Generating functions and integer partitioning
Partitions of $n$ into distinct odd and even parts proof
Why was the switch statement designed to need a break? Given a simple switch statement  switch (int) {     case 1 :     {         printf("1\n");         break;     }      case 2 :      {         printf("2\n");     }      case 3 :      {         printf("3\n");     } }   The absence of a break statement in case 2, implies that execution will continue inside the code for case 3. This is not an accident; it was designed that way. Why was this decisions made? What benefit does this provide vs. having an automatic break semantic for the blocks? What was the rationale? How to I make Cisco WebEx work with 13.10 64bit? I'm having a very hard time getting webex to work under Saucy.  Up until now I've been able to just install a java plugin, install ia32-libs, and I was good to go.  With Saucy ia32-libs is gone and it's up to us to figure out which 32-bit libraries we need to install.    So the question is, how do I install WebEx on 64bit Saucy without ia32-libs? How to align a  to the middle (horizontally/width) of the page What's in "standard system utilities" in the server install? My googlefu has failed me. What packages are part of the "standard system utilities" that is preselected during install?  TIA! (-: Table cells larger than they are meant to be I've created a map system for a game that runs on the principle of drawing the picture of the map from tiles. There are many reasons for this which I won't go into here but if you really want to know then I'm sure you can find out how to contact me ;)  I have  so you can see exactly where the problem lies and the source. The issue is the line between the top 2 tiles and the bottom 2 tiles, I can't figure out why it's gone like this and any help would be appreciated.  In the source is a marker called "stackoverflow", if you search for "stackoverflow" when viewing source then it should take you to the table in question.  I have also uploaded an . Why does a 12V 2A adapter measure only 0.358A on a multimeter? I assume that the multimeter should read 2A, why is it only 0.358A? If this is how it is supposed to be, why? If I add a load, how do I measure that this load is being drawn, does the multimeter need to be in series? I am currently looking at the various libraries that I can use to show a map in my custom Android App. I have found several like Mapsforge, OSMDroid, ArcGIS runtime for Android, Google Maps for Android and so on. I'm sure that I am missing a few.   Is there a comparison chart somewhere about the differences in functionalities and pros and cons of each one?   If there isn't one, we could make this question community wiki, to serve alongside  &amp; . Suppose that a deck of 52 cards containing four aces is shuffled thoroughly and the cards are then distributed among four players so that each player receives 13 cards. Determine the probability that each player will receive one ace.   The answer to this is given as$$\frac{13^4}{\binom {52}4}$$  My doubt is the following:   The book justifies ${\binom {52}{4}}$ as number of possible different combinations of the four positions in the deck occupied by 4 aces. That sounds like a case of arrangements to me, so shouldn't we think about permutations and not combinations if we are concerned about how the aces are to be arranged in the deck ?. Shouldn't the denominator be ${\binom {52}{13}}$ since you are choosing 13 cards for 4 people. I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), linear maps and their matrix representation and eigenvectors and eigenvalues. I am looking for a book that handles every of the aforementioned topics in details. I also want to build a solid basis of the mathematical way of thinking to get ready to an exciting abstract algebra next semester, so my main aim is to work on proofs for somehow hard problems. I got Lang's "Intro. to Linear Algebra" and it is too easy, superficial.  Can you advise me a good book for all of the above? Please take into consideration that it is for self-study, so that it' gotta work on its own. Thanks. Why is the derivative of a circle's area its perimeter (and similarly for spheres)? Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$ Following my  the book then asks      Use this to determine when the field extension  $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$  is biquadratic (where $a,b\in\mathbb{Q}$)   "this" means what proved in the linked post.  