I have a perfect GPA from 2nd year on wards, but a horrible first year... How badly will this affect PhD admission?
How much will a poor first semester affect my grad school chances?
What does **Ens** stand for? Earlier someone was asking about the category "Ens" described in Categories for the Working Mathematician. My question is more basic: What does Ens stand for?  Most of the categories have names that are self explanatory, and maybe this one does too.  But for the life of me I can't think of it, and a Google search was no help. Few days back I have installed ecryptfs, created a private directory using it. Now my Ubuntu login became super slow. I have tried removing ecryptfs from Synaptic. I found It, it can not be deleted that way. Somewhere I have read about this command  ecryptfs-setup-private --undo   But this command displays a rather confusing list of commands on terminal. I don't want to mess up my installation, neither want to loose my administrator account.  Now my question is, how can I safely remove /home/user/Private (.Private) and remove ecryptfs encryption ? Finding descendants of British great grand uncle who emigrated to Australia? From  I have received the information of the person with the possibility of great-grandfather.   However, I have a bigger problem from here which is whether he really is my great-grandfather because there was a brother to him in the information.   If I can find his brother's descendants, then I may be able to learn the kinship with DNA testing.   How can I find the living descendants of this great grand uncle?  I was born and grew up in Japan where research is easy for me but I do not know the best way in Britain and Australia.  C.Z.Ede is the name of the candidate for my great-grandfather and his information can be found at   There is also a Mr Peter Zohrab site () which mentions "Sydney Cuthbert Ede, Eagleville Station, Talbotville, Victoria, Australia".  Mr Peter Zohrab from that site suggested that I look for descendants of Sydney Cuthbert Ede in Australia or New Zealand. However, I have not yet found any. I am also inquiring at the church in which he was baptized. Nonabelian semidirect products of order $pq$? I just constructed the semidirect product in Lang, and I'm trying to tie some facts together. From Ash's Algebra, I know that if $p\lt q$ are distinct primes, if $q\not\equiv 1\pmod{p}$, then any group $G$ of order $pq$ is abelian.  Is the converse true, that for any primes $p\lt q$, if $q\equiv 1\pmod{p}$ then there exists a nonabelian group of order $pq$?  One example I found online is that $\mathbb{Z}_3\ltimes \mathbb{Z}_7$ is nonabelian, and here $7\equiv 1\pmod{3}$. I was considering then semidirect products $\mathbb{Z}_p\ltimes\mathbb{Z}_q$ where $q\equiv 1\pmod{p}$ and some homomorphism $\phi\colon \mathbb{Z}_p\to\operatorname{Aut}(\mathbb{Z}_q)$ I calculate that  $$ (1,0)(0,1)=(1+0,\phi_0(0)+1)=(1,1) $$ and $$ (0,1)(1,0)=(0+1,\phi_{-1}(1)+0)=(1,\phi_{p-1}(1)). $$ Is it true somehow that $\phi_{p-1}(1)\neq 1$ in each case to show the group is nonabelian? I guess if it did this would imply $\phi_{p-1}$ is the trivial automorphism, so maybe there's something there? If not, is there a way to show $\mathbb{Z}_p\ltimes\mathbb{Z}_q$ is nonabelian in these cases in general? Thanks. Diagram of an artificial neural network Using crontab to execute script every minute and another every 24 hours How do you format Facebook Wall posts? There doesn't appear to be any formatting links when I do a Facebook Wall post.  Is there any way to do formatting like HTML, markup, etc? If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$.   Proving the first direction of this is easy. That is, if $A = B$ then it is obvious that $A^2 = A^2$. I am wondering how to prove the other direction now. Maybe proving it by contradiction will be easier than directly. I'm studying for qualifying exams and ran into this problem.  Show that if $\{a_n\}$ is a nonincreasing sequence of positive real numbers such that $\sum_n a_n$ converges, then $\lim_{n \rightarrow \infty} n a_n = 0$.  Using the definition of the limit, this is equivalent to showing \begin{equation} \forall \varepsilon &gt; 0 \; \exists n_0 \text{ such that } |n a_n| &lt; \varepsilon \; \forall n &gt; n_0 \end{equation} or \begin{equation} \forall \varepsilon &gt; 0 \; \exists n_0 \text{ such that } a_n &lt; \frac{\varepsilon}{n} \; \forall n &gt; n_0 \end{equation} Basically, the terms must be bounded by the harmonic series. Thanks, I'm really stuck on this seemingly simple problem! Code snippet comments in code formatting break the formatting of the post In Walter Rudin's Principles of mathematical analysis Exercise 5.21, it is proved that for any closed subset $E\subseteq \mathbb{R}$, there exists a smooth function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$.   Since $E^c$ is open in $\mathbb{R}$, $E^c$ is a countable disjoint union of open intervals $(a_i,b_i)$. On an interval $(a,b)$, if we let $f(x)=\exp(\frac{1}{(x-a)(x-b)})$, $x\in(a,b)$; $f(x)=0$, $x\notin(a,b)$, ($f(x)=\exp(\frac{1}{(x-a)})$ or $f(x)=\exp(\frac{1}{(x-b)})$ on $(a,\infty)$ and $(-\infty,b)$ resp.), then $f$ is smooth. Hence we can get a smooth function on $\mathbb{R}$ such that $E$ is the zero point sets of $f$.  (1). How about a closed subset $E$ of $\mathbb{R}^n$? is it true that for any closed subset $E\subseteq \mathbb{R}^n$, there exists a smooth function $f$ on $\mathbb{R}^n$ such that $E=\{x\in \mathbb{R}^n\mid f(x)=0\}$?  