) ways of getting a flush. There are 52 C 5 possible hands altogether, so the probability of getting a flush is just (# ways of getting a flush)/(# possible hands) = 4*(13 C 5)/52 C...

I can't speak for everyone, but personally I find that presentation rather impenetrable! You will probably get a better response if you write it out in using superscripts etc.

I think you are on the right track. You need to show that there is an element x of order 3 that commutes with an element y of order 7, then z=xy would have order 21. If you can show C(H) has order 21 (or 63) then you are done (by Cauchy's theorem). So all you need to do is show that C(H) is...

That was just an error with my previous editing. Hopefully it is fixed now. If you spot another problem, try filling in the details yourself...it's the only way to learn! I have done this very much off the cuff, and intended it to be a "suggested method" rather than a full solution to be...

hmmm..yes, sorry about that. I've modified the argument above. Still no guarantee it is right! Yes, when I say <1> I mean e...itis just to distinguish the identity element from the trivial group.

I'm afraid you'll have to be a bit more specific in your request! I would say though, that practice makes perfect. It's a cliche, but you need to do a lot of problems at the same time as learning theory. Someone once said that "mathematics is not a spectator sport", or something to that...

There are no universally agreed ways to word specific theorems or definitions. However, discounting typos (and occasionally wikipedia!) you can be pretty certain that any two wordings of the same theorem/definition in print mean essentially the same thing. I suggest trying different sources...

I don't think you need to use lim sup/inf here. n1/n=eln(n1/n)=eln(n)/n. So you just need to show that ln(n)/n-->0. Try using l'Hopital's rule.

Here's a rough sketch: Suppose x is not in N. Let M=<x>. If xn=e then M has order dividing n. |MN|=mn/|M\capN|, where m is the order of M. MN is a subgroup of G by the second (or third, depending on your numbering!) isomorphism theorem. So mn/|M\capN| divides |G|. Now, |G| = tn, where...