Well, see if you recall this sequence: $a_n = \sum_{k \geq 0} \frac{k^n}{k!}$. It's Bernoulli or Euler or Stirling numbers or something like that.
I am trying to track down whether this question is a dup: math.stackexchange.com/questions/90629/…, but I cannot search math. So I am trying to search for these keywords.
@Srivatsan No, I was not trying to say that at all. I was just noting the breaking of polynomials up into the combinatorial polynomials. That is one of my favorites.
@robjohn I presume you know this: Let $p(x)$ be a univariate polynomial with rational coefficients. Then under what condition does the polynomial take integer values for all integer $x$?
@robjohn I think this cute result is a corollary of our above theorem: if a degree $k$ polynomial takes on integer values at $k+1$ consecutive integers, then it maps all integers to integers.
@tb odd. just encountered, that bottles with 'pure Iceland water' in our hotel rooms which they change every day are 5 dollars each and it will be included in the final price at the checkout. That's not big money, but that's just odd
also, there is a cool pool, but I haven't brought my swimming shorts. So, I bought it here - but the only shop around is Disney Land souvenirs, so there is Mickey on my shorts. Very small Mickey fortunately
I bought cigarretes here (at the Disney Land shop again :D ) for \$10 (in NL they are 5 euros and I though it's pretty much). When I told this thing them, they argued that in Norway (why Norway?) it's \$15 and I shouldn't complain
@robjohn I hope you don't mind about my impression - I will find things to complain about in the Netherlands and Russia as well (especially in the latter)
@AlexeiAverchenko problem is that those who snore have the tendency to wake up and then fall asleep again very quickly. While you, who want to sleep, hear them building up their breathing towards cutting down a jungle, are too nervous to fall asleep...
@JM well, talking about cigarettes - in NL they are of the same price everywhere where they sell it. In Russian we have different prices in supermarkets and say night clubs, but then some years ago we had a law that there should be a maximal price for each brand of cigarettes and now they are of the same price everywhere too
@Srivatsan check the previous posts. But it is a horribly low non-zero accept rate: $\color{red}{0\ \%} =$ I don't know that/how I should accept answers. $\color{grey}{17\ \%} =$ I know how to accept but the answers I got so far don't satisfy me.
I want to take an introductory course in modular forms next semester and I'm trying to figure out what kind of math to brush up on. We're using the textbook "A first course in modular forms" by Diamond.
I assume algebra/complex analysis, but I'm looking for a bit more direction than that.
Then I would say yes. There were quite a few questions on learning and roadmaps for some more advanced topics. Try to be clear on your background. You certainly mentioned the most important topics.
@SidRaval Remember: the more specific you are the easier it is for people to be of help: next semester can mean February or it can mean May. That makes a bit of a difference in terms of time you have for brushing up.
@tb Well, the prerequisites basically say advanced undergraduate algebra and complex analysis, which I have ostensibly had, though a couple years ago; so I'm trying to figure out more specifically what algebra to brush up on, and what complex analysis to brush up on. A friend says the complex is mostly in the background and the algebra is more important; and it seems group theory is more important than ring theory
but things like G-modules seem to come up and I'm trying to figure out what I can learn along the way and what I'll need to know very well before approaching the book
im in my first semester of grad school and was a little bored this semester so I'm trying to do more next semester, but I don't wanna get in over my head
@AsafKaragila A Futile Attempts multiple choice test. They give you ten minutes to answer 4-5 questions. Multiple answers can be right and if you miss one you lose all the points. Or something like that.
Yeah, my probability professor was known for these sort of tests. The year before I took the course they complained about it to the university so when I took the course you could submit an empty exam and get like 25-30 points and the score would go below that if needed. It was a clever trick on his side.
@SidRaval I understand. I had a short look at the book. I'm sure you'll be able to frame this into a good question. I was just intending to make sure that you didn't overlook the obvious things to check. Unfortunately I lack the expertise to say anything sensible on your specific question.
I have a formatting/display problem. The characters seems to be everywhere and then i click the ? in yellow circle for less info and it comes back to normal. But then it reverts back if i come back to the page.
@robjohn Minority Report was so-so, I did not hear good things about Screamers or its sequel, and just from their descriptions I would probably avoid Paycheck, Next and Impostor.
It takes a genius to engineer a movie which leaves you with huge open questions. Most people think "Oh, the audience wants answers. We need closed endings."
There are few willing to leave things open, but it's never "Was Roy Deckard a replicant?" sort of issues.
Or like in Total Recall that you have no idea if it's real or not...
@QED I agree. It added greatly to the effect. Also the fact that Keanu Reeves is not the best talker helped a lot, gave the brain-damaged-empty-hull-of-a-man feel to it.
"In memoriam. These were comrades whom I had; there are no better. They remain in my mind, and the enemy will never be forgive. The "Enemy" was their mistake in playing. Let them play again, in some other way, and let them be happy."
@robjohn there are 4 votes to close as not a real question that were cast before the question was clarified. Since there are a few users that don't look too closely before voting to close the idea was to remove that dangling sword over this question.
