My motivation for studying Hopf algebras is twofold:      I'm interested in representation theory and the algebraic structure of group rings.   I will also take a course on algebraic groups soon and I think it would be helpful to know about Hopf algebras for that.   So I'm looking for a good introductory book on Hopf algebras for self-study and especially for one that has many examples and applications to the two topics mentioned above.  (As for my background, I know abstract algebra,  commutative algebra and non-commutative algebra at a basic graduate level, I'm familiar with the basics on representation theory of (mostly finite) groups and category theory (including monoidal and symmetric monoidal, but not braided monoidal categories) and have some rudimentary knowledge of algebraic geometry. I know almost nothing about Lie algebras.)
I want to learn more about hopf algebras but I am having trouble finding a down to earth introduction to the subject with lots of motivation and examples. My algebra knowledge ranges from Dummit and Foote, Atiyah-Macdonald commutative algebra, and Hartshorne level algebraic geometry.  What are good places to look at for a hopf algebra beginner? My main motivation is for studying groupoid schemes from an algebraic point of view.
Derangements with repetitive numbers I have a very simple problem.  Lets assume that I have a well shuffled deck of 52 cards. I start drawing the top card always and when the card matches its rank I lose. J=11 Q=12 K=13.  If there were only 13 cards I could easily use the $\ \frac{!n}{n!}$ for derangements in order to solve this. The problem is that there are 52 cards so when I pass 13 I start from 1 again so I don't know what is the probability to win. Example of the game     1st card: 4 - Continue   2nd Card: A - continue   3rd Card: K - Continue   4th Card: K - Continue   5th Card: 6 - Continue   6th Card: 9 - Continue   7th Card: 10 - Continue   8th Card: A - Continue   9th Card: J - Continue   10th Card: 3 - Continue   11th Card: 2 - Continue   12th Card: 8 - Continue   13th Card: A - Continue   1st card: 5 - Continue   2nd Card 2 LOSE   So actually I have to count from 1 to 13 4 times and if I draw all 52 cards then I win. What's the probability? I would like to change a file extension from *.txt to *.text. I tried using the basename command, but I'm having trouble on changing more than one file.  Here's my code:  files=`ls -1 *.txt`  for x in $files do     mv $x "`basename $files .txt`.text" done   I'm getting this error:  basename: too many arguments Try basename --help' for more information Setting custom UITableViewCells height What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$  I tried to factorize $n^3+100$, but $100$ is not a perfect cube. I wish it were $1000$. This happens pretty much every time I try to bake normal maps. It's quite a broad error message and I still don't know exactly what the problems I'm having are, only that if I keep clicking things for half an hour eventually it sometimes just works.  My understanding of the things needed:   A "Generated" blender Image that the normals are written to (In UV/Image Editor, click Image->New)   Tell blender that this is the bake output, below (this is the really confusing bit which blender seems to try to guess and fails)  A UV Map for the low poly model (you only need the geometry of the high poly and it doesn't need a UV map) Under Bake, in the rendering tab:   Bake Mode = Normals Normal Space = Tangent Selected to Active = ✓ (for the next bit)  Select the high rez object first, then the low poly object With the two objects selected, click Bake (you may have to move the mouse to see the error pops up)   Now, from what I can tell the only  (with regard to the setup and apart from the internals of baking) is how blender finds the output image:   Cycles  Have a material using an ImageTexture node which points to your normal map output. Then  says the node must be selected, but  doesn't mention selecting. Blender Render  Have a texture attached to the material that uses the image.  is pretty vague on assigning the output image. Sometimes I've found hitting tab to go to edit mode and selecting the normal map image in the UV editor to help, or at least it seemed to.   I would like to know the exact details of what blender goes looking for when you hit Bake, rather than have to guess by following tutorials. For example, it seems to look for the high and low poly objects in your selection and based off the order you select them. How does it find the normal map/image to write to for both cycles and blender render? Does the Texture need to Influence Normals or does it just need to reference the Image? etc... How do I find out what tool a shortcut is triggering? I used to have problem with connecting two objects, because when I smooth the final object, there was a darker line on the connected parts (for example when I was making head, I've had eyes darker this way). Then I found out that I can get rid of it by hitting Ctrl+N, but I don't realy know what it does. I can just see that the lines are gone. So, what does Ctrl+N do? Will the below code cause memory leak in c++ class someclass {};  class base {     int a;     int *pint;     someclass objsomeclass;     someclass* psomeclass; public:     base()     {         objsomeclass = someclass();         psomeclass = new someclass();         pint = new int();          throw "constructor failed";         a = 43;     } }  int main() {     base temp(); }   In the above code, the constructor throws. Which objects will be leaked, and how can the memory leaks be avoided?  