Good afternoon, how do I switch from windows to Linux based operating system. I m currently using a 13 dell laptop. Further question is do I need a virtual machine or where do I start to get the linux system. Please advise of the best course of action. Cheers,   lionsray
I would like to see a full how-to guide on how to install Ubuntu.
I'm reading Galois Theory by Steven H. Weintraub (second edition), and finding that I'm at least somewhat short on the prerequisites. However the following proof looks wrong to me - am I misunderstanding something, or is it actually an incorrect proof?  Lemma 2.2.3. Let $F$ be a field and $R$ an integral domain that is a finite-dimensional $F$-vector space. Then $R$ is a field. Proof. We need to show that any nonzero $r \in R$ has an inverse. Consider $\{1, r, r^2, \cdots\}$. This is an infinite set of elements of $R$, and by hypothesis $R$ is finite dimensional as an $F$-vector space, so this set is linearly dependent. Hence $\sum_{i=0}^n{c_i r^i} = 0$ for some $n$ and some $c_i \in F$ not all zero.  It then goes on to show, given the above, that we can derive an inverse for $r$. However, if I consider examples like $r = 2 \in Q[\sqrt{2}]$, $r = \sqrt{2} \in Q[\sqrt{2}]$ or $r = 2 \in Q[X]/{&lt;X^2&gt;}$, the set $\{1, r, r^2, ...\}$ doesn't look linearly dependent to me. I do believe the lemma is true (and might even be able to prove it), but this does not look like a correct proof to me. Am I missing something? [Edit] Well yes, I am. Somehow I had managed to discount the possibility of any $c_i$ being negative, despite repeatedly looking at each fragment of the quoted text in an attempt to find what I might be misunderstanding. Why couldn't the Jedi detect Senator Palpatine as having powers? In Return of the Jedi, when trying to sneak into the base on a shuttle, Luke said he senses Darth Vader's presence and said he shouldn't have come lest he jeopardize the mission. Darth Vader also sensed Luke, but let him in anyways. Also, Yoda and Obi-Wan could detect the Force in young Anakin.  So if Jedi and Sith can detect each other, why couldn't they detect Senator Palpatine to begin with? It seems like a giant plot hole. I'm trying to show that $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$. A hint would be nice. What's the difference between "it excites me" and "that excites me"? Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers How would I show the following.  For all odd integers a,b, and c if z is a solution of $ax^2+bx+c=0$ the z is not rational.  How would I show this? This is what I did  Let a be an odd integer then for a integer k it has the form $a=2k+1$  then $b=2t+1$ for if c integer.  then $c=2r+1$ if s is an integer then I do  $(2k+1)(x)^2+2t+1(x)+(2r+1)=0$  But I find my self stuck on what to do any hint are appreciated. How to find an ellipse , given 2 passing points and the tangents at them? Please answer to a question , how to find an ellipse which passes the 2 given points and has the given tangents at them. And one related question is that the given condition can decide just one ellipse which satisfies it?  Thank you in advance.  Edit : May be , I can say the first answer (by Mr. André Nicolas) is for the general case. Is there no special case where only a finite set of ellipses satisfies the condition?  Edit : According to the answers and comments , I can compute an arbitrary chosen ellipse for my condition (using the method by Mr.Patrick Da Silva). But there are possibly many others which satisfy my conditions. Am I right? Determining size of grid cells created by vector grid tool of QGIS? I am working with QGIS 1.8.0 and Im making a vector grid on a map. Does someone know how big are the squares if the grid settings look like in the picture? How to find correctly the .bib file? Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian Possible Duplicate:             If $G$ is a group and $Z(G)$ the center of $G$, show that if $G/Z(G)$ is cyclic, then $G$ is abelian.  This is what I have so far:  We know that all cyclic groups are abelian. This means $G/Z(G)$ is abelian.  $Z(G)= \{z \in G \mid zx=xz \text{ for all } x \in G \}$.  So $Z(G)$ is abelian.    