Showing that $\frac{\mathbb{R}[x]}{\langle x \rangle}$ and $\frac{\mathbb{R}[x]}{\langle x-1 \rangle}$ are not isomorphic as $\mathbb{R}[x]$ modules.

Disprove or prove using delta-epsilon definition of limit that $\lim_{(x,y) \to (0,0)}{\frac{x^3-y^3}{x^2-y^2}} = 0$

Variance of sine and cosine of a random variable

Integral $\int_0^{2π} e^{e^{ix}} dx$

non isomorphism between $A^1$ and zero set of $y^2-x^3=0$'s coordinate ring by cohomology argument?

Computing the index $\left(\mathbb Z\left[\frac{1+\sqrt{5}}{2}\right]:\mathbb Z \left[\sqrt{5}\right]\right)$?

Sets that are both Sum-free and Product-free

Can we prove that infinite many primes begin with any given digitstring?

Prove that the maximum score difference between two consecutive teams in a tournament with $n$ teams is $n$

When does the game end?

How to prove closure property for $x\cdot y = \frac{x + y}{1 + \frac{xy}{c^2}}$?

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Compute fundamental group _visually_ by the polygonal representation of the space

Related