Intereting Posts

Average distance between two random points in a square
Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
Lebesgue Spaces and Integration by parts
Evaluating $\int_0^1 \frac{x \arctan x \log \left( 1-x^2\right)}{1+x^2}dx$
Nested exponent modulus, $2^{2^517} ( mod 23)$
Epigraph of closed convex hull of a function
About the interior of the union of two sets
Difference between two independent binomial random variables with equal success probability
Normal operators in Hilbert spaces
Words formed from NUMBER with N to the left of U
Convergence of series involving in iterated logarithms $\sum \frac{1}{n(\log n)^{\alpha_1}\cdots (\log^k(n))^{\alpha_k} }$
Taylor's series when x goes to infinity
Existence of an element of given orders at finitely many prime ideals of a Dedekind domain
Is an integral always continuous?
Row swap changing sign of determinant

Let $G$ be an open subset of $\mathbb{C}$. Prove that $(\mathbb{C}\cup \{ \infty\})-G$ is connected if and only if every connected component of $G$ is simply connected.

- Why do we take the closure of the support?
- In an N-dimensional space filled with points, systematically find the closest point to a specified point
- Finding a space $X$ such that $\dim C(X)=n$.
- Radius of convergence of entire function
- Disjoint compact sets in a Hausdorff space can be separated
- Definition of a universal cover and the universal cover of a point
- Fourier Transform on Infinite Strip Poisson Equation
- Radius of convergence for the exponential function
- induced map homology example
- Why does having fewer open sets make more sets compact?

If the connected open set $H \subset \mathbb C$ is not simply connected, there is a simple closed curve $C$ in $H$ that is not homotopic to a point in $H$. Therefore there must be points inside $C$ that is not in $H$. Such a point and $\infty$ are in different connected components of $({\mathbb C} \cup \{\infty\} – G$.

- A representation of Dirac-$\delta$
- Inequalities involving the probability density function and variance
- Extra Square in Partial Fraction
- Find the number of distinct real values of $c$ such that $A^2x=cAx$
- Binomial Coefficients Proof: $\sum_{k=0}^n {n \choose k} ^{2} = {2n \choose n}$.
- How can one write $z^{-1}$ as a Stieltjes function?
- Trig Fresnel Integral
- Are there any positive integers $a, b, c, d$ such that both $(a, b, c)$ and $(b, c, d)$ are Pythagorean triples?
- complicated derivative with nested summations
- How to teach mathematical induction?
- Show that $\lim_{x\to a^{+}} g(x) =g(a)$
- Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
- For $a=\cos(2\pi/n)$, show that $ = \ldots$
- Levin's u-transformation
- How to compute the integral $\int_{-\infty}^\infty e^{-x^2}\,dx$?