I'm looking for some books on abstract algebra which go into a lot of depth and still ensure I gain a lot of intuition.  Any suggestions?
I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
Changing units in QGIS: degrees to meters I have a global map with CRS WGS84-EPSG:4326 and I want to calculate the area of my polygons. From what I read, to change the unit from degrees to meters I need to change my CRS. However, there is no global system for this. Is there any solution to change the unit from degrees to meters for a global map? Core Data - Storing Images (iPhone) Custom post type - posts list - white screen of death i am getting a weird error - white screen in the list of posts for a specific Custom post type (just for that one)   tried deactivating all the plugins tried checking for error (debugging = true)   Still nothing the page just doesnt echos anything... (nothing in source too)  I am talking about such a url in the admin:     Here is register_post_type part i am using:    function register_submodelcpt() {     $labels = array(         'name'                  =&gt; __('Sub Models', THEME_NAME),         'singular_name'         =&gt; __('Sub Models', THEME_NAME),         'add_new'               =&gt; __('New Model', THEME_NAME),         'add_new_item'          =&gt; __('Add new Model', THEME_NAME),         'edit_item'             =&gt; __('Edit Model', THEME_NAME),         'new_item'              =&gt; __('New Model', THEME_NAME),         'all_items'             =&gt; __('All Sub Models', THEME_NAME),         'view_item'             =&gt; __('Watch Model', THEME_NAME),         'search_items'          =&gt; __('Search Models', THEME_NAME),         'not_found'             =&gt;  __('No Models found', THEME_NAME),         'not_found_in_trash'    =&gt; __('No Models found in trash', THEME_NAME),          'parent_item_colon'     =&gt; '',         'menu_name'             =&gt; __('Sub Models', THEME_NAME),      );      $args = array(         'labels'                =&gt; $labels,         'public'                =&gt; true,         'publicly_queryable'    =&gt; true,         'show_ui'               =&gt; true,          'show_in_menu'          =&gt; true,          'query_var'             =&gt; true,         'rewrite'               =&gt; array('slug' =&gt; 'submodels'),         'capability_type'       =&gt; 'post',         'has_archive'           =&gt; true,          'hierarchical'          =&gt; true,         'menu_position'         =&gt; 5,         'menu_icon'             =&gt; get_stylesheet_directory_uri().'/images/cpt/subcars.png',                     'supports'              =&gt; array('title', 'thumbnail', 'revisions', 'page-attributes')     );      register_post_type('submodelscpt',$args); } add_action('init', 'register_submodelcpt');   Did anyone encounter such an issuse? can you think of a reason this might happen?   Another weird thing when i change this:    To this:     The posts list loads correctly... Subject–verb agreement not clear in "Is two bars OK?" Is the following correct?     Can I get some chocolate for myself? Yes, you can but not much.   Is two bars OK?   Is there any rule to explain the sentence above?  The dialogue's taken from Grammar Textbook Round-Up Level #3. Simple homework question about normally distributed variables The question states:      Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is   normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$.   What is the mean and the variance of the random variable $Y$, where   $Y=X_1+...+X_n$.   How do I do this? What are the limitations of a typical kit lens as a general purpose lens? I have a Canon EOS 550d with the 18-55mm IS kit lens. I have done  (portraits, nature, night shots etc), and find the image quality to be pretty good. In fact most of the reviews have also been positive (at least in terms of image quality):   Quote:     indeed Canon's main concern may   ultimately become whether users have   as much incentive to upgrade to more   expensive optics as they did before       So, what are the key limitations of this lens (or any other similar kit lens) that would compel one to upgrade to a more expensive general purpose zoom lens (apart from the wanting to upgrade the zoom range)? Positive integer multiples of an irrational mod 1 are dense I'm not sure how to solve this one. Thank you!  $2.$ For any $\alpha\in \mathbb R$ we define $$\lfloor \alpha \rfloor = \max_{n\in\mathbb Z}\{\,n\mid n\leq \alpha\,\}$$ and $$\alpha\bmod 1 = \alpha - \lfloor \alpha \rfloor$$ Let $\alpha$ be irrational. (a) Given $n\in\mathbb N$ show that $\{\,k\alpha\bmod1\mid k\in\mathbb N\,\}\cap\left[0,\frac{1}{n}\right]\neq\emptyset$ (b) Prove that $\{\,n\alpha\bmod 1\mid n\in\mathbb N\,\}$ is dense in $[0,1]$. Characterizing non-constant entire functions with modulus $1$ on the unit circle Is there a characterization of the nonconstant entire functions $f$ that satisfy $|f(z)|=1$ for all $|z|=1$?   Clearly, $f(z)=z^n$ works for all $n$. Also, it's not difficult to show that if $f$ is such an entire function, then $f$ must vanish somewhere inside the unit disk. What else can be said about those functions?  