Joel Cohen
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 Jan 25 reviewed Approve Contrapositive - Convergence of a sequence Jan 21 reviewed Approve Computing the spherical coordinates in n-dimensions Jan 12 comment Convergence of $\int_0^{\infty}\sin (p(t))dt$ @vnd : Yes, that's my point. Jan 12 comment Convergence of $\int_0^{\infty}\sin (p(t))dt$ How do you go from a majoration of $e^x f(x)$ to one of $e^x |f(x)|$ (which means you should also have a minoration of $e^x f(x)$) ? Jan 8 comment Absolute value : Freshman exercise @ManalBouabdallaoui : I think Ian is suggesting that you examine separate cases depending on the signs of $x$ and $y$. Jan 5 revised How to find the Haar measure on the group of affine transformations on $\mathbb{R}^n$? added 35 characters in body Jan 5 revised How to find the Haar measure on the group of affine transformations on $\mathbb{R}^n$? Corrected change of variable formula to $d(A'A) = |\det A'|^n \, dA$ Jan 5 comment How to find the Haar measure on the group of affine transformations on $\mathbb{R}^n$? @Batominovski: Yes, thanks. Jan 5 answered Why is $\{p \in \mathbb{Q},:p<1\} | \{p \in \mathbb{Q}: p \geq 1\}$ a real number? Jan 4 answered How to find the Haar measure on the group of affine transformations on $\mathbb{R}^n$? Dec 24 comment Finding the optimal moves for a puzzle. If you define a vector $u_i = (u_{i,1}, \ldots u_{i,n})\in G^m$ where the components are $u_{i,j} = 0$ if $j \in S_i$ and $1$ otherwise, then the operator $T_i$ is just $g \mapsto g + u_i$. Essentially you're given vectors $u_1, \ldots u_k \in G^n$, and looking for integers $(N_1, \ldots N_k)$ such that $g + \sum_{i = 1}^k N_i u_i$ is optimal. I don't know if that helps. Dec 24 comment Calculating $\det(A)$ using permutations. Have you tried computing this determinant for small values of $n$ (like $2$, $3$, $4$) ? Dec 20 comment Converting a 1st order non-linear recurrence to a 2nd order Denote $\otimes$ the inverse operator. It is semi associative meaning there exists another operator $\times$ (which here is the usual multiplication) such that $(a \otimes b) \otimes c = a \otimes (b \times c)$. Nov 19 comment Determine maximal addend in Newton Binomial Expansion. I think the expansion should be $$\left(2n+\frac{1}{2n}\right)^{4n+1} = \sum_{k = 0}^{4n+1} \binom{4n+1}{k} (2n)^k \left(\frac{1}{2n}\right)^{4n+1-k} = \sum_{k = 0}^{4n+1} \binom{4n+1}{k} (2n)^{2k-4n-1}$$ Nov 16 comment What is this dynamics question asking me to do? I think the question is asking you what the limit of this expression is as $u$ goes to infinity. Nov 16 comment Why is $GL_2(\mathbb C)$ connected? @learnmore : Well, you don't need to know about Lie groups for this proof (you just need to know about exponential of matrices, which are defined with the usual series $\exp(A) = \sum_{n = 0}^{+\infty} \frac{A^n}{n!}$). I was just mentioning where this idea came from. Nov 16 answered Why is $GL_2(\mathbb C)$ connected? Nov 16 revised Finding all group homomorphisms $(\mathbb{Q},+)\to (\mathbb{Q}-\lbrace 0\rbrace,\cdot)$ added 901 characters in body Nov 15 answered Finding all group homomorphisms $(\mathbb{Q},+)\to (\mathbb{Q}-\lbrace 0\rbrace,\cdot)$ Nov 11 comment How to prove that this ring homomorphism is isomorphic? Remember the notation $F[x]/(m(x))$ is for the space of polynomials $F[x]$ modulo the ideal $(m(x))$. This not a fraction in the usual sense (which would make no sense here), but a space in which $m(x)$ and all its multiples are zero.