I am an engineering undergrad in my third year. The question that I am asking might sound like a duplicate but I seek some rough statistics. What classification might be roughly correct for institutions offering MSc degree for their average acceptation GPAs?  To visualize, I do not expect a 2.8/4 average student to be accepted to MIT except extreme cases. Would it be "roughly" correct to make a tabulation as follows:  top-20:   3.7/4  top-50:   3.5/4  top-100:   3.3/4  top-200:  3.0/4  I am aware of that it lacks real statistical information and there are many external factors shaping this kind of generalization, however, it would be helpful for making "realistic" degree applications. Any improvement would be appreciated.
Some prestigious universities like Caltech, Stanford, MIT and Berkeley never disclose their information regarding their cut off major and cumulative GPA for M.Sc and PhD programs in engineering. I also aware of the fact that graduate schools will look at the whole package and make their decision based on sets of factors like letter of recommendation, statement of purpose as well as GPA.   However, since application fee is pretty high it is not worth it to apply to schools that you know you have a slight chance of getting into it so, I would like to know what would be the acceptable GPA (Both major and Cumulative) for applicants to be competitive for top five schools in the world?
Proof for $e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$ Q1: Could someone provide a proof for this equation (please focus on this question):   $$e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$$  Q2: Is there any corelationn between above equation and the equation below (this would benefit me a lot because i at least know how to proove this one):  $$e = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right)^x$$ Minecraft Survival Mode What physical properties of materials trigger the capacitive touch screen? I have watched some youtube videos about capacitive touch screen      The videos show that a conductor(finger), in which charges can be induced, can be used to trigger the capacitive touch screen. However, I tried to wear a plastic glove to hold a metal rod to touch the screen and no detection is triggered.  I really want to know the physics theory about the capacitive sensing.  Can someone tell me what physical properties or shape trigger the capacitive touch screen?  Is there any examples that something WITHOUT conducting to human body can trigger the screen?  (P.S. I have read other posts about capacitive touch screen here and do not find a good answer so this is not a duplicate) I've installed ubuntu 17.04 and I want to upgrade it to 18.04. When I tried to do:   sudo do-release-upgrade   I got a message saying An upgrade from 'zesty' to 'bionic' is not supported with this tool. Need inputs to proceed on this.  sudo do-release-upgrade Checking for a new Ubuntu release Your Ubuntu release is not supported anymore. For upgrade information, please visit: http://www.ubuntu.com/releaseendoflife  Get:1 Upgrade tool signature [819 B]                                            Get:2 Upgrade tool [1,257 kB]                                                   Fetched 1,258 kB in 0s (0 B/s)                                                  authenticate 'bionic.tar.gz' against 'bionic.tar.gz.gpg'  extracting 'bionic.tar.gz'  Reading cache  Checking package manager  Can not upgrade   An upgrade from 'zesty' to 'bionic' is not supported with this tool. How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$? Define $f : [0,1] \to \mathbb{R} $ differentiable satisfying $f(0)=0$ and $0&lt;f'(x)&lt;1$. Prove:  $\displaystyle\int_{0}^{1} f^3(x) \, dx &lt; \left(\displaystyle\int_{0}^{1} f(x) \, dx\right)^2$ I found the following answer,  Define $F(x)=\displaystyle\int_{0}^{x} f^3(t) \, dt - \left(\displaystyle\int_{0}^{x} f(t) \, dt\right)^2$ We have $$F'(x)=f^3(x)-2 \left(\displaystyle\int_{0}^{x} f(t) \, dt\right)f(x)=f(x)\left[f^2(x)-2 \left(\displaystyle\int_{0}^{x} f(t) \, dt\right)\right]$$ and $$\left[f^2(x)-2 \left(\displaystyle\int_{0}^{x} f(t) \, dt\right)\right]'=2f(x)\left[f'(x)-1\right]$$ from which we can arrive at the conclusion.  But I felt a little confused. In the past I usually proved the inequality by classical inequalities and something like Taylor expansion to use the condition about derivative. But this answer is little out of my expectation. Do we have other proofs or ideas to arrive at $\displaystyle\int_{0}^{1} f^3(x) \, dx &lt; \left(\displaystyle\int_{0}^{1} f(x) \, dx\right)^2$? And other thoughts about solving these types of issues? I think when we talk about $\left(\displaystyle\int_{0}^{1} f(x) \, dx\right)^2 &gt;\ldots \,$ it's a little difficult to deal with. I don't quite know what tools to use. Cycles not rendering image or movie clip used as background in the viewport Let $X_1, X_2, \ldots X_n$ be random variables with mean $\mu$ and variance $\sigma^2$. We define the sample mean $\bar{X} = \sum_{i = 1}^n X_i$.  I am having trouble understanding why the variance of $\bar{X}$ is $\sigma^2 / n$.  