Thank you. Distribute objects optimaly So I've got a file with loads of simple objects. This will later be used to cut out these shapes out of plastic. So, using the material optimally is of outmost importance. I was wondering if there is any script or plugin that could automaticly arrange the objects within the artboard so they could fit best. I'm using leaflet to display a map.  I have a control section that I'd like to be open by default, but I can't find a way to do it through the . Is there a way to do this? Mean Squared Error (MSE) of parameter $p$ in binomial distribution: intuition Finding where source has branched from git How do I connect Android devices to a WiFi AP and mobile data network simultaneously? Allow cross-site queries in data explorer I think it would be useful if we could join across databases in the data-explorer.  For example, I'd like to query up a list of questions that I had a hand in migrating away from SO, and see what percentage of them were subsequently closed or re-migrated.  I realise I could download the various data dumps and do this on my own machine, but it would be nice if it were allowed on the online version.  Is this possible/practical? Passing a dictionary to a function as keyword parameters I'd like to call a function in python using a dictionary.  Here is some code:  d = dict(param='test')  def f(param):     print(param)  f(d)   This prints {'param': 'test'} but I'd like it to just print test.  I'd like it to work similarly for more parameters:  d = dict(p1=1, p2=2) def f2(p1, p2):     print(p1, p2) f2(d)   Is this possible? Here's a situation that came up during a back lot league softball game a few weeks ago. (Note: While our league has some of its own rules we try to defer to MLB rules in all causes that aren't specifically addressed.)  There is a runner on second (R2) and a runner on first, with no outs. A ground ball is hit to the third baseman (3B) who cleanly fields the ball away from third base. Seeing that R2 is running toward him, 3B does not go to third and instead waits to tag the incoming R2. R2, in an attempt to buy some time for the other runners, stops advancing to third base. As soon as R2 stops, 3B declares R2 is out (without making a tag) and throws the ball to first to make a play.  During the discussion after the play, the 3B claimed that any player advancing on a force cannot stop moving toward their next bag or they are automatically out (the same way a runner leaving the baseline to avoid a tag is considered out). Our rules don't have a specific clause that addresses this situation and I couldn't find anything in official MLB rules (though it's possible I missed something, as 3B claims it is an MLB rule).  So, is 3B’s claim correct? That if a runner who is forced to advance to their next base stops (in particular to avoid/delay a tag) they are automatically out? During the next quarter at uni, I'll be taking a course in real analysis and since I prefer studying with an additional text I thought I'd come here to look for some book recommendations.  My background: I'm comfortable with linear algebra and single variable calculus, but shakey on multivariable calculus. I did have a slight introduction in to geometry.  For linear algebra I found the common recommendation of Hoffman &amp; Kunze to be very helpful (although the abstractness came as a bit of a kicker at first).   For Single variable calculus I used the book Calculus by Adams and Essex, which I found frustrating to work with, because it often left me guessing at what they were trying to do or why they were doing it. I also felt that they exercised a certain lack of rigour. (Which may be due to the subject which would make it hard to derive from axioms.)  Details: Though it would be a complementary text, I'd prefer one which will still hold value as a work of reference at a later point in my studies. I've heard that Rudin's Principles of mathematical analysis is one of the better textst out there, but also read several comments discouraging Rudin's book as a first introduction to real analysis, hence my quest to gather more information and maybe get some more personalised recommendations.  The course: The mandatory course literature will consist of lecture notes, but 4 texts are suggested as recommended reading.   T.M. Apostol, Mathematical analysis. Addison-Wesley (1974) J. Dieudonné, Foundations of Modern Analysis. Academic Press (1960) A. van Rooij, Analyse voor Beginners.Epsilon Uitgaven, no. 6 (2003)   R.S. Strichartz, The way of analysis (1995)   Thanks in advance! What will Sony do if someone uses my account as primary on another ps4 without my knowledge? What will Sony do if someone uses my account as primary on another ps4 without my knowledge? Will the account be banned? Or will the other guy that has my account as primary be banned? After how long? I have no credit card on my account so I don't care too much but I want to know.   He uses my account on his ps4 as a primary account. I think to use my digital games as free (Sharing, but without my knowledge). How to split strings into text and number? What free/open source image design programs can you recommend? Are there any free/ open source image designing programs that you can recommend?