int main() {     base *temp = new base(); }   How about in the above code? How can the memory leaks be avoided after the constructor throws? Is either "can" or "could" more polite? Using the properties panel I can add, with "+"  button, only eight UV maps. Is it possible to have more than 8 of them? What is the advantage on saving the money for the overlord when you have 9 drones, and not filling your supply first and then getting the overlord?  In my theory, in the first case you get to wait the saving time with 9 drones, and get to wait almost the same time with 10 drones in the second case. Second case should be better, since 10 drones mine faster than 9? So why does everybody go with the first case?  All this is assuming you go 12 pool or something like that, where you will get more drones after the overlord. 6- and 8-pools are obviously different. How to get domain name from URL Batch renaming files I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this? Ubuntu 17.10 Upgrade Broke VMWare Workstation 12.5 Hi after upgrading to Ubuntu 17.10, vmware is now not starting.    I get the message:    /usr/lib/vmware/bin/vmware-modconfig: Relink `/lib/x86_64-linux-gnu/libbsd.so.0' with `/lib/x86_64-linux-gnu/librt.so.1' for IFUNC symbol `clock_gettime'   I am aware that there are patches available and I am attempting to apply these and recompile. I have run from the solution at :    cd ~   #Copy the vmmon source tar ball to your temporary location cp /usr/lib/vmware/modules/source/vmmon.tar .    #Extract the tar ball tar xf vmmon.tar    #Download the modified file that mkubecek posted and overwrite the one from the tar ball for VMware Workstation 12.5: wget -O ./vmmon-only/linux/hostif.c https://raw.githubusercontent.com/mkubecek/vmware-host-modules/b50848c985f1a6c0a341187346d77f0119d0a835/vmmon-only/linux/hostif.c     #Wrap up the newly modified files into a tar ball replacing the original one sudo tar cf /usr/lib/vmware/modules/source/vmmon.tar vmmon-only    #Rebuild the VMware kernel modules sudo vmware-modconfig --console --install-all   Failed to get gcc information.  gcc --version gcc (Ubuntu 7.2.0-8ubuntu3) 7.2.0 ...   Unforunately, vmware-modconfig is failing because of a dependency it seems on a particular gcc version. Am I on the right track? Any help with this issue would be much appreciated.  EDIT Thank you Steve, the below has gotten vmware going again. I've included minor correction. Tested and confirmed I could run a virtual machine.   sudo su    # do all below as root cd /usr/lib/vmware/modules/source tar xvf vmmon.tar  tar xvf vmnet.tar wget -O ./vmmon-only/linux/hostif.c https://raw.githubusercontent.com/mkubecek/vmware-host-modules/b50848c985f1a6c0a341187346d77f0119d0a835/vmmon-only/linux/hostif.c vim vmnet-only/bridge.c cd vmmon-only/ make cd ../vmnet-only/ make cd .. mkdir /lib/modules/4.13.0-16-generic/misc cp *.o /lib/modules/4.13.0-16-generic/misc insmod /lib/modules/4.13.0-16-generic/misc/vmmon.o insmod /lib/modules/4.13.0-16-generic/misc/vmnet.o rm /usr/lib/vmware/lib/libz.so.1/libz.so.1 ln -s /lib/x86_64-linux-gnu/libz.so.1 /usr/lib/vmware/lib/libz.so.1/libz.so.1 vmware-networks --start exit  # run vmware as normal user /usr/lib/vmware/bin/vmware Notepad doesn't open files created by Gedit? Suppose that I have a &lt;div&gt; that I wish to center in the browser's display (viewport). To do so, I need to calculate the width and height of the &lt;div&gt; element.   What should I use? Please include information on browser compatibility. Prove: If a sequence converges, then every subsequence converges to the same limit. I am trying to determine if the sum $\sum_{n=1}^\infty \frac{n+4^n}{n+6^n}$ is convergent or divergent.   In attempting to solve this problem I began by seeing if I could do the divergence test - in this case it is not helpful. The terms $4^n,6^n$ look like geometric series type terms but the $n$ in the numerator and denominator are troublesome. I first tried factoring $n$ out of the expression:  $$\sum_{n=1}^\infty \frac{n+4^n}{n+6^n} = \sum_{n=1}^\infty \frac{1+\frac{4^n}{n}}{1+\frac{6^n}{n}}$$  Next I tried comparing to the series $$\sum_{n=1}^\infty \frac{\frac{4^n}{n}}{\frac{6^n}{n}} = \sum_{n=1}^\infty \frac{{4^n}}{{6^n}} = \sum_{n=1}^\infty{\left(\frac{2}{3}\right)}^n$$  This is a convergent geometric series as $r = \frac{2}{3}\lt1$  now I reason that the series $\sum_{n=1}^\infty \frac{1+\frac{4^n}{n}}{1+\frac{6^n}{n}}$ is neither smaller not greater than the series $\sum_{n=1}^\infty{(\frac{2}{3})}^n$ Am I able to conclude anything in this case by a direct comparison test or can I only conclude that the first series is convergent if the second is greater than the first?  Thanks Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$ Should I always disconnect event handlers in the Dispose method? Standard error of a ratio I have a linear regression and two estimates, say A and B and their standard errors. I need to find the standard error of a ratio A/B [or A/(1-B)].  I guess the main problem is that I don't know the correlation between A and B. I also guess that makes this unsolvable, since the correlation plays a major role. Is this correct?  If I knew it, what would be the way to calculate the standard error?