I find a good books for number theory...  An Introduction to the Theory of Numbers (by G.H hardy)or Burton, Rosen..etc  is it good?? (i want a book which best of best in number theory)  i want a lot of theorm and background. etc.  (level is under~~graduate)
Books on Number Theory for anyone who loves Mathematics?(Beginner to Advanced &amp; just for someone who has a basic grasp of math)
I know cell phone cameras are the lowest rung, but when reading reviews of phones, the reviewers always have sample shots that are much better than what I can manage.  What are some ways to take decent shots with a cell phone camera?  (I'm thinking of the higher end Android or iPhone cameras). Rigorously proving equal tension on both ends There is always one point in introductory mechanics that has been continuously bothering me ever since I had taken my freshman physics course - Why does a massless rope have its tension equal on both ends?  I have been searching for a good explanation on various textbooks at different levels, but none of them provided me a satisfactory explanation. They either   State directly "we assume the string is massless and the pulley has no friction, therefore the tension must be the same throughout the string" without further any elaboration and continue the calculation, Claim without any reasons that "whenever the rope and the pulley are massless and frictionless, the tension will be the same on both sides", or Explain using a lot of hand-waving arguments regarding infinite acceleration, non-zero moment of inertia, etc. , in one line or two.   Although those hand-waving arguments of type $(3)$ do sound quite reasonable to me and will convince me for a while every time I review them. But after a while, I will start feeling not well about this whole tension concept again.  Therefore, I am looking for a rigorous (in the physicist's sense) proof of exactly why and when do the tension in rope will be uniform, and hopefully from that I can clean up all of my conceptual difficulties. no border around hyperlinks with hyperref Subrings of integral domains have the same identity element. If $R$ is an integral domain and a subring $S$ has identity $1_S$, how would you show that $1_S=1_R$ (here $1_R$ is the identity of the ring $R$)? I am unsure about what an integral domain really is and how the subring comes into play here. Why does the Euclidean algorithm work for polynomials? What is the proof? Suppose I know that I can find the $\gcd$ of two integers with the Euclidean algorithm. What is the 'extension' so I can use this method also for polynomials?  Edit: I found an easy answer with less rigor which is approachable without knowledge of matrices:    also the first 3 subchapters of Virtualbox Kernel driver not installed Visiting USA as a German with Iranian parents The screenshot below says it all, really. The object is offset in both the X and the Z axes, though only the X axis says 1. No other modifiers are on it, no constraints, no locked axes, and I can't think of anything else that would affect this. How can I make it stop doing this? Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields I am trying to solve the following problem:     For each rational prime $p$, describe the decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields, where $\mathbb{Q}_p$ is the field of $p$-adic numbers.    I know that the tensor product of $2$ extensions of a field one of which is finite is Artinian and is therefore a product of Artinian local rings, but I do not know how to compute these Artinian local rings. Please if you can help me with this, I'll really appreciate it. When I create a UV sphere and add the subdivision surface modifier, the following wrinkle appears.    How can I avoid it?  I've read the article  but there seems to be no clear solution.  UPDATE 1  I've used the word 'apply' in the first sentence of the initial version of this question. It's misleading since I want to preserve the modifier without 'applying' it. Rather, what I meant is 'adding' the modifier.  UPDATE 2  I followed josh sanfelici's solution, but still there is an artifact at the pole.  Here is the screen: (A rendered view with a sun lamp)    Maybe it's the limitation of the general-purpose subdivision modifier.  BTW, when the cast modifier is added after the subdivision modifier, the sphere becomes perfect (even for my original wrinkled sphere).  But since I want to edit the resulting sphere (for example, scaling X, Y, etc) while modifier is added but not applied, it's not usable. 16.04 VirtualBox VM (from vhd file) hangs at "non blocking pool is initialized" I'm trying to boot Canonical's Azure 16.04 .vhd file in a VirtualBox VM and it hangs at "non blocking pool is initialized".  It works in Hyper-V, so it may only be a bug in virtual box (5.0.20). How to escape braces (curly brackets) in a format string in .NET How can brackets be escaped in using string.Format? For example: String val = &quot;1,2,3&quot; String.Format(&quot; foo {{0}}&quot;, val);  This example doesn't throw an exception, but it outputs the string foo {0}. Is there a way to escape the brackets? A gold reviewer badge? For your continued efforts in reviewing posts, even though the system sometimes messes up and doesn't let you actually review things and keeps displaying them over and over and over. So also, for your patience in putting up with the glitches in the review panel too! Haha  Anyways, a gold reviewer badge: 20000 reviews, over 4000 actioned  I just multiplied both numbers by 20. Think those numbers seem challenging? Is anyone up near those numbers or should it be multiplied by 10 instead? I prefer the higher amount because it would be gold and something harder to work for. :) But we also have to consider the longevity of when all these posts are eventually reviewed and it's only new posts being created.  