J. Doe

### Questions (79)

 4 Calculate the sum $\sum_{n=1}^\infty {(-1)^n\over 1+n^2}$ 3 Calculating $\int_0^{2\pi} e^{e^{i \theta}} d\theta$ 2 Galois group of $x^6+1$ over $\mathbb{F}_2$ 2 Find the component $c_{-k}$ in Laurent expansion of $1/((z^{a_1}-1)\cdots(z^{a_k}-1))$ about $1$ 2 Calculate $\int_{-\infty}^\infty{x^2\,dx\over (1+x^2)^2}$

### Reputation (370)

 +5 Find all the middle fields of the extension $\mathbb{Q}/\mathbb{Q}(\exp({2\pi i\over 7}))$ +5 Is $\mathbb{F}_p(X)/\mathbb{F}_p(X^2)$ Galois extension? +10 Galois group of $x^6+1$ over $\mathbb{F}_2$ +5 Find the component $c_{-k}$ in Laurent expansion of $1/((z^{a_1}-1)\cdots(z^{a_k}-1))$ about $1$

 3 Find a example of $A$ be $4 \times 4$ matrix such that $A$ has rank $2$ but $A^2 =0$? 1 Prove $|z_1|-|z_2|\leq|z_1-z_2|$ 1 Proof of a.s. uniqueness of probability convergence limit -1 Find a measurable function $g:\mathbb{R}\to\mathbb{R}$ s.t. $\mathbb{E}(g(\mathcal{N}(0,1)))=2$ -1 Prove that for a homogeneous function of degree one all directional derivatives exist

### Tags (111)

 3 matrices × 4 1 proof-verification × 3 3 linear-algebra × 2 1 limits × 3 3 nilpotence 0 complex-analysis × 23 3 matrix-rank 0 probability × 15 1 complex-numbers × 4 0 abstract-algebra × 14

### Accounts (7)

 Mathematics 370 rep 1313 bronze badges Stack Overflow 123 rep 22 bronze badges Economics 121 rep 22 bronze badges Computer Science 101 rep Super User 101 rep 11 bronze badge