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bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 30
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Data scientist and math blogger.


Feb
25
answered How to invert this exponential function to solve for x: $y = a \exp(bx) + c \exp(dx)$?
Feb
25
comment How to invert this exponential function to solve for x: $y = a \exp(bx) + c \exp(dx)$?
this is not really "polynomial" -- your assumption that B and D are integers fails with the given numbers.
Feb
22
comment Prove that if $p^{a}$ is a factor of the canonical factorization of ${{2n}\choose{n}}$ then $p^{a} < 2n$?
Also, it appears numerically that if $p^a$ is a factor of ${n \choose k}$, then $p^a \le n$; that is, this doesn't depend on the fact that ${2n \choose n}$ is a "central" binomial coefficient. So once you come up with a proof, see if it can work on general binomial coefficients as well.
Feb
21
answered How to find the distance between a point and line joining two points on a sphere?
Feb
19
comment Is there a way to quickly estimate the reciprocal of a number?
Seconding this way of coming up with 2.575.
Feb
19
comment Is there an n such that $2^n|n!$?
Moron, you're right. I've changed that.
Feb
19
revised Is there an n such that $2^n|n!$?
edited body
Feb
19
answered Is there an n such that $2^n|n!$?
Feb
17
comment Is there a calculator out there that shows the full answer instead of shortening it?
What you want is not usually called a "calculator" but a "computer algebra system".
Feb
11
comment Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
An alternate version of this proof is to show that $3(n+1)^5 + 5(n+1)^3 + 7(n+1) - (3n^5+5n^3+7n)$ is always divisible by 15. As it turns out, this is trivial since once you expand the polynomial out all the coefficients are divisible by 15.
Feb
11
answered Solving a set of recurrence relations
Feb
10
comment What should be in every grad student's library?
I'm a fan of the Chicago list as well. The main difficulty I have with Amazon reviews of textbooks is that a large number of reviewers there seem to have disliked a class they took using a book, and take it out in their review of the book itself.
Feb
7
comment two phds in math
Why would someone want two PhD's in math? On the other hand, my PhD program in math had a couple people who already had PhDs in physics. A lot of people in my department did mathematical physics; I don't know the detailed histories of these people but presumably while they were getting the PhD in physics they became more interested in mathematics.
Feb
5
comment Why is integration so much harder than differentiation?
Qiaochu: I think this is a good question even if one operation is harder. Why should integration be the "hard" one?
Jan
31
comment Recurrence Relation Homework Struggles
I'm upvoting this because I was going to suggest the change of variables.
Jan
30
comment Help with converting the derivative of $\cos^3(x)$
Perhaps part of the purpose of the problem was to force the students to do this unnecessary manipulation.
Jan
21
comment a question related to two competing patterns in coin tossing
This can be found , I think, in Flajolet and Sedgewick's excellent book Analytic Combinatorics (which is available online for free - use google). I do not have the time right now to find exactly where in the book this appears, though, but perhaps someone else does.
Jan
14
comment Time until x successes, given p(failure)?
What do you want to know? I'm guessing you're asking about the time to completion -- either the average time to completion or some more specific information about the distribution -- but I think a sentence or two is missing here.
Jan
4
comment Prove that $\sum_{i=0}^n2^{3i} \binom {2n+1}{2i+1}$ is never divisible by 5
A hint (although I haven't tried this in detail): call this number $f(n)$. Then $f(n)$ might satisfy some linear recurrence. Plug integers mod 5 into this recurrence and see what happens.
Jan
1
awarded  Nice Answer