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50 Questions

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36	Problems regarding $\{x_n \}$ defined by $x_1=1$; $x_n$ is the smallest distinct natural number such that $x_1+…+x_n$ is divisible by $n$.
7	Find all differentiable functions $f$ such that $f\circ f=f$
6	Very curious sequence of integrals $I_n=\int_0^1 \frac {(x(1-x))^{4n}} {1+x^2}\mathrm dx$
5	Describing image under $f(z)=e^{2\pi iz}$
4	Computing the minimal polynomial over $\mathbb{Q}(\sqrt{3})$

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623 Reputation

+3	Finding mass of a sphere whose density is given
+5	If $f$ is analytic in a disk $\|z\|<R$ then so is $g(z)=\overline{f(\bar z)}$ in the disk
-2	Minimal polynomial over the field $\Bbb Q$
+5	If $\langle\nabla f(x) - \nabla f(y), x-y\rangle \geq 0$ then $H_f \geq 0$

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13 Answers

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1	Question on Residues (Complex Analysis)
1	Prove if $f(z)=0$ when $z$ is on $C$, then $f'(z_0)=0$ where $z_0$ is on $C$.
1	Cauchy's Problem
1	continuity with contraction
1	Prove the following is a field

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35 Tags

2 complex-analysis × 20	1 continuity
1 real-analysis × 10	1 classical-analysis
1 linear-algebra × 2	1 residue-calculus
1 abstract-algebra × 2	0 field-theory × 8
1 functional-equations × 2	0 geometry × 7

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Mathematics

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