I am looking at program for grad school in applied mathematics. If I currently A 3.56 GPA, will it be a challenge to get into grad school?
When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it.
Need help to understand Maximum Likelihood Estimation for multivariate normal distribution? In maximum likelihood estimation for the parameter, mean $\mu$ of multivariate normal distribution, I end up with the following result:  $\mu_{MLE} = \dfrac{1}{n}\sum_{i=1}^n x_i$  The way I understand the above equation is the following way below, but I am wondering if the above equation means the following equation:  $\mu_{MLE} = \begin{bmatrix}\mu_1\\\mu_2\\\vdots\\\mu_n\end{bmatrix} = \begin{bmatrix}\dfrac{1}{n}\sum_{i=1}^n x_1\\\dfrac{1}{n}\sum_{i=1}^n x_2\\\vdots\\\dfrac{1}{n}\sum_{i=1}^n x_i\end{bmatrix} = \begin{bmatrix}E(X_1)\\E(X_2)\\\vdots\\E(X_n)\end{bmatrix} = \begin{bmatrix}\bar{X_1} \\ \bar{X_2} \\ \vdots \\ \bar{X_n}\end{bmatrix}$   And also Maximum Likelhood Estimation for $\Sigma$, I have ended up with the following equation:  $\Sigma_{MLE} = \dfrac{1}{n}\sum_{i=1}^n(x_i-\mu)(x_i-\mu)^T = \begin{bmatrix}Var(\sigma_{11}) &amp; Cov(\sigma_{12}) &amp; \dots &amp; Cov(\sigma_{1n}) \\ Cov(\sigma_{21}) &amp; Var(\sigma_{22}) &amp; \dots &amp; Cov(\sigma_{2n}) \\ {}&amp; \vdots&amp;  \\ Cov(\sigma_{n1}) &amp; Cov(\sigma_{n2}) &amp; \dots &amp; Var(\sigma_{nn})  \end{bmatrix}$  Somehow, I got the equation following some algebraic steps, but I can't see how this part, $\dfrac{1}{n}\sum_{i=1}^n(x_i-\mu)(x_i-\mu)^T$, works and produces the covariance matrix. Hope to hear some explanations. Let $A$ be a squared matrix, and suppose there exists an $n\in \Bbb N$ in a way that $A^n=0$. Show that $I-A$ is invertible and that $(I-A)^{-1}=I+A+\cdots+A^{n-1}$    I don't have a clue where to start from. Add new alias to Gmail without SMTP (forwarding-only address) Cannot install Ubuntu in VirtualBox due to "this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot" error I was trying to install Ubuntu 12.04 in VirtualBox 4.2.12r84980. I see    this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot   But I am using a 64 bit Windows 8, and trying same .iso for trying Ubuntu. Then what is the problem? Scala Lists of lists of integers Is it possible for many domain names to share one IP address? Is it possible for many domain names to share one IP address? For example, www.xjtl.com, www.fmie.com, sdmfl.com, etc.  Hundreds of domain names share just one IP – when you do a DNS query for each of them, the same IP is returned.  Are there any laws or Internet rules that disallow this? Meta Meta Privilege I just took a look at meta today and noticed something weird in the meta privileges. If you look at the meta privilege list, you can see that at . I know that there is no meta for meta, and the link they give you in the privilege page leads you to meta.stackexchange.com, right where you started. Why do they have this privilege? I have a feeling that this is a bad recursive joke. You must be  member of meta to get the privilege of being a member of meta! :) I am not sure which conjunction to use in the following context:        I know about programming but I have a little bit of confusion in Java programming.   I know about programming although I have a little bit of confusion in programming.    I know about programming however I have a little bit of confusion in Java programming. Why does the connection time out when connecting to a server? My friend had hosted a Minecraft server before and brought it back up today with my help. He and anyone in his LAN can connect. However we have had a few people try to connect, including me, and when we try to connect it gives the message:  Failed to connect to the server Connection timed out: connect  What does this exactly mean? How do we fix this? I am needing to auto increment a field based on groups within a feature class. I have 8 plots within a given polygon and I need to assign them an ID from 1-8 for each set of plots within each polygon. The polygon would have its own unique ID number to be used to group the plots.  I assume it would be an alteration of this:  rec=0 def autoIncrement():  global rec  pStart = 1   pInterval = 1   if (rec == 0):    rec = pStart   else:    rec = rec + pInterval   return rec Difference in number of communities on main site Table of Contents with Chapter I'm attempting to modify the Table of Contents in my document. Currently, chapter one in my document is listed as   1   Introduction   What I would like to see is  Chapter 1   Introduction   Seems like an easy enough thing to ask for, but can't seem to find a good way to do this. Any feedback would be most appreciative. I used VIRTUALBOX to install Ubuntu 12.04 on my windows pc. I used apt-get to install Python 2.7 that shipped with 12.04. I followed the directives I saw on this site to install Numpy, Scipy, Matplot all failed. I download tar source file of these modules. How do I install them manually? Someone pls help, I'm getting frustrated. I would like to say something like     The boy, Adam's, favorite toy was a bike.   