%  This is a really simple example of how to use LaTeX.
% Tom LoFaro, Gustavus Adolphus College 2009.

% Anything after a percent sign is a comment.

%Necessary first line. It defines the type of document and some options.

\documentclass[12pt]{article}

% The part of the tex file between the documentclass
% and \beginc{document} line is called the preamble.  
% Things having to do with setting up the document are done
% in the preamble.  You will not need to mess with it (most likely)
% except to title your docuements like I've done below.

\title{MCS 220 Survey and \LaTeX \ Practice}
\author{Insert your name here}

% I've defined a bunch of theorem-like environments here 
\newtheorem{prop}{Proposition}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{definition}{Definition}
\newtheorem{remark}{Remark}
\newtheorem{example}{Example}
\newtheorem{corollary}{Corollary}
\newtheorem{terminology}{Terminology}
\newtheorem{notation}{Notation}
\newtheorem{exercise}{Exercise}
\newtheorem{note}{Note}
\newtheorem{comment}{Comment}
\newtheorem{claim}{Claim}

% Below I define some shortcuts for some common symbols.

\def\pf{\smallskip\noindent{\sl Proof:}\quad} % the proof statement starting a proof
\def\qed{\enspace\vbox{\hrule\hbox{\vrule\kern4pt % qed statement ending same
      \vbox{\kern4pt\kern4pt}\kern4pt\vrule}\hrule}}
\def\R{\mbox{\bf R}} % boldface R for the real numbers
\def\Q{\mbox{\bf Q}} % boldface Q for the rational numbers
\def\Z{\mbox{\bf Z}} % boldface Z for the integers


\begin{document}

\maketitle

This document is just a beginning of the semester survey done in
\LaTeX \ so that I can get to know you and you can practice with
\LaTeX.  \ Answer each of the following questions.  My comments should
help you with the \LaTeX \ commands.

\begin{enumerate}
\item What is your home town?  %name in italics using {\it }

\item What is your favorite sports and/or activities are you involved
  in at Gustavus? %in bold face using {\bf }

\item What is your favorite math class so far?

\item If 
\[ f(x) = x^3 + e^x \]
then the derivative is... 
% note how exponents are given using ^

\item A sequence is defined by
\[ x_n = \frac{n^2}{n+1}. \]
What is a formula for $x_{n+1}$?
% note how subscripts are given using _.

\item Using the sequence in the last problem what is 
  \[ \lim_{n \to \infty} x_n? \]
% note how the stuff below the lim is enclosed in brackets.
% What does \to print?

\item What greek letters are used in the definition of the limit?
(how 'bout epsilon and delta but I want you to typeset them inline.)

\item Write an integral to express the area between the $x$-axis the
  the graph of $y=x^2 + 1$ from $x=0$ to $x=\pi$. 
% \int for the integral sign _ for the lower limit ^ for the upper.

\item Express $1+\frac{1}{2}+\left(\frac{1}{2}\right)^2 + \cdots$ using
  a summation.
%\sum gives you the sigma.  lower and upper stuff using _ and ^ again.
\end{enumerate}

\end{document}







