37,546 reputation
381141
bio website sos440.net
location Los Angeles, CA
age 27
visits member for 3 years, 9 months
seen 18 mins ago

I am currently a UCLA student, particularly interested in probability theory.

I love mathematics, especially calculating some sort of integrals and summations with inner aesthetic appealing.

Language fluency: (G:green, A:amber, R:red)

  • Korean: Native
  • English: (Reading: G, Listening : A, Speaking : R, Writing : A)
  • Japanese: (Reading : A, Listening : A, Speaking : A, Writing : R)

Jan
23
awarded  Popular Question
Jan
19
revised Prove $\int_{-\pi}^{\pi}\sin \sin x \,dx=0$ without using the fact that $\sin(x)$ is odd.
deleted 80 characters in body
Jan
19
answered Prove $\int_{-\pi}^{\pi}\sin \sin x \,dx=0$ without using the fact that $\sin(x)$ is odd.
Jan
16
comment There does not exist a holomorphic map between torus and Riemann sphere
Consider the contour integral of $f'/(f-c)$ along the boundary of a fundamental region (translated unit square in this case). Can you find the value of this contour integral? Can you figure what this result means in terms of the number of solutions of $f(z) = c$ on that region?
Jan
15
revised proving that $3^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}}}}< 8$
added 170 characters in body
Jan
15
answered proving that $3^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}}}}< 8$
Jan
12
answered Convergence of the sequence $x_n=\tan x_{n-1}$
Jan
11
comment $\exp(-|x|^\alpha),\alpha>2$ is not a Fourier transform of a probability distribution
Hint 2. What can you say about $X$ when $\Bbb{E}[X^{2}] = 0$?
Jan
11
answered Prove $1! + 2! + 3! + \ldots + n! =y^3$ has only one solution in the set of natural numbers?
Jan
11
comment How can I evaluate $\int_0^{\pi/2}\frac{x\cos{x}}{3\sin^2x+1}dx$ and $\int_0^{\pi/2}\frac{x\cos{x}}{\sin^2x+3}dx$?
@ClaudeLeibovici, You are right. I usually prefer to leaving this function as it is since it saves space.
Jan
10
comment integration of $\large\int \frac{u^2}{(1-u^2)^2}$ $ du$
I mean, you made a sign mistake in your answer…
Jan
10
answered integration of $\large\int \frac{u^2}{(1-u^2)^2}$ $ du$
Jan
10
comment integration of $\large\int \frac{u^2}{(1-u^2)^2}$ $ du$
I guess $$ \sinh 2t = \frac{2\tanh t}{1-\tanh^{2}t}. $$
Jan
10
answered How can I evaluate $\int_0^{\pi/2}\frac{x\cos{x}}{3\sin^2x+1}dx$ and $\int_0^{\pi/2}\frac{x\cos{x}}{\sin^2x+3}dx$?
Jan
10
awarded  sequences-and-series
Jan
9
revised Proving generalized Cassini's identity using determinant?
deleted 12 characters in body
Jan
9
asked Proving generalized Cassini's identity using determinant?
Jan
9
comment Convergence of $\sum_{n=1}^{\infty} a^{-\frac{1}{c+1}}\prod_{k=1}^{n} \frac{a}{a+k^{c}}$ as $a\to\infty$
@citronrose, that is because you are mistaken. If you calculate correctly, you can check that my formula also produces $f(c) \to 1$ as $c\to \infty$.
Jan
9
comment Why are angles in “degrees” dimensionless?
As long as you choose other units and modify the trigonometric function accordingly, you can actually introduce 'dimensional' quantity measuring the size of an angle. This is quite artificial, however, in the sense that the trigonometric functions in terms of radian have Taylor expansion, e.g. $$\cos x = \sum_{n=0}^{\infty}\frac{(-1)^n}{(2n)!} x^{2n}. $$ This formula would have contained bunch of unit-cancelling factors if you have chosen a dimensional unit (because we cannot add quantities of different diemsnions). So it is much natural to consider degrees dimensionless.
Jan
9
comment Convergence of $\sum_{n=1}^{\infty} a^{-\frac{1}{c+1}}\prod_{k=1}^{n} \frac{a}{a+k^{c}}$ as $a\to\infty$
@citronrose, and for the exponential part, I utilized the Taylor expansion of $e^{x}$. This is possible because that error term is uniformly bounded.