Is it sufficient to say that since $G/Z(G)$ and $Z(G)$ are both abelian, $G$ must be abelian? Scaling vs Offsetting in Quasi-Poisson GLM I  modeled insurance claim frequency assuming a Quasi-Poisson distribution in R. My frequency dependent variable was calculated, in advance of modeling, as the number of claims per underlying exposure. Someone  that it would be incorrect to do this, and that the correct method was to model the observed claim counts and use the underlying exposure as an offset.   Can someone explain the theoretical and practical differences between scaling and offsetting? I ran the code both ways and noticed that the deviance residuals are significantly smaller when using offsets, but otherwise there were no material differences in variable selection.   P.S. Note the similar but still different question . What is the normal operating temperature for the MacBook (2016 generation)? Every $R$-module is a quotient of a free module I'm reading through my notes, and I have a theorem as the title says. As proof I have only a picture.    where $v:m\mapsto(0,...,0,1,0,...,0)$ and 1 is at $m$-th position. I know, that $\oplus_M R$ is a free module generated by set  $M$, but is this all? I do not see how the statement is proved. I have an iPhone 4s with iOS7 and somehow I see iCloud music which I haven't downloaded yet on my iOS device. How can I get rid of these, I do not need to see them. Summation equation for $2^{x-1}$ I am using natbib and agsm for harvard-style referencing. My related code is  \usepackage{natbib} \bibliographystyle{agsm}   Then I am using \citep{} for citations. My problem is that in text I am getting     (Author et al. 2012)   but and I want     (Author et al. 2012)   Does anyone know how to change this and get 'et al' in italics in the text?  I am using TexPad and BibDesk and I have not been able to find the .bst files in Terminal.  I know that it is often correct to have the 'et al.' unitalicised but my university regulations requires italics. Is there a word that contains all the vowels? "Jealousy" contains most of the vowels but lacks 'i'. Is there a word in the English language that contains every vowel (and preferably 'y')? How does the User Card popup work? We are experimenting with enhanced user card mouseover popups and have enabled them network wide. You can tell which users will trigger the popup because they have a 3-D drop shadowy look to their gravatar:    Hover your mouse over the gravatar and wait. Note that the user card mouseover popup will only be displayed if the following conditions are met:   Is the profile complete, and long enough? We enforce a minimum length requirement. The user's reputation must be >= 1k  If you have more links than are able to be displayed after truncation, those extra links will be shown in the bottom of the dialog. We order links at the bottom consistently -- if you include a twitter, google plus, linked in, or facebook those links are prioritized. It will be visible on a question and answer detail page, any page with a list of questions, and the /users list. It will not be shown when a question or answer is wiki'd. It will not be shown when excerpt summary is defined as &lt;!-- summary: &amp;nbsp; --&gt; we support explicitly specifying your user card excerpt summary using the following syntax:  &lt;!-- summary: This is my profile, there are others like it but this one is mine. --&gt;   The above example will result in:    This is now mostly complete.  The goal is allow people to show  off how awesome they are inline, without having to click through to the full user profile page. Let $U_1, \cdots, U_n$ be $n$ i.i.d continuous uniform random variables on $(0,1)$ and their order statistics be $U_{(1)}, \cdots, U_{(n)}$.  Define $D_i=U_{(i)}−U_{(i−1)}$ for $i=1, \cdots, n$ with $U_0=0$.  I am trying to figure out the distribution $\lim_{n\to\infty} \#\{i = 1, \cdots, n \mid nD_i \geq z\}/n$. This must be very well known, but I cannot find a reference. Books on Number Theory for Layman Is it possible to run Snow Leopard on a LATE 2011 MacBook Pro? I want to buy a new MacBook Pro, from Apple. However I want to run Snow Leopard instead of Lion.  I did some Google searches and found a few success stories of people who got SL to run on their early-2011 MBPs. I didn't find much of any experiences of people doing the same on a late-2011 MBP though, so I'm wondering (and really hoping!) if it's possible?