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Jul
2
awarded  Curious
May
25
awarded  Enthusiast
Apr
15
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?
Apr
8
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 $b-a$.
Apr
8
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
Apr
3
comment Powers of permutation matrices.
sorry I misread your question
Apr
3
comment Powers of permutation matrices.
because all possible permutation is finite, prove it by contradiction.
Mar
26
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?
Mar
16
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.
Mar
10
revised Why heat equation is not time-reversible? (Time arrow in mathematics)
remove irrelevant stuff
Mar
10
accepted Why heat equation is not time-reversible? (Time arrow in mathematics)
Mar
10
accepted Why are we interested in irreducible representation but not faithful representation?
Mar
10
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?
Mar
10
asked Why are we interested in irreducible representation but not faithful representation?
Mar
9
revised Prove that $f_n$ converges uniformly on $[a,b]$
Remove compactness
Mar
9
comment Prove that $f_n$ converges uniformly on $[a,b]$
Yes. I read the link and also found that we don't need compactness
Mar
9
comment Construct a rational matrix $A$ s.t. $A^m = I$
thank...let me spend some time on reading the papers
Mar
9
accepted Construct a rational matrix $A$ s.t. $A^m = I$
Mar
9
awarded  Commentator
Mar
9
comment Prove that $f_n$ converges uniformly on $[a,b]$
I found a good answer here. I knew it from a "inductive" proof of Heine-Borel theorem and the question leads me to think of compactness of $[a,b]$.