What is the proper way to say this? Why do liquids boil when their vapor pressure equals the ambient pressure? Given that the boiling point of a liquid is the temperature at which the vapor pressure is equal to the ambient (surrounding) pressure, what significance does a liquid's vapor pressure have in the formation of bubbles that happens at and above the boiling point?    The definition of boiling point seems to imply that the pressure inside of the bubbles must be at least as great as the liquid's vapor pressure in order to balance the outside pressure, but is there any particular reason why the pressure inside of the bubbles is related to the vapor pressure?    The vapor pressure seems to be a measurement describing the tendency of the molecules to escape from the surface of the liquid, but I don't see how that relates to bubble formation within the liquid.  This question has bothered me for a while, so any help would be much appreciated. Capacitor on USB cable? I was messing around with a USB camera. I wanted to change the cable because is trimmed but as I was cutting it I saw a small thing (image below). As I was trying to cut the casing and see what it has inside I saw a spark. I tried to connect it with another cable but I don't know if I'm gonna damage the camera or the USB port.    What is it and can I connect the camera without it? Showing $\int_{\mathbb R} \mid F(x)-G(x)\mid dx = \int_0^1 \mid F^{-1}(u)-G^{-1}(u)\mid du$ with $F$, $G$ CDF functions Let's $X$ and $Y$ have CDF functions admitting moment of order $1$. Let's be $F$ cdf of $X$ and $G$ cdf of $Y$.  I want to show that $$\int_{\mathbb R} \mid F(x)-G(x)\mid dx = \int_{0}^{1} \mid F^{-1}(u)-G^{-1}(u)\mid du\,.$$ What noun or adjective would one give to a person that is intolerant of stupidity? A person that becomes annoyed, angry, or of very short temper when conversing or interacting with people of a lower intelligence?  For example:       The man is very xyzxyz; his son can't do multiplication very well.     or     She is a(n) xyzxyz. She gets very frustrated when people forget things.   I'm looking almost for a scientific/medical/psychological term. One that would fall into the same kind of group as words like haemophiliac, masochist, nihilist, etc. Currentsection TOC in scrartcl? I like to get a toc at beginning of some of my sections, like in beamer where I can use \tableofcontents[currentsection] is there a possibility in scrartcl?  Something like this:  \documentclass[10pt,a4paper]{scrartcl} \usepackage[ngerman]{babel}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}  \begin{document}  \tableofcontents %complete  \section{First}  \section{Second} \tableofcontents %just subsection and subsubsection \subsection{SecondSub} \subsubsection{please} \subsection{this} \subsection{SecondSub2} \subsection{parts}  \section{Third} \subsection{another}  \end{document}   Looks like:  Inhaltsverzeichnis %complete  1 First  2 Second 2.1 SecondSub.......................2 2.1.1 please........................2 2.1.2 this..........................2 2.2. SecondSub2.....................3 2.2.1 parts.........................4  3 Third 3.1 another ........................5   1 First  2 Second  Inhaltsverzeichnis %just subsection and subsubsection 2.1 SecondSub.......................2  2.1.1 please........................2  2.1.2 this..........................2 2.2. SecondSub2.....................3  2.2.1 parts.........................4  2.1 SecondSub  2.1.1 please   2.1.2 this  2.2. SecondSub2  2.2.1 parts   3 Third  3.1 another LaTeX: optional arguments with square brackets LaTeX is trying to add a missing $ that I don't want to the following code. Minimal working example:  \documentclass[letter,12pt]{article}  \newcommand{\monkeyBeans}[2][]{   \parbox{4in}{#1} }  \begin{document}  \parbox{4in}{$[a, b]$}   \monkeyBeans[$[a, b]$]{yo monkey}  \end{document}   If I try any of the following lines in my document instead of the call to monkeyBeans, there is no error:  \parbox{4in}{$[a, b]$}  \monkeyBeans[yo monkey]{$[a, b]$} \monkeyBeans[$(a, b)$]{yo monkey} \monkeyBeans{$[a, b]$}{yo monkey}   What is the deal with square brackets in optional arguments?