So, I would like to ask those of you who have had this experience for some advice.   What book is best for GRE subject exam? I have noticed that some books online have mistakes, so I would like if you can give me specific publisher for GRE subject exam in physics book. I would appreciate any advice on how to prepare for it. How to get best out of my studying period?
Every once in a while, we get a question asking for a book or other educational reference on a particular topic at a particular level. This is a meta-question that collects all those links together. If you're looking for book recommendations, this is probably the place to start.  All the questions linked below, as well as others which deal with more specialized books, can be found under the tag  (formerly ).  If you have a question to add, please edit it in. However, make sure of a few things first:   The question should be tagged  It should be of the form "What are good books to learn/study [subject] at [level]?" It shouldn't duplicate a topic and level that's already on the list   Related Meta:
python3 is not supporting gtk module Why Was It 'Essential' That Voldemort Kill Harry Potter? I would like to configure my Ubuntu 12.04 server to synchronize its clock with a specific NTP server. Where to set this up? How to draw neat polygons around scatterplot regions in ggplot2 How does one check what websites a person logs into using their Google account? Most of us have seen on the profile page a loss of reputation citing as a reason "User was removed". This reason comes with the useful link:  which explains (emphasis mine):     This message means that a user who voted for one of your posts had their account deleted (either by request or due to violating the network's terms of service). As a result, all of their votes were removed, and the reputation you gained or lost from them was undone. The resultant reputation change could be any amount; it could even be a reputation gain if enough of the removed votes were downvotes. All the reputation changes from a single user's deletion are rolled into a single event in the reputation page labelled "User was removed".      This removal occurs whenever a user is deleted, unless that user had a very high reputation score. Because high-reputation users have usually cast a great many votes, removing all of them could be that much more disruptive to other users. In such cases, the staff use a special deletion that preserves the votes, resulting in no reputation change for those who had been voted on by that user.   However, I have got recently such a message on one of beta sites, where I have no posts. Here is  on that site. As you can see, I have only got points from association bonus,  and the last event in my reputation history is the reputation loss with the message 'User was removed'. (Notice that the post, where I made suggested edit, was not deleted. And the users who approved the posts are Community♦ and one another user, who did not delete their account.)  You can also see from  on that particular site that I have posted no questions/answers there so far. Which means there are no votes on my posts which could have been removed.     Why this did happen? How can I lose reputation points in this way if I have never made a post on that site?   I am not sure if this is a . (Feel free to remove the tag if it does not fit the question.) (EDIT: The answer and the comments posted so far indicate, that it is not a bug, so I have removed the tag from the question.) But if there is some reason why reputation posts can be lost even without having some posts and actual votes on the posts, then the description of "User was removed" seems to be a bit imprecise. (Of course, if it is a very rare edge case, it is probably not that important to have it included in the explanation.)    Just a short disclaimer: I do not care that much for the 2 points I lost. (Obviously, it would be very silly to make a fuss just for 2 points, and even more on a site which I do not frequent that much.) But if this could be indication of some hidden bug, it might be interesting to know more about this.    