I have completed my undergraduate (bachelor's of engineering) degree. I am looking to go for a masters, but I lack some prerequisite math courses on my transcript. Is there a way to get credited math courses (like stochastic calculus, probabilistic theory, etc.)? I am from India, planning on applying mainly to european institutes. I have done good number of mathematical courses. But, lack only 2 courses for fulfilling the prerequisite. My planned universities dont have a pre master that I know of. Note: The most important part is being able to get the credits and transcript. As I cannot share just a certificate. I havent been accepted. I need to complete the courses to meet the prerequisite for my application.
Background I was ignorant as an undergraduate and didn't focus heavily in any specific area. I finally graduated with a single math/computer science degree that consisted of 5 math classes beyond multivariable calculus and a few relatively basic computer science classes (algorithm analysis, SQL database design, etc.). My only research experience is in economics. Now, I work at a research institution in economics where I primarily write Stata/MATLAB code. Question I'd like to get more mathematics under my belt over the next few years in order to either enroll in a PhD program in economics/finance or a M.S. program in finance. What are my options for getting more math experience that I can use in graduate school admissions? Options These are the options I thought of so far, but I would like to know more if possible.  Study enough courses through a system like Open CourseWare to gain enough experience to enroll in more advanced undergraduate classes part time, which my employer might pay for, and then ideally move into an M.S. program in applied math.  Return to my alma mater for a M.S. degree in math that would at least give me a basis to either move into another math graduate program with higher rankings or a lower-ranked graduate program in the fields of my choice.  Join the Air Force and hopefully take advantage of the GI bill to take more courses somewhere and gain entrance into an M.S. program in applied math.  (Sadly) Forgo advanced mathematics and find a consulting job, which although unpleasant in the field of economics (in my opinion), wouldn't be difficult to obtain given my research background in the field.   Do I have any other options? I also plan to take the GRE subject test in mathematics to prove that I have at least minimal knowledge, regardless of what course I pursue (since many graduate programs will require it).
Polygon label repeated for each tile Show a message if directly accessing a deleted answer or comment Currently, if you access a deleted question you will get a short message informing you that the question has been deleted. However, if you click on a direct link to a deleted answer or comment (which you can get via notifications), nothing is displayed.  This is naturally quite confusing as you will get the message about a new answer or comment via notifications, click on the link and simply see nothing.  Therefore, I propose to display some sort of message to the user, informing her/him that the answer or question has been deleted. Note that this is different from always showing a deleted answer/comment, as I specifically request it in case you access the specific URL.  One example for a comment would be:   One example for a deleted answer is:   This question is related to ,  but requests a feature to circumvent the problem altogether. Let's consider two statements: Zorn's lemma and theorem about existence of maximal ideals in commutative ring with $1$.  It's easy to prove that Zorn's lemma implies existence of maximal ideals.  I wonder if the converse proposition is true, i. e., does existence of maximal ideals implies Zorn's lemma? My approach was to construct a ring structure on an ordered set which satisfies Zorn's lemma condition such that existence of maximal ideal implies existence of maximal element in the set, but I didn't succeed. The following is the first part of Proposition 2.9 in "Introduction to Commutative Algebra" by Atiyah &amp; Macdonald.     Let $A$ be a commutative ring with $1$. Let $$M' \overset{u}{\longrightarrow}M\overset{v}{\longrightarrow}M''\longrightarrow  0\tag{1} $$ be sequence of $A$-modules and homomorphisms. Then the sequence (1) is exact if and only if for all $A$-modules $N$, the   sequence  $$0\longrightarrow \operatorname{Hom}(M'', N)  \overset{\overline{v}}{\longrightarrow}\operatorname{Hom}(M,  N)\overset{\overline{u}}{\longrightarrow}\operatorname{Hom}(M', N)  \tag{2} $$ is exact.   Here, $\overline{v}$ is the map defined by $\overline{v}(f)=f\circ v$ for every $f\in\operatorname{Hom}(M'', N)$ and $\overline{u}$ is defined likewise.   The proof one of direction, namely $(2)\Rightarrow (1)$ is given in the book, which I am having some trouble understanding. So assuming (2) is exact sequence, the authors remark that "since $\overline{v}$ is injective for all $N$, it follows that $v$ is surjective". Could someone explain why this follows?  Given that $\overline{v}$ is injective, we know that whenever $f(v(x))=g(v(x))$ for all $x\in M$, we have $f=g$. I am not sure how we conclude from this surjectivity of $v$.  Thanks! Let $M$ be the space of all $m\times n$ matrices. And $C=\{X\in M|rank(X)\leq k\}$ where $k\leq \min\{m,n\}$. How to proof that C is a closed subset of M? What are the differences between "su", "sudo -s", "sudo -i", "sudo su"? I've been using SSH Tunnel manager to easily set up and stop port tunneling over SSH to various servers at my company. That saved me the pain of opening up a new terminal window which will hang out there just for the sake of having a tunnel open.  