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 Feb10 answered Markov Chain with heterogeneous transitions Jan24 comment Building a proper homomorphism between groups. I think you can just simply write $f(x) = f(g^m) = m$ Dec16 awarded Caucus Dec9 asked Continued fraction approximation to a function and its derivative Jul2 awarded Curious May25 awarded Enthusiast Apr15 comment Reliability of linear regression to predict future I think popovitsj may want to discuss the concept of consistent estimator and also Gauss-Markov theorem? Apr8 comment How to show this: $\sum_{k=2}^{n}\frac{\ln{k}}{k^2}\approx \ln{n}\cdot\left(\zeta_{n}{(2)}-\frac{\pi^2}{6}\right)+C$ To relate $\zeta'(x)$ and $\zeta(x)$ and something like $f(b)-f(a)=f'(c)(b-a)$ for some $c \in (a,b)$. Imagine $\ln(n)$ is $f'(c)$, $\zeta_n(2) - \zeta(2)$ is $b-a$. Apr8 comment How to show this: $\sum_{k=2}^{n}\frac{\ln{k}}{k^2}\approx \ln{n}\cdot\left(\zeta_{n}{(2)}-\frac{\pi^2}{6}\right)+C$ I don't have an answer. Did you try any method related to mean value theorem? The resulting formula looks like it Apr3 comment Powers of permutation matrices. sorry I misread your question Apr3 comment Powers of permutation matrices. because all possible permutation is finite, prove it by contradiction. Mar26 comment Why are we interested in irreducible representation but not faithful representation? Thank you very much for your answer. I have spent many times on finding out in particle physics (self-study and google around, I am not in an university) to try to figure out your example. Basically, the symmetry of nature (in standard model) is $SU(3) \times SU(2) \times U(1)$ somehow describe the nuclear strong force, weak force and electromagnetic force. Then, the irreps of an element of $SU(3) \times SU(2) \times U(1)$ would describe a particle. Why trivial representation is important is that it is used to describe an elementary particle. Did I get it right? Mar16 comment How do computers compute the expected value of an infinite distribution? If you want any arbitrary distribution, monte carlo method / MCMC is good candidate for your work. Mar10 revised Why heat equation is not time-reversible? (Time arrow in mathematics) remove irrelevant stuff Mar10 accepted Why heat equation is not time-reversible? (Time arrow in mathematics) Mar10 accepted Why are we interested in irreducible representation but not faithful representation? Mar10 comment Why are we interested in irreducible representation but not faithful representation? Yes. It is the result from First Isomorphism Theorem, do you mean that if I want to have a faithful representation of $G$, I just find a "bigger" group $H \supset G$, and then find a representation of $H$, finally we use $H / \operatorname{ker} h$ to do our works? Mar10 asked Why are we interested in irreducible representation but not faithful representation? Mar9 revised Prove that $f_n$ converges uniformly on $[a,b]$ Remove compactness Mar9 comment Prove that $f_n$ converges uniformly on $[a,b]$ Yes. I read the link and also found that we don't need compactness