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Questions (113)

 10 Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$ 8 Show bounded harmonic function on $\mathbb{C}$ is constant. 8 What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$ 7 What property of a matrix causes $\|e^{tA}\|_2$ to oscillate as $t\rightarrow\infty$? 7 Show that the countable product of metric spaces is metrizable

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 +5 Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$ +10 Accidents of small $n$ +5 Show bounded harmonic function on $\mathbb{C}$ is constant. +5 How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer

Answers (7)

 4 Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$ 4 Accidents of small $n$ 2 Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$ 1 Complex Analytic Proof of the Gaussian Integral $\int_{-\infty}^{\infty}e^{-z^2}dz=\sqrt{\pi}$ 0 Show both relaxations of boolean LP give equal lower bounds

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 4 abstract-algebra × 18 1 residue-calculus × 3 4 commutative-algebra × 3 0 real-analysis × 15 4 examples-counterexamples × 2 0 measure-theory × 12 4 big-list 0 probability × 9 3 complex-analysis × 28 0 number-theory × 7

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