Here is what I worked out thus far:  $$\begin{gather} \sigma_\bar{X}^2 = E((\bar{X} - \mu)^2) = E(\bar{X}^2 - 2\bar{X}\mu + \mu^2) = E(\bar{X}^2) - 2\mu E(\bar{X}) + E(\mu^2) = E(\bar{X}^2) - \mu. \end{gather}$$  However, I'm not sure what to do with the $E(\bar{X}^2)$. I just installed Lyx 2.1 on my computer for the first time. I wanted to create my first trial pdf but switching to viewing mode is for some reason not working with the Acrobat Reader DC. I tried many options found on the web but I am afraid my little knowledge is not sufficing to make it work.  I would really appreciate a detailed answer :)   Thanks. How do I make Div Container 100% width only on homepage of site? In .NET, the  is used in a lot of places throughout the .NET base class libraries. Implementing it properly is especially important to find items quickly in a collection or when determining equality.  Is there a standard algorithm or best practice on how to implement GetHashCode for my custom classes so I don't degrade performance? Automatically highlight undefined references connectedness of uniform topology I would like to revise the default new user registration form in Drupal 7. Rather than to requst "username", I want to request "full name" with helper instructions to enter the text "username is your full name as you would normally use it."  There may be some other minor formatting changes I would like to make as well.  I cannot find an admin menu item to access anything relating to this question. And I am unable to locate a file within any director that has any text that would indicate it is the source for the new user registration form.  I realize this is a bit unconventional, however it is useful for our needs. I am aware of a module that allows the input of First Name / Last Name, but in processing it changes the input to first initial/lastname, ie Tom Thumb = username of "tthumb". The module "Realname Registration" would be just what I am looking for if it would only translate the username the same as the input.   That wouldn't necessarily solve the other formatting edits, but I would be very happy just to be able to manually edit the registration form help text under the username field, instructing the new user to register using thier real name.  Thanks for any help that you can provide.  J.M. What is the best way to check whether a given object is of a given type? How about checking whether the object inherits from a given type?  Let's say I have an object o. How do I check whether it's a str? Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ by defining a bijection $f:A^{B \cup C} \rightarrow A^B \times A^C$.  Any hints on this one?  Thank you! How to install Flash player on Ubuntu? Even though I have the latest Adobe Flash player 11.2 for Linux in Firefox -   - a particular online flash game still requests that I update to the latest flash player.  I've tried this online game on my laptop (Windows 8 with Flash Player 11.8) and it has no problems.  Is there a way to trick Ubuntu or this game into thinking Flash Player 11.8 is "installed"? Server 2012 Core (no GUI): Remote Server manager not working I am trying cmd --> MMC --> Server Manager and then connecting to my Server 2012 no GUI  but i keep getting the following error The WinRM client cannot process the request  I am unable to upload images right now  This is not related to other post "How to Remote Manage Windows Server 2012 in Server Manager?" because title and description of that post is quite different from what i am asking I have a Sony VAIO S series with Windows 8 preinstalled, and I installed Ubuntu 12.10 on a new partition. When the PC boots Grub is display, and I can choose between Windows 8 (didn't worked at the beginning, had to change Grub settings) and Ubuntu 12.10. When I select Ubuntu 12.10 everything is OK, but when I use Windows 8, and I restart Grub isn't displayed anymore (Windows 8 boots immediately).  I booted a Ubuntu 12.10 LiveUSB, used efibootmgr, and found out that Windows 8 (each time it boots) changes EFI default bootloader from Grub to Windows Boot Manager.  How do I change this in Windows 8? I read something about bcdedit, but it does not work or I don't know how to use it... The usual Schrodinger Lagrangian is $$ \tag 1 i(\psi^{*}\partial_{t}\psi ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi, $$ which gives the correct equations of motion, with conjugate momentum for $\psi^{*}$ vanishing. This Lagrangian density is not real but differs from a real Lagrangian density  $$ \tag 2 \frac{i}{2}(\psi^{*}\partial_{t}\psi -\psi \partial_{t}\psi^{*} ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi $$ by a total derivative.  My trouble is that these two lagrangian densities lead to different conjugate momenta and hence when setting equal time commutation relations, I am getting different results (a factor of 2 is causing the problem). I can rescale the fields but then my Hamiltonian also changes. Then applying Heisenberg equation of motion, I don't get the operator Schrodinger equation.   Is it possible to work with the real Lagrangian density and somehow get the correct commutation relations? I would have expected two Lagrangians differing by total derivative terms to give identical commutation relations (since canonical transformations preserve them). But perhaps I am making some very simple error. Unless all conjugate momenta are equivalent for two Lagrangians differing by total derivatives, how does one choose the correct one?   I guess the same thing happens for other first order systems like Dirac Lagrangian also. npm commands not working on WSL with zsh