Anyways, my stats for those who are interested (I wouldn't get the badge to start because I only have ~2000 actioned):  Upvoted            189 Downvoted          11 Edited             926 Commented          127 Voted to Close     44 Flagged            447 Reviewed           21609   As far as the name of the badge, I really like "The Owl is Watching" but not sure if that would be too long. Sounds snazzy though. Ideas?    Personally, I was on a quest to try and clear out all the posts in a single tab before it started showing me the same things over and over (and over) and then it got frustrating because I wasn't even making progress. Quest denied. :(    Lately I've noticed a massive build-up of unreviewed posts. When the review panel was first implemented, there would only ever be maybe 50 unreviewed posts at a time (in a given tab) for my monthly view. Now I log in and there's a thousand or two thousand pending. I think a lot of people quit reviewing after the first badge, so having a gold badge with a high threshold would really improve activity in the review panel and keep people going to improve the community. Wrong numeration in toc longer then one page I tried anything I could find with \cleardoublepage and \newpage and so on; mostly they use \addcontentsline. I don't need to use it as listof=totoc already puts it into the toc so even if I use \addcontentsline instead I get the same result.  \documentclass[     fontsize=11pt,     DIV10,     ngerman,     paper=a4,      twoside=false,     titlepage,     parskip=half,     listof=totoc,     bibliography=totoc,     index=totoc,     captions=tableheading,     foottotes=multiple,     final ]{scrartcl}  \usepackage[     automark,     headsepline,     ilines ]{scrpage2}  \usepackage[ngerman]{babel} \usepackage[babel,german=quotes]{csquotes} \usepackage[dvips]{graphicx}  \begin{document}  \ofoot{\pagemark} \pagenumbering{Roman} \clearpage \tableofcontents \clearpage \listoffigures \clearpage \pagenumbering{arabic} \section{Test} \label{sec:Test}  Test  \subsection{Test} \label{sec:Test}  \begin{figure}[H]  \centering \caption{Testfig} \label{fig:testfig} \end{figure}  \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test} \subsection{Test} \label{sec:Test}  \end{document} Making mathematical animations with Mathematica In Java, how do I call a base class's method from the overriding method in a derived class? How can I SELECT rows with MAX(Column value), PARTITION by another column in MYSQL? Let $G$ be a matrix Lie group and let $H$ be a Lie subgroup of $G$. My understanding is that all $g \in G$ are matrices, since $G$ is a subgroup of the general linear group. Then aren’t all elements $h \in H$ matrices, since $h \in G$?  From what I can gather $H$ is a matrix Lie group if $H$ is a closed subset of $G$. But if $H$ is not a closed subset of $G$, why is it not a matrix Lie group? Is the reasoning in the first paragraph wrong? I just renewed my antivirus (Kaspersky's) yesterday. After that, I logged onto Chemistry.SE (which I frequent often) but then I was greeted with this  Which was definitely not how it looked like earlier that morning. I wasn't able to  Open the reputation and badges tab Vote on questions, answers and comments (even answers to MY questions) Comment on questions or answers. 'Favorite' a question Attach tags to a question Post questions  etc., etc. But when I logged on to the Physics and Biology SEs (which I also frequent), the page format hadn't changed, but I still faced the same problems as above. Does anyone know how to fix this? P.S- I'm not a computer/formatting whiz, so you'd have to try avoiding the jargon when helping me out, sorry.... (Also I use Chrome...in case that's important.) Also @Oded recommended checking out the browser developer tools and having a look at the CSS, but as I said, I'm no Software/formatting whiz...so I'm still lost....  On @Shadow Wizard 's advice I've taken a screen shot of the 'error' notification (I had to scroll down to get all 10 'errors' on screen, hence the need for separate screen-shots) So our 6-month-old boy still doesn't sleep through the night. He still wakes up at least once and wants to eat.  He takes 3 naps during the day, ranging from 30 minutes to 1.5 (sometimes 2) hours.  We usually put him down for the night at least 2 hours after his latest nap, but we haven't been able to get him down to 2 naps per day because he gets pretty cranky during the evenings. Depending on the duration and times of his naps, his bedtime ranges between 10 and midnight.  We have started feeding him a small amount (2 tablespoons dry) of rice cereal after his morning and evening naps in the hopes that he'll have a fuller stomach through the night, but he still wakes up hungry after sleeping between 3 and 6 hours. I can handle the 6 hours, since that means I get 6 hours of pretty much uninterrupted sleep, but it's usually more like 3-4.  Any suggestions?