27,238 reputation
23792
bio website mixedmath.wordpress.com
location Providence, RI
age 24
visits member for 2 years, 1 month
seen 5 hours ago
stats profile views 3,131

I'm working on my Math PhD at Brown University. I've finished my first year, and now I pursue my interests in analytic number theory.

I happen to loosely update a math blog at mixedmath.wordpress.com. I put a lot of MSE things on there too, though a lot of the material caters to whatever class I'm teaching at the time (this fall, calc I).


1d
comment Dihedral groups
As I read this question, I get the (perhaps wrong) impression that you are simply asking me to be precise in doing your homework. I fear that many other members of the community will feel the same way, and will downvote or try to close this question. I encourage you to edit your question, include what you've tried (and correspondingly try something), check the faq, and perhaps read a few more questions to see what people expect.
2d
comment How to prove that $\int_0^{\infty} \log^2(x) e^{-kx}dx = \dfrac{\pi^2}{6k} + \dfrac{(\gamma+ \ln(k))^2}{k}$?
These numbers seem very closely related to the Laurent expansion of the Gamma function about $0$, but I don't know why this is the case or how to use this.
2d
comment Is there a rigorous definition of a Young tableau?
'filling' means you label each box of the Ferrers diagram with a number, sometimes according to some rules of increasing (e.g. increasing in each column and row, or nondecreasing in row and strictly increasing in each column). They can be presented differently depending on the application. But usually, there is no uncertainty about their definition. What rigor do you feel is missing?
2d
answered Matrix $BA\neq$$I_{3}$
2d
comment Getting better at math?
Ah, and now I feel a bit silly. I'd stopped reading updated comments and I hadn't realized this had been asked before. Now I feel a bit cheated
2d
answered Getting better at math?
2d
comment RSA: Prove that all messages encrypt to itself
I thought so too ;p
2d
answered RSA: Prove that all messages encrypt to itself
May
16
revised Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$
added 54 characters in body
May
15
comment Continuous function that is only differentiable on irrationals
@Landscape: Ah, I see I left out the very important absolute value - thank you for that
May
15
revised Continuous function that is only differentiable on irrationals
added 2 characters in body
May
15
answered Continuous function that is only differentiable on irrationals
May
15
answered Finding the degree of the derivative of a complex rational function
May
14
comment Metric on the space of Lipschitz continuous functions
You ask for how to start this question. I would suggest you look at the definition of a metric space and check the definitions one by one.
May
12
comment how can I do the following integration?
I think that you would be better received if you took the time to use proper spelling, capitalization, and grammar.
May
10
answered Supremum of $\underset{n \to \infty }{\lim} \underset{x\in [0,1]}{\sup} \left | \frac{x+x^{2}}{1+n+x} \right | $
May
10
comment Dense set in $L^2$
The condition can't be weakened. As soon as the complement is of positive measure, the indicator function on that complement will be far in Lp terms. Rather, you need the condition mentioned.
May
10
comment Proving that if $\inf S\notin S$, then it is an accumulation point of $S$
I agree - do what the hint tells you to do.
May
9
comment Show that $h \equiv 1 \pmod p$, where $h$ is the number of subgroups of order $p$ and $p$ divides the group order.
Reason similar to the reasoning used to prove the sylow theorems.
May
9
comment Prove $\frac{1+\cos{(2A)}}{\sin{(2A)}}=\cot{A}$
I have rolled back to TMM's edit, since it is exceptionally clear and easy to read.