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Mathematical physics text with plenty of applications I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those texts focused on the math methods useful for physicists and assumed the applications of those methods would be covered in some other text. What I'm looking for is a book which introduces some math and then looks at its applications (back and forth) rather than a text which just goes over some math. (Example of books which are NOT what I'm looking for: Mathematics for physicists by Dennery, Math methods for physicists by Weber and Arfken etc)  I've taken courses in multi-variable calc, linear algebra, real analysis, and I'm currently taking a course in abstract algebra. But so far I've only seen applications of multi-variable to physics. I'm looking for books which look at the applications of the other subjects mentioned above to physics, of course books which cover subjects beyond those mentioned are also welcome.   So far I'm liking the flavor of the text "A Course in Modern Mathematical Physics" by Szekeres, but I'd prefer a text which got to the physics side of things more quickly (in the Szekeres text the first eight chapters are strictly on pure math).   After some amazon searching it looks like Theoretical Physics by Joos, Mathematical Physics by Henzel, and Physical Mathematics by Cahill may be good bets? Add an image directly from the clipboard I've tried to find other questions covering this, but (surprisingly) I did not find any.  When I want to add a screenshot to a post, as far I know the only way to do it is to save it as a file and then upload the file, using Stack Overflow's image hosting. OK, much better than finding a hosting site yourself, but sometimes I wish I could just paste the image from the clipboard.  It's not as straightforward as it may seem, I know. , and it needs a Java applet to get it done. How does Loki survive his fall at the end of Thor? In one of the concluding scenes of the movie Thor, it's shown that Loki deliberately let go of the Scepter, and falls deep into the vast intergalactic sea sort of thing. How does he survive and return in The Avengers? I'm code reviewing a change one of my co-workers just did, and he added a bunch of calls to Date.toMonth(), Date.toYear() and other deprecated Date methods.  All these methods were deprecated in JDK 1.1, but he insists that it's ok to use them because they haven't gone away yet (we're using JDK 1.5) and I'm saying they might go away any day now and he should use Calendar methods.  Has Sun/Oracle actually said when these things are going away, or does @deprecated just mean you lose style points? linebreak in description title How does LSTM prevent the vanishing gradient problem? LSTM was invented specifically to avoid the vanishing gradient problem. It is supposed to do that with the Constant Error Carousel (CEC), which on the diagram below (from ) correspond to the loop around cell.  (source: ) And I understand that that part can be seen as a sort of identity function, so the derivative is one and the gradient stays constant. What I don't understand is how it does not vanish due to the other activation functions ? The input, output and forget gates use a sigmoid, which derivative is at most 0.25, and g and h were traditionally tanh. How does backpropagating through those not make the gradient vanish ? Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain I want to show that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw)\subset\mathbb{A}^4$, is not a unique factorization domain.    Morally, all we need to do is find some nonzero element that can be written in two distinct ways as a product of irreducible elements, but nothing is coming to mind immediately. Thoughts? Horizontal line inside a matrix I tried to make a horizontal line inside a matrix by the attached code. However, it didnot work the compiling process gives a time out message. It work normally without the \hline command. Any help!  \documentclass[journal,draftcls,onecolumn,12pt,twoside]{IEEEtran} \usepackage{array} \usepackage{blkarray} \begin{document} \begin{equation}  \centering W_b(1)=\begin{blockarray}{cccccc} \begin{block}{(ccccc)c}  a      &amp; b     &amp;     &amp;  &amp;  &amp; \matindex{\leftarrow d=0} \\ \ddots &amp; \ddots&amp;     &amp;  &amp;  &amp; \matindex{\vdots} \\    &amp;     a &amp; b   &amp;  &amp;  &amp; \matindex{\ \ \ \   \leftarrow d=d_b-1} \\   %\hline  c      &amp; d     &amp;     &amp;  &amp;  &amp; \matindex{\leftarrow d=d_b} \\   \ddots &amp;\ddots &amp;     &amp;  &amp;  &amp; \matindex{\vdots} \\    &amp;   c   &amp;  d  &amp;  &amp;  &amp; \matindex{\leftarrow d=D}  \end{block} \end{blockarray}, \label{eq:eq4}  \end{equation}  \end{document} How can I change pdf page size? I would like to split pages in pdf so that each page would be divided into 2 pages ( e.g. form 100 pages I would go into 200 but smaller - exactly half size).  I need this to read pdfs on my ebook reader.  Anybody knows how can this be done ? Looking for succinct way of describing the act of solidifying an idea into reality Looking for a succinct way of describing the act of solidifying an idea into reality. "Building [idea] out" seems too generic but I'm trying to avoid a long winded, step by step explanation of the process.  Any ideas would be greatly appreciated. Thanks! Finding square root without using sqrt function? Noticing that the "Human Verification" image did not show, I found that the src, , shows that sstatic.net is giving an SSL vertificate for *.stackexchange.com.. If I have flagged a post, show me a "flags" link in my profile This was a question from my textbook. This is how I approached it.   For the first part, you can do c(10,5) so you choose 5 of the 10 to be on a team.   For the second part, you have 10 ways to choose the "best player" and you multiply it by c(10,4) to pick the other 4 players. However, I am not sure how you can exclude the "worst player". Although this sounds subjective, I believe the question is saying that the "best" and "worst" players are distinct, whereas the other players aren't. Words for "a bit sad" and "a bit happy"? Why is it true that "I before E, except after C"? Difference between "speed up something" and "speed something up" Both seem to be in common usage, but is there a nuanced difference about when one is more appropriate than the other? Thanks. Why does the order of parameters matter for sp_trace_create? solving third-order nonlinear ordinary differential equation set 4-bit nibble in an int type