Books in commutative algebra
How to learn commutative algebra?
What are the criteria used to represent Stack Exchange sites on the sites page? (Grid view) I noticed that  has been changed, and by default sites are shown by balloons.  What is not clear to me is why some sites are shown with a bigger balloon than other sites. For example, WordPress Answers has less questions, answers and users than Programmers, but its balloon is bigger. What are the criteria used to show the sites on that page? Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$ Can this integral be solved with contour integral or by some application of residue theorem? $$\int_0^\infty \frac{\log (1+x)}{1+x^2}dx = \frac{\pi}{4}\log 2 + \text{Catalan constant}$$  It has two poles at $\pm i$ and  branch point of $-1$ while the integral is to be evaluated from $0\to \infty$. How to get $\text{Catalan Constant}$? Please give some hints. Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $ Let $K\subseteq \mathbb{R}^n$ be a compact set and $E\subseteq \mathbb{R}^n$ a closed set, such that: $$\inf\{d(x,y):x\in K, y\in E\}=0$$ where $d(x,y)=\sqrt{\sum_j(x_j-y_j)^2}$ Prove: $E\cap K\neq \emptyset $  I tried to work with the definitions of compact and closed sets, and I understand that from what's given of the distance between elements in $K$ and $E$, that they are very close,  but couldn't really get further. Any help appreciated. Are the rationals a closed or open set in $\mathbb{R}$? I know plants are green due to chlorophyll.  Surely it would be more beneficial for plants to be red than green as by being green they reflect green light and do not absorb it even though green light has more energy than red light.  Is there no alternative to chlorophyll? Or is it something else? I want to upgrade the hard drive in my 2012 Macbook Pro to an SSD. I have the parts, but had a question about how to clone the contents of my current drive so I can install it onto the SSD.  I've seen tutorials where people suggest connecting the new SSD to the Macbook prior to installation and using a Carbon Copy Cloner to clone the drive, and then installing the SSD drive.  My question is, can I do a Time Machine backup of my current hard drive on an external hard drive, install the SSD, and then use the Time Machine backup from the external to transfer it onto the newly installed SSD? Is this the same as using the clone program above? WHERE IN (array of IDs) I have webservice which is passed an array of ints. I'd like to do the select statement as follows but keep getting errors. Do I need to change the array to a string?  [WebMethod] public MiniEvent[] getAdminEvents(int buildingID, DateTime startDate) {         command.CommandText = @"SELECT id,                             startDateTime, endDateTime From                             tb_bookings WHERE buildingID IN                             (@buildingIDs) AND startDateTime &lt;=                             @fromDate";      SqlParameter buildID = new SqlParameter("@buildingIDs", buildingIDs); } Forgot which email I used, can't login I forgot what email I used for my other ploxtic id: how do you find out what my email was?   The account is user:2078229. Shell Script for logging into a ssh server I tried writing a shell script which can do automatic login into a ssh server using password which is mentioned in the script. I have written the following code:  set timeout 30 /usr/bin/ssh -p 8484 root@172.31.72.103 expect  {    "root@172.31.72.103's password"     {       send "password\r"     } }   This code is not running properly, still it is asking for the password. Can somebody please help me in solving this How do you convert CString and std::string std::wstring to each other? CString is quite handy, while std::string is more compatible with STL container. I am using hash_map. However, hash_map does not support CStrings as keys, so I want to convert the CString into a std::string. Writing a CString hash function seems to take a lot of time. CString -----&gt; std::string  How can I do this? std::string -----&gt; CString:  inline CString toCString(std::string const&amp; str) {     return CString(str.c_str());  }  Am I right?  EDIT: Here are more questions: How can I convert from wstring to CString and vice versa? // wstring -&gt; CString std::wstring src; CString result(src.c_str());  // CString -&gt; wstring CString src; std::wstring des(src.GetString());  Is there any problem with this? Additionally, how can I convert from std::wstring to std::string and vice versa? Content replacement from external website How does Linux know where its swap partition is? I've read that you need to put the swap partition on HDD rather than SSD.   My questions are the following:    When and how is the "checking" done by the distribution (or something else) to find its Swap partition?  Does it happen during boot?  It just checks all available disks and searches for a partition with 'swap' flag?  What happens if there are several partitions like that?  Also, how many swap partitions do I need to have if I run, for example, two different distributions on the same disk, let's say Fedora and Ubuntu? How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$? Prime factorization knowing n and Euler's function My task is to factorize $n$ knowing it has two factors and $\varphi(n)$. How can I do it?  Thanks for any advice. Is it possible to create 3D red/cyan anaglyphs in a hand drawing? There are plenty tutorials online on how to create 3D red/cyan anaglyphs from existing photos in Photoshop or similar software. However, I'm wondering if it is possible to draw a 3D image by hand on for example a whiteboard using markers.  My plan is to tape together a red and blue marker and draw with it using the same rotation/inclination of the marker across the drawing. Will this give a 3D effect when viewed through red/cyan glasses? Or is the 3D anaglyph method more complex than just offsetting red and cyan lines? Sort arrays of primitive types in descending order What does why would I do it mean in this context? I've often heard people saying this. And even I say it when someone accuses me of doing something that I didn't do.  I'd say:  Why would I do that?  But what's the grammar behind it?  Is it future from the past tense or something or what? It's obviously not a conditional construction 😒  Context from SE01 EP02 Austin &amp; Ally  Austin: what does the jacket have to do with the music video?  Trish: It's a line in Ally's song, "my jacket's in the lost and found."  Ally: "my jacket"? It says "I like it." The line is "I like it when you hang around."  Dez: "hang around"? I thought it said "kangaroo." ♪ I like it when you kangaroo. ♪.  Ally: Why would I write "I like it when you kangaroo"? How do I choose between "as to", "on", "of", and "about"? I am using \tableofcontents to create TOC in my document. however it is appearing as shown in the image. As the numbers increase the gap between the number and text is reducing.   Thanks for your help Aku How do I escape a backtick ` within a code block?  This is probably a duplicate, since I'm sure it's a common concern, but I can't find a question that addresses this specifically.  How do I write List'1 with the "1" character still in the code-text format?