An open set in $\mathbb{R}^n$ cannot be written as a disjoint union of countable open balls hence the proof above is not valid. The partition of unity only claims that for an  open set $U$, there exists open $V$ in $U$ such that $\bar V\subseteq U$ and a smooth function $f$ on $\mathbb{R}^n$ such that $supp f\subseteq U$, $f|_V=1$.   (2). The taylor series of $f(x)=\exp(\frac{1}{(x-a)(x-b)})$ does not converge around points $a,b$ hence $f$ is not analytic at $a,b$. Is it true that for any closed subset $E\subseteq \mathbb{R}$, there exists an analytic function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$? How does the CS:GO ranking system work? I just want to write a script which changes my directory.  I put the below commands in the file /home/alex/pathABC  #!/bin/sh cd /home/alex/Documents/A/B/C echo HelloWorld   I did   chmod +x pathABC   In the Terminal, while in /home/alex, I ran ./pathABC, but the output is just HelloWorld and the current directory is not changed.  So what is wrong? What games save to the Steam Cloud? How can I use std::maps with user-defined types as key? Destroying a Planewalker before its ability is used Say my opponent plays a planeswalker during their first main phase.  I have a  or some other effect that will kill it after it is already in play, but before they use any of its abilities.  I could respond to them using a +1 ability, but I want to kill it before that effect goes on the stack.  In most casual situations, it would basically come down to whether I say "Hero's Downfall" first, or they say "+1" first.  But I can't imagine that's how it's supposed to work.  Is there a time between when the planeswalker hits the battlefield and when they activate its abilities that they must let me respond? It seems to me that situations like this arise frequently, and they are resolved simply by who speaks up first, which is horrible for such a rules-oriented game. "A quarter past five" or simply "Quarter past five"? I usually say “It’s a quarter past” (for instance) “five”.  But I think I’ve heard (or read) “It’s quarter past ...”, too, with no indefinite article: is that correct?  Which is more common (if both constructions are in use)?  Is the omission of the article more colloquial (informal, popular, whatever)?  Is there a difference between British and American English?  Thank you very much. Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$ Suppose I want to find the minimal polynomial of the number $\sqrt[3]{2} + \sqrt{3}$.   Now that means I want to find a  unique polynomial that is irreducible over $\Bbb Q$ such that $f(x)=0$. Now I know that because   $\sqrt[3]{2} + \sqrt{3}$ belongs to $\Bbb Q( \sqrt[3]{2} , \sqrt{3})$  it might be degree $2$, $3$ or $6$ and does not belong to $\Bbb Q( \sqrt[3]{2})$ so it cannot be of degree $3$ or  $\Bbb Q( \sqrt{3})$ so it cannot be of degree $2$.  So it is of degree $6$. I think my sayings are a bit intuitive and not formal and lack rigorous. Couldn't it belong to another extension of degree $2$? or $3$? I can't answer that. Why checking only those $2$ is enough? Or is it wrong at all to say that? Nginx installation error in Ubuntu 16.04 :~$ sudo apt-get remove nginx* && sudo apt-get install nginx-full*  Reading package lists... Done Building dependency tree        Reading state information... Done  After this operation, 5,579 kB of additional disk space will be used. Do you want to continue? [Y/n] y Get:1 http://in.archive.ubuntu.com/ubuntu xenial-updates/universe amd64 nginx-full-dbg amd64 1.10.0-0ubuntu0.16.04.1 [3,789 kB] Fetched 3,789 kB in 33s (112 kB/s)                                              Selecting previously unselected package nginx-common. (Reading database ... 189767 files and directories currently installed.) Preparing to unpack .../nginx-common_1.10.0-0ubuntu0.16.04.1_all.deb ... Unpacking nginx-common (1.10.0-0ubuntu0.16.04.1) ... Selecting previously unselected package nginx-full. Preparing to unpack .../nginx-full_1.10.0-0ubuntu0.16.04.1_amd64.deb ... Unpacking nginx-full (1.10.0-0ubuntu0.16.04.1) ... Selecting previously unselected package nginx-full-dbg. Preparing to unpack .../nginx-full-dbg_1.10.0-0ubuntu0.16.04.1_amd64.deb ... Unpacking nginx-full-dbg (1.10.0-0ubuntu0.16.04.1) ... Processing triggers for ufw (0.35-0ubuntu1) ... Rules updated for profile 'Apache Full' Rules updated for profile 'Nginx HTTP'  Processing triggers for systemd (229-4ubuntu4) ... Processing triggers for ureadahead (0.100.0-19) ... Processing triggers for man-db (2.7.5-1) ... Setting up nginx-common (1.10.0-0ubuntu0.16.04.1) ... Setting up nginx-full (1.10.0-0ubuntu0.16.04.1) ... Job for nginx.service failed because the control process exited with error code. See "systemctl status nginx.service" and "journalctl -xe" for details.  invoke-rc.d: initscript nginx, action "start" failed.  dpkg: error processing package nginx-full (--configure):  subprocess installed post-installation script returned error exit status 1 dpkg: dependency problems prevent configuration of nginx-full-dbg:  nginx-full-dbg depends on nginx-full (= 1.10.0-0ubuntu0.16.04.1); however:   Package nginx-full is not configured yet.  dpkg: error processing package nginx-full-dbg (--configure):   dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                            Errors were encountered while processing:  nginx-full   nginx-full-dbg  E: Sub-process /usr/bin/dpkg returned an error code (1) Information on month old flights Where can I get flight info for a flight a month ago for an insurance claim? Flight stat sites will only show a weeks worth of data.