~~Update~~
So I met with the assistant dean today since I had to turn in a full written report by tomorrow morning. She was pretty upset and clearly doesn't like me and all in all it was a pretty awful experience. She says there's a possibility of a lawsuit and that I might be fired and she...
@Office_Shredder, Yah I certainly wouldn't lie, if I have to make a full report then I'll have to incriminate the student and that sucks but I wouldn't know what else to do. No one knows about my PF account and I doubt this is serious enough for people to start going online searching for info...
Hopefully this is the correct stack exchange for this, if not feel free to tell me where to move it where it would be more appropriate.
So I am a teaching assistant and masters student in the math dept. at a large state university. I was holding a discussion section this morning for the...
I imagine myself flipping a coin repeatedly and recording the outcomes. With only the WLLN being true, I expect to periodically encounter long strings of mostly heads or mostly tails, causing the running average to fall outside some epsilon's distance from the mean. These strings would occur...
French universities generally require that you pass a language exam at the B2 level (intermediate-advanced), you can find examples of these tests online along with information on the scores required to pass. L'Ecole Polytechnique is I believe a rather prestigious university.
With regard to...
You could check out the Times Higher Ed World University Rankings for Europe. I don't think that European universities are quite as stratified as American ones are, but I get the impression that many of the best are in German speaking cities, and as usual in the major cities: Berlin, Munich...
With a bachelors in computer engineering and a masters in computer science, you would be a good candidate for a phd in quantum computing. There is currently interesting work to be done in designing the hardware/firmware required to make quantum computers a reality. In fact I think Booz Allen...
This is something which has been on my mind for a while now after considerable exploration (online) of the job market.
I see a lot of postings for various math jobs in industry requiring a masters in applied math. So let's say the focus of my degree was on discrete math and I did my thesis...
Homework Statement
Show that there is no non-abelian group G such that Z(G)=\mathbb{Z}_2, which satisfies the short exact \mathbb{Z}_2\rightarrow G\rightarrow\mathbb{Z}_2^3.
The Attempt at a Solution
I have knowledge of group theory up through proofs of the Sylow theorems. I know the center...
Number theory is an extremely fascinating and beautiful subject, but only at the graduate level, introductory number theory classes suck and should be abolished for fear of turning people off to the subject, take optics.
He says by "naive" he means elementary. Incidentally, I took an elementary number theory class and didn't particularly like it. Which is only interesting because now I intend to become a number theorist.
So going from there we use the fact that the order topology is Hausdorff and find two open disjoint sets one containing f(x) and the other containing g(x), from here I would like to map back under f^-1 and g^-1 to two open sets in X and from here take the intersection of them which would contain...
Proving a Set is Closed (Topology)
Homework Statement
Let Y be an ordered set in the order topology with f,g:X\rightarrow Y continuous. Show that the set A = \{x:f(x)\leq g(x)\} is closed in X.
Homework Equations
The Attempt at a Solution
I cannot for the life of me figure...
Comparing Partions of a Natural Number
Homework Statement
Let r(n) denote the number of ordered triples of natural numbers (a,b,c) such that a + 2b + 3c = n, for n\geq 0. Prove that this is equal to the number of ways of writing n = x + y + z with 0\leq x \leq y \leq z for x,y,z natural...