Is it possible to do a phd in computer science with an undergraduate degree in electrical engineering?
Graduate school admission with a degree in a different field
Verb/Subject Agreement Make/Makes Show a connected metric space (X,d) is $\epsilon$-chainable for $\epsilon &gt;0$       $\epsilon$-chainable Definition      (X,d) is $\epsilon$-chainable if given any two points $a,b \in X$, $\exists$ a finite set $\{ x_0,x_1,...,x_n\}$ of points in X with $x_0 = a$, $x_n=b$ and $d(x_{n-1},x_n)&lt;\epsilon$, $\forall$ n      Clopen Definition      A set is clopen $iff$ its boundary is empty      Connected Metric Definition      Let $(X,d)$ be a metric space. It is connected $iff$ it has no proper subsets which are clopen      The following are equivalent:         $X$ is connected   The only subsets of $X$ that are clopen are $\emptyset$ and $X$   $\nexists$ non-empty, disjoint, open sets $A$ and $B$ such that $X=A\bigcup B$   $\nexists$ non-empty, disjoint, closed sets $A$ and $B$ such that $X=A\bigcup B$         Theorem      Let $(X,d)$ be a metric space, and let $S$ be any subset of $X$. Then $S$ is closed $iff$ $S^c$ is open.     So how would someone show this exactly?  Let the set $A$ be the set of all elements in $(X,d)$ that can be reached from $a\in X$ in a finite number of steps with length less than $\epsilon$.  Does this mean that there should be no isolated points? (an isolated point would be at distance infinity from any other point, or distance zero from itself, since $\epsilon &gt;0$ we don't want this?)  Knowing that $X$ is connected $\implies$the only subsets of X that are clopen are $\emptyset$ and $X$  Also, by construction of A;   A is the set of all $\epsilon$-chains between any element and $a$  And, so $A^c = \emptyset$ if $A$ was $\epsilon$-chainable (because A has to have a path from all elements to a, for this to be true, the complement wouldn't have anything in it)  Leaving only $A$ as the remaining clopen set  Does this make any sense? Or should an alternative be used, and how to formalize it.  Thanks. Discoveryd Alternative to Replace mDNSResponder Argument? This is a direct follow-on to . , I'd add the "-AlwaysAppendSearchDomains" argument to the mDNSResponder plist file so that all local resolver lookups added the search domains, regardless of whether there was a period in the label to be looked up. For example, whether I try to ssh to hostname foo.bar or foo, the search domain of baz.com should be tried, not only for the latter case, as was (and is) the default behavior.   Now, it looks like the mDNSResponder is gone, replaced with discoveryd. I cannot find a similar option to get it to always appending the search domain. Suggestions? I'd rather not go the route of using a non-default local resolver, but I'd consider it as an option. For now, I'll just type in the long FQDNs, but I'd really rather not.  Thanks, Pete When looking at my objects in 3d view I'm seeing a gray cone that seems to be hiding other objects.   Can anyone help me turn this off and explain what it is please.  Screenshots attached. How to handle fragmentation of auto_increment ID column in MySQL Should "move-to-chat" be provided on demand (as a button perhaps)? What is a loss function in decision theory? My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to errors? I am starting to learn some Regex, therefore I use this command repeatedly:  grep pattern /usr/share/dict/american-english    Only the part with pattern changes, so I have to write the long expression "/usr/share/dict/american-english" again and again.   Someone made the remark that it is possible to expand an argument of a command from the command history by typing cryptic character combinations instead of the full expression.  Could you tell me those cryptic character combinations ? 20GB of Temporary Files, Only 50MB in Temp Folder I recently discovered that the Settings app is showing around 20GB of space used by temporary files. But when I go to remove them I can only remove about 28MB. When I open the temp folder by using Run and then %temp% it only shows around 40-50MB of files right after boot. How can I remove these 20GB of invisible files? I only have a 240GB SSD so space is quite scarce. Here are a few photos:    I run Windows 10 Home Activated. I have tried Disk Cleanup but this removed only around 30MB of files.  