Let $f(z)=z+\frac{1}{z}$ for $z\in \mathbb C$ with $z\ne 0$. Which of the following is always true? (a) $f$ is an analytic on $\mathbb C$\ $\{0\}$ (b) $f$ is a conformal mapping on $\mathbb C$\ $\{0\}$ (c) None of the above (a)$f(z)=z+\frac{1}{z}=z+\frac{\overline z}{|z|^2}...

Let $f:\mathbb R^m \to \mathbb R^m$ be a differentiable function. let $Df(x)$ be the derivative of $f$ at $x\in \mathbb R^m$. which of the following is/are correct? (a)$Df(0)(u)=0, \forall u \in \mathbb R^m$ (b)$Df(x)(u)=0, \forall u \in \mathbb R^m$ and some $x\in \mathbb R^m$ ...

I think we can merge the tags which are related to Maths tests like gre-exam or gmat-exam (or whatever I am not aware of in this site) as a single tag. Another missing one is that: we can merge many tags like multivariable-calculus, vectors and ... as Advanced Calculus. Indeed if want to do it, w...

There are 384 questions tagged gre-exam. This appears to be a meta tag that I cannot really imagine anyone watching or searching for. I think it should be deleted.

Recently I noticed a tag "gre-exam" in this question. A quick search ([*-exam]) showed existence of similar tags for GMAT as well. In light of it, I wanted to ask the possibility of creating a tag csir-net-exam (or similar), as a lot of us aide to math.SE to prepare for it. I have already spotte...

I'm studying for quals/prelims. Tests you take in your first year or two of PhD (at least in America). Sometimes I want to browse problems that specifically came up in some qualifying/preliminary exam. When I look for "measure theory" there are elementary or high level questions mixed in with th...

Say $M$ is a matrix over your favorite field. Let $P$ be the collection of nonvanishing minors of $M$, partially ordered by inclusion in the apparent way. The vague question is: What can one say about the poset $P$? A little more explicitly, say $M$ is $m \times n$. Let $B_m$ and $B_n$ be the B...