My thoughts: First, I don't know what to say when $a^2-b$ is not a square. When $a^2-b$ is a square I think that the extension is of degree $2$ if $a=b$, this leaves the case $a\neq b$ which I am also having problems with and I don't know what to do (I have some cases like if $m,n$ are different primes then the degree of the extension is $4$, but I don't have something that is general)  Can someone please help my do this exercice  ? Proving that the map from a topological space to a fiber bundle is open. jQuery select and wrap textNode Using shell's read command with live editing functionality (readline like) Is there a standard (POSIX) way of asking the user some data from within a shell script, with  for example, while allowing live edition of the text being typed (what readline does)?   I know bash has read -e varname that allows for the person launching the script to use keyboard arrows for exemple, to edit or correct what has just been typed without deleting the last entered characters with backspace.   However, read -e is . And still, it is pretty cumbersome to delete all that has been wrote if you realise you made a mistake at the beginning of your long sentence... Given that $$f\left(\frac{x+y}{2}\right)\leqslant \frac{f(x)+f(y)}{2}~,$$ how can I show that $f$ is convex. Thanks.      Edit: I'm sorry for all the confusion. $f$ is assumed to be continuous on an interval $(a,b)$. How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$ Nick Fury told Captain America that he has been "asleep" for nearly 70 years. If Dominic Cooper was playing Howard Stark Senior (grandfather of Tony Stark) then it is fine, but if he was playing Howard Stark (father of Tony Stark) then after 70 years he should be around 90 or above.  Tony Stark, his son, should be 60 to 70 years.  Is that possible?  Tony doesn't look 70 years in The Avengers. I am trying to follow the  and . I tried to push some of my Lightning components which depend on a managed package in App Exchange. I would like to know how to install a managed package using Salsforce DX CLI so that i can use that command in my travis.YML file for my CI integration.  Here is the script for my Travis file  sudo: true dist: trusty cache: false env: - URL=https://developer.salesforce.com/media/salesforce-cli/sfdx-linux- amd64.tar.xz before_install:  - export SFDX_AUTOUPDATE_DISABLE=true - export SFDX_USE_GENERIC_UNIX_KEYCHAIN=true - export SFDX_DOMAIN_RETRY=300 - wget -qO- $URL | tar xJf - - "./sfdx/install" - export PATH=./sfdx/$(pwd):$PATH - sfdx update - sfdx force:auth:jwt:grant --clientid $CONSUMERKEY --jwtkeyfile  assets/server.key --username $USERNAME --setdefaultdevhubusername -a DevHub script: - sfdx force:org:create -f config/project-scratch-def.json -s -a  PackageInstallation - sfdx force:org:list - sfdx force:org:display - sfdx force:user:password:generate -u PackageInstallation - sfdx force:org:display - sfdx force:org:open -u PackageInstallation - sfdx force:source:push -u PackageInstallation - sfdx force:apex:test:run -u PackageInstallation -c -r human   I get the following error as my components depend on the app exchange components:     No COMPONENT named markup://ldt:datatableDev found : I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. Let $H$ be a subgroup of $G$ with $[G:H]=n$ and $G$ finite.  Let $G$ act on left cosets of $H$ by left multiplication.  Let $N$ be the kernel of the action.  Show that $[G:N]$ divides $n!$.  Ok so I have a theorem that says that if $G$ is simple then it embeds into $S_n$.  So if $G$ is simple than I'm done because $G$ divides $n!$ and thus $N$ divides $n!$ and hence $[G:N]$ divides $n!$.  Now I also know that $N$ is the largest normal subgroup of $G$ contained in $H$.  Thus if $G$ isn't simple then it contains some non-trivial normal subgroup $K$ and thus $K\cap H$ is normal in $H$ and by the 2nd Iso Theorem $H/K\cap H\cong KH/H$...    As you can see I'm not sure where to go from here. I was hoping to prove that $K\cap H$ wasn't trivial and thus that $N$ couldn't be trivial since it must contain $K\cap H$, but I'm not sure I can, and even if I could I'm not sure that would help me in showing that $[G:N]$ is small enough to divide $n!$.  Can anyone give some guidance?  Thanks.