AlanH
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 Mar 22 comment Recurrence relation for the number of ternary strings containing 2 consecutive zeros vs not containing How do you obtain the closed form without OEIS? Mar 22 comment Reference request for practicing integration @amWhy So if cost wasn't an issue, you would suggest Zwillinger's book? Mar 22 comment Discretization of Inhomogeneous Dirichlet Boundary Conditions for 2D Poisson's Equations @Kaster I've been meaning to get back to you. I've been quite busy, but as soon as I can, I'll post it! Mar 18 comment Generating function: number of partitions that add up to at most $n$ Yeah, I meant product. I don't understand why that changes the number of partitions of the integer $n$ to number of partitions that add up to at most $n$. I guess I don't understand the convolution part. The only time I've been introduced to that was in differential equations. Mar 18 comment Generating function: number of partitions that add up to at most $n$ Is it just $f\cdot g?$ I don't understand why it is if this is the case. Mar 18 comment Combinatorial proof involving partitions and generating functions @BrianM.Scott Okay, so I think I get your solution, but I'm not entirely convinced (my lack of understanding). When you say every partition of $r$ can be extended uniquely, that doesn't mean it's the only way to do so right? Because I could, in some haphazard manner, just throw the $r+k$ dots on to the right side of the current partition of $r$. Mar 15 comment Proofs that every mathematician should know? Where are all the fundamental theorems to this fundamental list? :P Not that I'm one to say anything. Mar 14 comment Discretization of Inhomogeneous Dirichlet Boundary Conditions for 2D Poisson's Equations That's what I thought! But the notes I have say the mass matrix, $A$, should be a size $25\times25$ matrix, but only consisting of 5-point stencil, not any of the values you have in orange/beige. Hence my confusion. Mar 14 comment Discretization of Inhomogeneous Dirichlet Boundary Conditions for 2D Poisson's Equations BTW, what did you use to create the diagrams? Mar 14 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) Is there some sort of repository of these mental math tricks? I'd love to see more of this stuff Mar 11 comment Uniformly Most Powerful Test and Rejection Region of Poisson Distribution This question seems more suitable for Cross-Validated (you might have better luck there). Just an FYI. Mar 10 comment Further clarification needed on proof invovling generating functions and partitions (or alternative proof) How is one supposed to realize that it is to make sense for $n \leq 2^m$? Its sort of misleading o.w. since the dots indicate it goes on forever. Feb 27 comment Grad degree that mainly deals with probability/game theory/optimization? Would it really be more beneficial (both in my preparation for such a program, and getting in to one) to strengthen my knowledge in probability, analysis, and linear algebra than take OR related courses? I figured if I did the former, there would be no way other way to show that I have interest in the subject. Feb 27 comment Grad degree that mainly deals with probability/game theory/optimization? Hi Mike, I know this was posted a long time ago, but I happened to come across this as I was interested in optimization. I too was thinking of taking some optimization and algorithms courses prior to applying to some programs. My logic for taking these courses was that I needed some way to show them I was interested in the subject (research wouldn't be possible as I'd be a non-degree student). But then I came across your post and you said it would be more useful to know algebra, analysis and probability. (see below)... Feb 19 comment Finding the coefficient of $x^{25}$ in $(1 + x^3 + x^8)^{10}$? How does the 10 play a role? Feb 19 comment Finding the coefficient of $x^{25}$ in $(1 + x^3 + x^8)^{10}$? @rlgordonma Thanks Feb 16 comment Finding coefficient of generating function Awesome. That confirms my solution :) Feb 15 comment Elementary Generating Function Models Could you explain why the coefficient of $x^{20}$ is $\binom{50}{20}5^{20}$. Specifically, why you it's $5$ that is raised to the power of $20$. Feb 15 comment Elementary Generating Function Models @joriki Yeah, I initially put the abbreviations there to address that issue, but I now realize that the abbreviations don't help much either. Thanks. Feb 12 comment Combinatorial proof. What is this question asking? @DouglasS.Stones Yeah, I knew that, but I didn't know what was being indexed. At least it wasn't apparent to me.