10,451 reputation
22251
bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 31
visits member for 4 years, 6 months
seen 9 hours ago

Data scientist and math blogger.


Jan
20
comment Mathmatical notation for a term of a polynomial
I think that's the closest there is to a standard notation. (But I honestly wouldn't use it without definition unless speaking to an audience of people who deal with generating functions all the time.)
Jan
15
comment Find a quartic (degree 4) polynomial with integer coefficients whose roots are the primitive 12th roots of unity
The polynomial $(z-\alpha_1) (z-\alpha_2) \cdots (z-\alpha_n)$ has roots $\alpha_1, \alpha_2, \cdots, \alpha_n$.
Jan
14
comment Expectation of maximum of Binomial RVs
possible duplicate of Bounds for the maximum of binomial random variables
Jan
9
comment Visually stunning math concepts which are easy to explain
The basic idea is pretty simple: ${i \choose k} = {i \choose k-1} + {i-1 \choose k-1}$, and this recurrence holds $\mod p$ as well.
Jan
9
comment Visually stunning math concepts which are easy to explain
I'd also note that it's possible to compute ${i \choose k} \mod p$ without computing $i \choose k$. For large $i$ this would matter.
Dec
15
comment Taylor approximation for $\ln(1.3)$
Your book probably should say $0.255$.
Dec
15
comment Expected value of this deceptively simple variable
To find $E(Z)$: note that $Z$ is either 1, 0, or -1. With what probability does it take each of those values?
Dec
10
comment What is the probability that a Poisson random variable is prime?
Asymptotically I'd expect $Q(\lambda, 0)$ to be "the probability that a number near $\lambda$ is prime", i. e. about $1/\log \lambda$.
Dec
9
comment Can you select random entry from unknown number of entries?
If I recall correctly this is called "reservoir sampling", also worth googling.
Dec
8
comment Why is $\frac {1\cdot2\cdot3\cdot…\cdot n}{(n+1)(n+2)…(2n)}\le \frac 1 {n+1}$
See my edits to answer that question.
Dec
5
comment Chance on pairs when picking 'Sinterklaas tickets'
In the limit of large $n$, the number of 2-cycles of a permutation on $n$ elements is Poisson-distributed with mean $1/2$. (For $k$-cycles, it's $1/k$.) In particular, it's zero with probability $e^{-1/2}$. Restricting to derangements doesn't change this too much. This is a high-level explanation for the asymptotic result quoted in OEIS.
Nov
24
comment Will it become impossible to learn math?
I don't know this book, but I am intrigued. I think this may shed some light on the original question: there could be an upper limit on the depth of possible research imposed by the human lifespan.
Nov
19
comment Numerical value of $\sum_{p \in \mathcal P} \frac1{p\ln p}$
Your difference should be $1/(2 \log 2)$, not $1/2$.
Nov
19
comment How to draw greek letters on paper / blackboard?
I have seen $\phi$ and $\varphi$ used by the same lecturer in the same lecture (in physical chemistry). One was pronounced "fee" and the other "fie". I found this lecture essentially impossible to follow because I thought of those two glyphs as interchangeable.
Nov
19
comment Prove that $\sum_{n=0}^{\infty }\frac{(2n+1)!!}{(n+1)!}2^{-(2n+4)}=\frac{3-2\sqrt{2}}{4}$
Yes - that numerical value corresponds to your analytical value.
Nov
19
comment Prove that $\sum_{n=0}^{\infty }\frac{(2n+1)!!}{(n+1)!}2^{-(2n+4)}=\frac{3-2\sqrt{2}}{4}$
As a check on this value, when the sum is computed numerically one gets 0.1035533906.
Nov
17
comment Characteristics of odd parts in a partion
Guessing this is a homework question, so I'll give a hint. Have you seen a proof that the number of partitions with only odd parts is the same as the number of distinct parts, using generating functions? You can adapt that proof to this problem.
Nov
1
comment How do calculators evaluate inverse trig functions?
I do like it. The question to me seems to be whether one wants the more conceptual (yours) or calculational approach; yesterday calculation felt worthwhile to me, but in the light of morning I can see how the more conceptual approach is superior.
Oct
31
comment How do calculators evaluate inverse trig functions?
God plays dice is my blog. The commenter "logosintegralis" there took a stab at using Pade approximants to derive that approximation.
Oct
29
comment Expected number of turns for a rook to move to top right-most corner?
The fact that the move is to move to a random square in the same column or row - i. e. change one coordinate uniformly at random - explains why G7 is no closer to H8 than A1 is.