UPDATE: After turning on hidden items I found a folder name WINDOWS-BT, after doing some research it turned out to be a folder for the previous windows version. I deleted it using TakeOwnerShip pro and this removed around 12GB of temporary files, but 8GB still remain. I am currently downloading TreeSize free to find out where the other 8GB is.  UPDATE 2: Hi, I downloaded TreeSizeFree and I didn't really find anything there.   The biggest folder is 87GB of Program Files which mainly consists of my GTA V install. The Program Files (x86) folder was mainly made up of my Steam games (CS:GO, Besiege, etc). The 5.5GB [3 Files] location was noted as being my pagefile.    The Windows folder shows up as 25GB when in Settings it is only 18GB, this could explain where the other 8GB are coming from. What are some things I should look for in there?  FINAL UPDATE: After deleting the Windows-BT folder it reappeared a few hours later. I decided to check from system updates and surely enough one was downloaded and pending to be installed. After installing the update the Windows-BT folder disappeared on it's own and a new folder taking up 20GB called Windows.old was created. I then followed this  to remove the .old folder and I had all my disk space back! NOTE: Disk Cleanup wasn't able to find the Windows.old folder, this is why I had to delete it from the settings app. When should we use proximity rule in "either/or", and "neither/nor"? Why should events in C# take (sender, EventArgs)? It's known that you should declare events that take as parameters (object sender, EventArgs args). Why? Does the lack of sleep affect my health? In the past month, I've been really busy with the university and stuff, and I don't sleep as much as I used to. I usually sleep 4-5 hours a night.  I haven't been doing that extensively ( I always kept a good sleeping routine), but can the lack of sleep affect my health on the long term ? Is your MAC address revealed when you hit up a website? Given two functions $f$ and $g$, is there a formula for the Fourier transform of $f \circ g$ in terms of the Fourier transforms of $f$ and $g$ individually?  I know you can do this for the sum, the product and the convolution of two functions. But I haven't seen a formula for the composition of two functions. Usage of :- (colon dash) in bash Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule] I am working on a problem I am pretty close to solving but I can't figure out the last part. I used some algebraic manipluation to break the problem down. The problem is:     Show that the following congruence is true      a^b = ((a mod n)^b) (mod n)      for any positive integers a, b, and n.      Hint: Number a can be written as a = q*n + r, where q = floor brackets a/n, and r = a mod n.   My attempt it:     (q*n +r)^b = ((a mod n)^b) * (mod n)      (q*n)^b + (a mod n)^b = ((a mod n) ^b) * (mod n)      (a)^b -(r)^b = ((a mod n) ^b) * (mod n)      (a)^b = modn  ----> divided by ((a mod n)^b)   Am I doing this correctly and if so how can I prove this is true? Is there a trick I am missing? I think that by simplifying it further I would just keep going in a loop.  Thanks! How to make sure an application keeps running on Linux I'm trying to ensure a script remains running on a development server. It collates stats and provides a web service so it's supposed to persist, yet a few times a day, it dies off for unknown reasons. When we notice we just launch it again, but it's a pain in the rear and some users don't have permission (or the knowhow) to launch it up.  The programmer in me wants to spend a few hours getting to the bottom of the problem but the busy person in me thinks there must be an easy way to detect if an app is not running, and launch it again.  I know I could cron-script ps through grep:  ps -A | grep appname   But again, that's another hour of my life wasted on doing something that must already exist... Is there not a pre-made app that I can pass an executable (optionally with arguments) and that will keep a process running indefinitely?  In case it makes any difference, it's Ubuntu. Keep only essential packages How do I integrate the following $$\int \frac{dx}{\sin^3 x + \cos^3 x}$$ ?  It appears that I am supposed to break this up into $(\sin x + \cos x)(1-\cos x \sin x)$, but the next thing to do is not apparent to me. Is there a \subsubsubsection command? I could do \subsection{} and \subsubsection{} but not \subsubsubsection{}. This command does not seem to be available in LaTeX. Is there an alternative command?