I have also noticed two related questions       In both cases in some answers or in comments as a possible explanation was given that probably a post, where a suggested edit was made, has been deleted. As you can see from the links I, this is not the case here. How can I take screenshots of YouTube videos in full screen? If a student needs a reference letter for graduate admissions or that sort of thing, some profs will ask the student to write a reference letter for themself before sending it off to the prof for minor edits and finalization. This seems to be a somewhat common practice given that some graduate schools ask for several letters of recommendation even when it is not reasonable for the student to have developed deep connections with that many professors, and that most professors are just too busy to write quality letters for all the students that ask them to.  Is it acceptable to write most of the reference letter and have the prof make minor edits? Do academic institutions frown upon this practice? Would it be considered an academic offense if a student wrote a reference letter for themselves and had a prof sign it? If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$. Having some trouble proving this:     If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show: $\lim _{x\to \infty } (f(x+1)-f(x))=0$   Attempt: from $\int \lim _{x\rightarrow \infty } f^\prime(x) \mathrm{d}x=0$ we can say that $f^\prime(x)=const$ would we then have to show that  $\lim _{x\to \infty } (f(x+1))$ is also a constant? From there if we show that both are equal then the difference is zero. I am on the right track?  Thank you for the help. Cooking steak in frying pan, problem with oil splatter I was using canola oil and put the stove top setting on "high - 9". I read plenty of guides suggesting there will infact be oil splatter, but it was pretty excessive and burning my arm with one drop getting near my eye before I stopped. I turned the heat setting down to "medium - 4", where the oil splatter seemed to drop substantially. Before I try to make steak again I'd like to get some clarification  So my questions are:   Which heat setting am I supposed to use? Is that type of oil splatter normal or should I try using a different oil, and if so, what oil? Should oiling the meat instead of the pan help the problem? Software for measuring internet traffic? I'm interested in finding a free piece of software for Windows XP &amp; 7 that allows us to measure both incoming and outgoing internet traffic, but not traffic between users of the local network.  I live in a shared household with three others, and we're interested to see which of us is using the largest amount of our monthly internet quota. We're all happy to install the necessary software.  Any suggestions? Is anti-gravity (i.e. repulsive gravity) possible in theoretical physics? Is  (i.e. repulsive gravity) possible in string theory?  I have read some articles about scientists making assumptions about the existence of anti-gravity, but is it possible in string theory? How do I create a Windows 7 USB installer with preinstalled software? I was wondering if it was possible to make a bootlable image of a Windows 7 Pro OEM Installation CD that I have and put it on an USB stick for faster/easier installation. I am asking because we have a couple of PC´s where I´d have to install the OS using the same key (MAK).  Also is it possible to kind of populate that image with software that would have to be installed anyways on all machines (like Chrome, Outlook, etc)?  It would be really helpful to just install a Windows 7 image with customized software already installed. I would just make an image of an OS and use that, but the hardware of the machines differ. $ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form] I came across this theorem:   For all integers a,b,c and m&gt;0, if d = GCD(c,m) then a*c ≡ b*c (mod m) iff a ≡ b (mod m/d).  The =&gt;proof states this:  a*c ≡ b*c (mod m) =&gt; m|(a-b)*c                    =&gt; m/d | (a-b)*c/d                   =&gt; m/d | (a-b)                   =&gt; a ≡ b (mod m/d)   I don't understand how to go from step 2 to step 3. The proof states that this is possible because m/d and c/d are coprime. To me this means GCD(m/d, c/d) = 1 but how does this cancel out the whole term? Normalization of basis vectors with a continuous index? I have an infinite basis which associates with each point, $x$, on the $x$-axis, a basis vector $|x\rangle$ such that the matrix of $|x\rangle$ is full of zeroes and a one by the $x^{\mathrm{th}}$ element. The book on Quantum Mechanics by Shankar says that the inner product between a basis vector and itself is not one, why not? Why can't these basis vectors be normalized to one, only to the ? Maximize $\mathrm{tr}(Q^TCQ)$ subject to $Q^TQ=I$ Let $C \in \mathbb{R}^{d \times d}$ be symmetric, and   $$Q = \begin{bmatrix}       \vert &amp; \vert &amp;    &amp; \vert \\       q_1   &amp; q_2   &amp; \dots &amp; q_K  \\       \vert &amp; \vert &amp;    &amp; \vert       \end{bmatrix} \in \mathbb{R}^{d\times K}$$  where $d \geq K$. Using Lagrange multipliers,   $$\begin{array}{ll} \text{maximize} &amp; \mbox{tr} \left( Q^T C Q \right)\\ \text{subject to} &amp; Q^T Q = I\end{array}$$    I am unfamiliar with these kind of constraints with this method, and after reading  I believe the same specific and simple result given is also applicable, and therefore the lagrangian would be:  $$\mathcal{L}(Q,\lambda)=\mathrm{tr}(Q^TCQ)-\left&lt;\lambda,Q^TQ-I\right&gt;$$  where $\lambda\in\mathbb{R}^{K\times K}$, and $\left&lt;\cdot,\cdot\right&gt;$ is the element wise inner product (what kind of makes sense to me since we're actually adding as many constraints as there are elements in these matrices.  In attempting to do that I start taking $\frac{\partial \mathcal{L}}{\partial Q}=O\in\mathbb{R}^{d\times K}$, and compute that LHS element by element; for the $(l,m)$ one:  \begin{equation} 0=\frac{\partial \mathcal{L}}{\partial Q_{lm}}=(CQ+C^TQ)_{lm}-\underbrace{\frac{\partial}{\partial Q_{lm}}\sum_{i,j}\lambda_{i,j}(Q^TQ-I)_{ij}}_{=\lambda_{lm}\frac{\partial (Q^TQ)_{lm}}{\partial Q_{lm}}}=2(CQ)_{lm}-\lambda_{lm}\frac{\partial (q_l^Tq_m)}{\partial q_m(l)} \tag{1}\end{equation}  where in the last step I've used the definition I made at the beginning for $Q$, and $q_m(l)$ denotes the $l$-th component of the column vector $q_m$.  In trying to compute the very last term:  $$\frac{\partial (q_l^Tq_m)}{\partial q_m(l)}=\frac{\partial \left[q_l(1)q_m(1)+ \ldots + q_l(d)q_m(d)\right]}{\partial q_m(l)}= \begin{cases}     q_l(l)\equiv Q_{ll}    &amp; \text{if } l\neq m\\     2q_l(l)\equiv 2Q_{ll}  &amp; \text{if} l=m \end{cases}$$  The whole equality (1) then can be written:  $$0=2(CQ)_{lm}-\lambda_{lm}Q_{ll}(1+\delta_{lm})$$  where $\delta_{lm}$ is the Kronecker delta.  The equation for the other stationary point of the lagrangian, $\frac{\partial \mathcal{L}}{\partial \lambda}=O\in\mathbb{R}^{K\times K}$, for the $(l,m)$ element as well:  $$ 0=\frac{\partial \mathcal L}{\partial \lambda_{lm}}= \frac{\partial }{\partial \lambda_{lm}}\sum_{i,j}\lambda_{i,j}(Q^TQ-I)_{ij}=(Q^TQ-I)_{lm}\tag{2}$$  what obviously leads to $(Q^TQ)_{lm}=\delta_{lm}$.  All this should tell that the columns of $Q$ are eventually the $K$ first eigenvectors of $C$, but I don't know how to continue from here to prove that, supposing I didn't make a mistake. Please I would sincerely appreciate any help.    Edit:  I have rewritten the inner product as a trace of a product of matrices (after seeing ):  $$\left&lt;\lambda,Q^TQ-I\right&gt;=\sum_{i,j}\lambda_{i,j}(Q^TQ-I)_{ij}=\mathrm{tr}(\lambda^TQ^TQ) $$  and have thus managed to do the derivative without losing the matrix format (using formulas from the ):  \begin{align} O=&amp;\frac{\partial \mathcal{L}}{\partial Q}=\frac{\partial}{\partial Q}\mathrm{tr}(Q^TCQ)-\frac{\partial}{\partial Q}\underbrace{\mathrm{tr}(\lambda^T(Q^TQ-I))}_{\mathrm{tr}(\lambda^TQ^TQ)-\mathrm{tr}(\lambda^T)}\\=&amp;(CQ+C^TQ)-(Q(\lambda^T)^T+Q\lambda^T)=2CQ+Q(\lambda+\lambda^T) \end{align}  And this leads to:  $$CQ=Q\underbrace{\left(-\frac{\lambda+\lambda^T}{2}\right)}_{:=\widetilde{\lambda}};\quad CQ=Q$$  If the defined matrix $\widetilde{\lambda}=Q^TCQ$ were diagonal we would already have the result. When would you use the Builder Pattern? What are some common, real world examples of using the Builder Pattern?  What does it buy you?  Why not just use a Factory Pattern? "Thanks for having me" Recently, I finished my phone job interview with the phrase "Thanks for having me". It was a reply to the other person's "Thank you for your time". So, does "thanks for having me" sound alright in this context? How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments? biblatex and autonum don't work together biblatex and autonum don't seem to work together in the newest version. Consider the following MWE:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[backend=biber]{biblatex} \usepackage{autonum}  \begin{document}  \end{document}   I get the following error messages:  0 File ended while scanning use of \ettl@for@do1 0 pdflatex: \pdfmatch: repetition-operator operand invalid pdfTeX warning: pdflatex: \pdfmatch: repetition-operator operand invalid)Runaway argument?{{\blx@bibdata@i {\blx@tempb }}\blx@bibfiles \eappto \blx@tempa {\blx@xml@comme   After commenting out either biblatex or autonum, the errors disappear.