### Questions (46)

 5 Finding $f\in\mathbb{Q}[x]$ such that $f(\sqrt{2}+\sqrt{3})=\sqrt{2}$ and $\deg(f)\leq 3$. What's wrong with my approach? 4 The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$ 3 Prove that if the chord length depends only on |s-t|, then it is a line or a part of a circle. 3 on a connected normal space, applying Urysohn's lemma to show that $f^{-1}(r)$ has nonempty interior for each $r \in \mathbb{Q}\cap I$ 3 Homeomorphism of unit disc onto itself interchanging two points. [duplicate]

### Reputation (507)

 -2 Find the value of infinite series. +20 I don't understand the proof of following exercise from Do Carmo's differential geometry. +10 basic question about closed curve -2 Find the interval on which $\sum_{n=1}^{\infty} (1+\frac12+\frac13+…+\frac1n)\frac{\sin(nx)}{n}$ converges uniformly.

 3 What is different $(a_0, a_1, …, a_d) = (1)$ and $gcd(a_0, a_1, …, a_d) = 1$ in arbitrary UFD? 1 on a connected normal space, applying Urysohn's lemma to show that $f^{-1}(r)$ has nonempty interior for each $r \in \mathbb{Q}\cap I$

### Tags (58)

 3 abstract-algebra × 4 0 complex-analysis × 10 3 unique-factorization-domains × 2 0 continuity × 4 1 general-topology × 9 0 differential-geometry × 4 1 connectedness × 3 0 finite-groups × 3 0 real-analysis × 10 0 analysis × 3