This worked great (well , sort of) but SSH Tunnel Manager is a PowerPC application. With Lion, it is not supported any more.  What is a good replacement? I understand that they force you to implement methods and such but what I cant understand is why you would want to use them. Can anybody give me a good example or explanation on why I would want to implement this. Command to display and execute code (math formulae) Similar to  I would like to have a command to display and execute code. The code should be displayed with the listings package.  For example something like  \documentclass{scrartcl} \usepackage{amsmath,listings} \newcommand*{\codeExample}[1]{Code: \lstinline!\string{#1}! yields #1} \begin{document}   \codeExample{$\lVert a\rVert$} \end{document}   should for best of cases display $\lVert a \rVert$ as verbatim (\lstinline!...!) code and after that the rendered math code. Is something like that possible? The code above yields several mistakes. I think I miss something to avoid #1 being tokenised? I've got a couple of URL autocomplete suggestions where Chrome suggests the wrong URL consistently.   How can I delete the incorrect entry from the address bar's suggestion list? The page I want shows up too but it's never the first result. How to use the symbol \angle at the section title Disable chat migration notification if one of the users has insufficient rep? Simple request, really.  Can we add a detection for the     Please avoid extended discussions in   comments. Would you like to   automatically move this discussion to   chat?   prompt, so that if one of the users in the "extended discussion" has under 20 rep it doesn't appear?  I think a lot of the users this apply to will have low rep and it may take some back and forth to get good info out of them.  New suggestion: how about if a sufficiently high-rep user is clicking on the link, the low-rep user gets a field promotion sufficient to chat? Low-rep users are particularly prone to post questions to lead in this direction of needing to move to chat. Suppose we have a set  $S=\{a,b\}.$ Obviously, the total number of binary operations on $S$ is the number of all the pairs such that $$*(a,b)=a \, \text{or}  \, b,$$ which gives  $ 2 \cdot 2 \cdot 2 \cdot 2=2^4$ possible ones. Is there a way to find which of these $16$ binary operations are associative without writing all the operation matrices and checking it by hand? Why is a finite integral domain always field? This is how I'm approaching it: let $R$ be a finite integral domain and I'm trying to show every element in $R$ has an inverse:   let $R-\{0\}=\{x_1,x_2,\ldots,x_k\}$,  then as $R$ is closed under multiplication $\prod_{n=1}^k\ x_i=x_j$,  therefore by canceling $x_j$ we get $x_1x_2\cdots x_{j-1}x_{j+1}\cdots x_k=1 $,  by commuting any of these elements to the front we find an inverse for first term, e.g. for $x_m$ we have $x_m(x_1\cdots x_{m-1}x_{m+1}\cdots x_{j-1}x_{j+1}\cdots x_k)=1$, where $(x_m)^{-1}=x_1\cdots x_{m-1}x_{m+1}\cdots x_{j-1}x_{j+1}\cdots x_k$.   As far as I can see this is correct, so we have found inverses for all $x_i\in R$ apart from $x_j$ if I am right so far. How would we find $(x_{j})^{-1}$? @class vs. #import It is to my understanding that one should use a forward-class declaration in the event ClassA needs to include a ClassB header, and ClassB needs to include a ClassA header to avoid any circular inclusions. I also understand that an #import is a simple ifndef so that an include only happens once.  My inquiry is this: When does one use #import and when does one use @class? Sometimes if I use a @class declaration, I see a common compiler warning such as the following:     warning: receiver 'FooController' is a forward class and corresponding @interface may not exist.   Would really love to understand this, versus just removing the @class forward-declaration and throwing an #import in to silence the warnings the compiler is giving me. How to use enum values in f:selectItem(s) When —the bartender at the Cantina at Mos Eisley spaceport in the first Star Wars—says:     “We don’t serve their kind here.”   In reference to C-3PO and R2-D2 entering the bar, it’s certainly a bit prejudicial, but are these commonly held views in this universe? We don’t see it happen anywhere else in the films but is it implied elsewhere? True Ubuntu on Chromebook ARM "A/An" preceding a parenthetical statement When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an) I read it in English in the United States, somewhere in the 1990s. I got it off of the big bookshelf in our family room, which means it could be a good bit older; some of the books were my Dad's. At the beginning, a young boy (maybe an early teen?) leaves his house, where he lives with his parent or parents, and takes a test to become a spaceship pilot for the military. Part of the test judges reaction speed, and he fails the test. He later learns (I think when he's approached by an agent of the government) that he "failed" because he has some sort of enhanced fortune that meant that he was actually giving the results before they could be displayed on the screen. At the time, I remember thinking that the book felt a bit like a Star Wars rip-off.  Years later, I read that one of the Star Wars books (probably now Legends) had Luke similarly failing the Imperial Academy test because he gave his answers too quickly, and it amused me that I was uncertain as to which had come first.  I don't remember anything concrete about the cover, although I have a general impression that it was white. Definitely futuristic. My impression was that the boy was wearing a white uniform for the testing and that the government agent who spoke to him had a grey beard, but I might be mixing bits of Star Wars in there.