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So I just settled into a rented apartment, and was trying to fall asleep (couldn't). An hour later, I discovered that I had six bites on my upper legs, in somewhat of a pattern. I suspected bed bugs, but these didn't itch at all. ~15 hours later, there's no sign that they were there. Ideas on identification of the bugs?

I am thinking about applying for an actuarial internship/entry level job. It asks me about outside activity (school, work, etc.). This is sort of silly, but I play online poker, and have actually made quite a decent amount of profit (580%). Normally I would not even think about putting this on, as gambling (or, as poker players prefer, playing the game of skill that is poker) is not exactly something that endears to employers. However, actuarial science is a field in which math, especially probability, and risk-reward is very important. So, should I put poker as one of my activities, or no? I'm personally leaning towards leaving it out, but I'm on the fence.

So I have about a month to burn before I get tied down by obligations. I'm a college student out of school for a while (until my internship). Ideas on interesting things to do would be appreciated. I'm looking to have fun, but also to learn something on the way (hopefully of some value...) Any and all answers are welcome...I won't judge ^.-

I know Vampire Weekend is from Columbia. Are there any other bands? It's pretty fun to listen to the lyrics, cause they often are mad confusing...

Okay, here's the deal. I'm curious if it is bad to pass/fail a history class (not in my major). I have a decent grade in a class through the midterm and first paper (A- and B+, respectively), which isn't a concern at all if I can get an A-.... However, my courseload has just been ridiculous (I took too difficult of classes...), and I have attended about half of the classes since the midterm. So, does it look bad on the transcript to have a pass/D/fail? For jobs?

How do you network in a conference type situation? I'm a college student and have very little idea. Sources, answers, etc. are all welcome. While we're at it, how can I find people who are willing to offer advice?

I heard rumors that it is because of the lack of circulation indoors, etc. But what is the scientific reasoning behind it?

Just curious...the reports say that he and his college roommate James Davis were in the ring of fraudulent investments but failed to specify the college. And wikipedia does not help either.

I'm trying to prove that the norm of z is nowhere differentiable using the definition of the limit in the complex plane. My thought is to square it, prove that the resulting function is not analytic, and taking the square root. Other methods/thoughts would be appreciated.

If S and T are open sets, prove that S U T is an open set. This seems obvious, but I cannot translate the logic into mathematical statements.

I can read newspapers pretty quickly, using speed reading techniques I've acquired in classes. However, when I read dense works such as Hobbes, Plato, etc., I find it difficult to keep a brisk pace. Is it possible to read much faster than the typical 250 words/minute average reading speed even on works where it is imperative to follow a train of logic carefully?

Anyone done this? I'm currently a student at Columbia University torn between the bright lights of New York and the old world charm of Oxford/London. Not especially keen on being gone for my entire junior year and studying one subject, but then again, this feels like a chance of a lifetime and...I guess I'm really really indecisive.

Find the rank and signature of each real quadratic form:

q(x,y,z)= -4x^2 - y^2 - 4z^2 - 4xy + 8xz + 4yz

I have an answer, but don't know if it's right...

Prove that if P is an invertible matrix, then Rank(AP) = Rank(A) for any matrix A.

Hint: Col(AP)=Col(A)

My thoughts are that because P is an invertible matrix, its rref must be the identity matrix. The rank of A times the identity matrix equals itself, and thus rank(AP)=rank(A). But I don't think this is rigorous enough.

Thanks for the help in advance.