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22148
bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 31
visits member for 4 years, 5 months
seen 16 hours ago

Data scientist and math blogger.


Mar
10
comment Finding the distance between two triangles, one inside the other
I meant "bottom left". Sorry.
Mar
10
answered Finding the distance between two triangles, one inside the other
Mar
10
comment Normal Distribution
You should also be aware that different books use different tables: some books will have tables for $P(Z \le z)$, some from $P(0 \le Z \le z)$, and at least one common statistics textbook has a table of $P(-z \le Z \le z)$.
Mar
10
comment No radical in the denominator — why?
Personally I'd argue that $1/(4+\sqrt{3})$ is in some sense ``simpler'' than $(4-\sqrt{3})/13$, in that I can pretty quickly say $1/(4+\sqrt{3})$ is around $0.17$ but $(4-\sqrt{3})/13$ is a bit harder to work with. This is because I have a good sense of which numbers are which reciprocals of which other numbers, so $1/x$ generally seems simple to me from a mental-computation point of view.
Mar
10
answered No radical in the denominator — why?
Mar
9
comment General formula for $\sum_1^{p-1} \frac{1}{x}$, where $p$ is an odd prime
The conjecture that you need to make should be obvious if you just compute $A_p/B_p$ for the first few odd primes.
Mar
9
awarded  Nice Answer
Mar
9
answered Probability of 3 people in a room of 30 having the same birthday
Mar
8
answered Improper integral
Mar
8
comment $T(1) = 1 , T(n) = 2T(n/2) + n^3$? Divide and conquer
It's also possible that $2T(n/2)$ is ``short'' for $T(\lfloor n/2 \rfloor) + T(\lceil n/2 \rceil)$ -- that is, to solve a problem of size $n$ we break it up into two subproblems of size as close to equal as possible, and it takes time $n^3$ to put those answers together. Of course one generally ignores the floors and ceilings when thinking about asymptotics.
Mar
7
answered Simple proof that $8\left(\frac{9}{10}\right)^8 > 1$
Mar
7
comment Minimize $\sum f(p_i)$ for given $\prod p_i$
If you wanted to maximize $lcm(\{ p_i \})$ for a given $\sum_i p_i$, you'd end up with Landau's function (en.wikipedia.org/wiki/Landau's_function). Perhaps that will help.
Mar
4
comment Where to go with Mathematics?
Pete: it may be expressly part of our job, but that doesn't mean that students necessarily think we're willing to do it. (This is totally separate from whether we are or not.)
Mar
4
comment $\sum \frac{1}{f(k)}$ converges iff $\sum \frac{f^{-1}(k)}{k^2}$ converges
Can we just define $f(x)$ for non-integer $x$ by linear interpolation?
Mar
4
comment $\sum \frac{1}{f(k)}$ converges iff $\sum \frac{f^{-1}(k)}{k^2}$ converges
@Fabian: you're right. thanks.
Mar
3
comment $\sum \frac{1}{f(k)}$ converges iff $\sum \frac{f^{-1}(k)}{k^2}$ converges
Just a note: if $f(k) = k^\alpha$ for some $\alpha > 0$, then this reduces to the claim that $\sum k^{-\alpha}$ converges iff $\sum k^{\alpha-2}$ converges, which is true. This is of course not a proof, but it's a good sanity check.
Mar
3
comment Does exceptionalism persist as sample size gets large?
Henry's comment is correct; that's why I used words like "typical" that don't have technical meanings.
Mar
3
answered Does exceptionalism persist as sample size gets large?
Mar
2
comment Factoring $a^{10}+a^5+1$
Ross, thanks for the compliment!
Mar
2
comment How to compute the series $\sum_{n=0}^\infty q^{n^2}$?
If you want some reassurance about the two errors always being very close to $1/2$ before you sit down and do the dirty work of proving it, try some different values of $q$.