@Sush OMG ... I forgot that when captain and fundraisers's positions can be interchanged as well so the answer is $\sum_{k=1}^n k^2\binom nk=n2^{n-1} + 2 {n \choose 2} 2^{n-2}$
In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error commi...
No. I'm involved in the process of creation too deeply and don't have time to look back. If wanna do that, I have my own database with problems and solutions.
@user4140 by the way, you can use the search field ...
I just want to ask a very simple question about math. Finding mistakes in programming is called debugging, but what do we call finding mistakes in math?
I need to find the image of $\cosh z$ in $x ≥ 0$, $0 ≤ y ≤ \pi/2$. I've convinced myself that it's $x ≥ 0, y ≥ 0$, but I'm not sure how to prove it.
Basically, I took the image of lines of the form $x + ia$ and found it's $\sinh (x) ⋅ \left(e^{-x}⋅cos a - i \sin (a)\right)$ which sort of suggests that I can express every complex number in that area. I'm suspecting I'm missing something obvious.
The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975 , . It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 :
Vos Savant's response was that the contestant should switch to the other door.
The argument relies on assumptions, explicit in exten...
The way that worked for me: There are 3 doors. You pick one. There is a 1/3 chance of the car being behind your door, and a 2/3 chance it's in one of the other two doors. The gamemaster opens one of the other two doors. You still have a 1/3 chance of being "right," but now the 2/3 chance is "concentrated" to that one remaining door. (I've got to run, so can't respond... but that's my $0.02...) :)
Hi! I have a little problem understanding definition of graded structures (rings, algebras). Namely there is a condition $R_m R_n \subset R_{m+n}$. But it is nowhere said what does $R_m R_n$ mean. Is it just a ring of pairs?
Hey, not sure if this is the right place to ask as it didn't seem like this would be worth posting a question, but could somebody help me to understand how to solve this integral: $$\frac{1}{\left(z^2+x^2\right)^{3/2}}$$
Hey. I actually have a question about Math Overflow, but I think the answer for Math SE would be the same, so I'm going to go ahead and ask here.
I asked a question on MO. So far, it has received exactly one answer, and that answer is incorrect (the author says so in a comment on the answer). I'm afraid of people looking at the question page and assuming that it has already been answered correctly.
What should I do here? Would it be appropriate to downvote the answer, or perhaps to ask the author to delete it? Should I edit it to add a notice saying it's incorrect? Or maybe I should just leave it alone?
@TannerSwett Personally I think whoever has even a slight interest in your question will click on it regardless of the number of answers. Unless it is too elementary, which I doubt.
I don't think that does a whole lot on MO, but it makes it clear you're not satisfied with the current answer. But usually, the fact that a question doesn't have an accepted answer means the OP_ is not satisfied. I really doubt people who are otherwise interested in the topic wouldn't click on your question because of it.
Finding more populous tags is definitely a good idea, though; only 95 questions are tagged formal-proofs, so it's unlikely more than a few people look through that list regularly. So the only people who find your question are those who are looking through old questions or those searching.
A lot of people use MSE and MO by only looking at questions in their favorite tags.
A polynomial map is equal to another polynomial map iff they take on the same values at each point. So this is different from formal polynomials. So since in $\Bbb{Z}_p$, $x^{p-1} = 1$ for all $x \neq 0$, and is $0$ on $0$, we have that there are a finite number of polynomial maps in $\Bbb{Z}_...
NP, just a guide. I used Adblock to hide that particular one. Lots of people do it - I find the inability to silence animated GIFs in Google+ infuriating.
I thought dividing by 0 wasn't well defined. Why does my book think otherwise? It says that my final equation for the line after being transformed by a 3x3 matrix is $$ \dfrac{x+6}{0} = \dfrac{y}{1} = \dfrac{z+12}{1} = \lambda $$
The transformation $ T : \mathbb{R}^{3} \to \mathbb{R}^3 $ is represented by the matrix $ \mathbf{\text{T}} $ where $$ \mathbf{\text{T}} = \begin{pmatrix} 2 & -1 & 3 \\ -1 & 4 & -2 \\ 3 & 2 & 4 \end{pmatrix} $$ The plane $ \Pi $ has equation $ 2x - y + 3z = -6 $. Show that the image of $\Pi$ under $T$ is a line and find Cartesian equations of this line.
@FernandoMartin Is there a way that you could combine both equations to make a final equation, or do you think it's sufficient to simply state those two above?
@FernandoMartin You mean $(6, y+12, z)$ right? I hardly ever use that book, but since my exam is based on most of its content, I thought I might give it a quick once over.