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Oct
19
answered How to prove $\nabla\cdot \vec{B}=0 \Rightarrow \exists \vec{A}:\vec{B}=\nabla \times \vec{A}$
Oct
5
awarded  Critic
Sep
6
answered $ \sum_{k=1}^{\infty} \ln{\left(1 + \frac{1}{4 k^2}\right)}$ Computing this sum
Jul
17
comment What does the variance/SD of a set signify?
See the chebyshev inequality.
May
17
comment What's the sum of $\sum_{k=1}^{\infty} e^{-k(x-k)^{2}}$?
Look up the Euler Maclaurin formula....Mathematica can do the integral, and it involves the erf function.
May
6
asked Describe growth of $\epsilon n$
Mar
22
awarded  Commentator
Mar
9
accepted Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Phew - now I can drink the coffee slowly, rather than chugging it. That helps a huge amount, much appreciated!
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Thanks much. There are still (at least) two things I'm not getting. You say $\exp(n \log(1-p^k)) \approx \exp(n p^k)$, shouldn't it be $\exp(n \log(1-p^k)) \approx \exp(-n p^k)$ (negative sign)? And why are we solving $npk \approx 1$ Since this is the size of the term $f(k,n)$, wouldn't we want it to be $\exp(n p^k) \approx 1$?
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Thanks for the helpful comments. I too had thought about splitting the summation into two parts, one with terms close to zero, the other with terms close to one, but didn't see how to choose the splitting point appropriately. How did you decide on $\frac{\log n}{\log\frac{1}{p}}$?
Mar
8
asked Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
Feb
23
answered Examples to show intersection of two uncountable sets can be countably infinite
Feb
7
answered Confused about permutation cycles - Question on joint cycles of odd length
Feb
1
answered Popular math books with depth
Oct
22
awarded  Yearling
Sep
8
answered Central limit theorems, Almost sure invariance principles and Brownian motion
Aug
23
answered Introduction to Information Theory
Jul
25
comment Help solving: Problem on Normal Distribution of Data
Clearly this is a fictional example. Phone call durations do not come from a normal distribution - calculate the probability that a call takes less than 0 seconds, it is not zero!
Jun
22
answered Is Aluffi's book a good second text for Algebra?