% 
% file: sample.tex 
% author: Phil Rogaway
% History: 
%   2003.10.14 - created
%   2021.12.27 - Revised 
%
% This is LaTeX template to get you started using LaTeX
% for making problem-set solutions.
%
% Everything after a %-sign is a comment. It is ignored
 
\documentclass[11pt]{article}
\usepackage{amsmath}
\setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in}
\setlength{\textheight}{9in}
\setlength{\textwidth}{6.5in}
\setlength{\topmargin}{-0.5in}

% Sample macros -- how you define new commands
% My own set of frequently-used macros have grown to many hundreds of lines.
% Here are some simple samples.

\newcommand{\Adv}{{\mathbf{Adv}}}    %example macro 
\newcommand{\getsr}{{\:\stackrel{{\scriptscriptstyle\hspace{0.2em}\$}}{\leftarrow}\:}}  % a more complex macro
\newcommand{\Func}[1]{{\mathrm{Fun}[{#1}]}}        % These macros take one
\newcommand{\Randd}[2]{{\mathrm{Rand}[{#1},{#2}]}} % and two arguments

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{\bf Problem Set 1 Solutions}
\date{\today}
\author{\bf Jane P.\ Student}

\begin{document}
\maketitle


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Problem 1} 

Here you'll put your solution to problem~1.  
A most \emph{excellent} solution to problem~1.
Make all of your solutions excellent and you will make
me happy.  Don't you want me to be happy?

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section*{Problem 2} 

One of the most important aspects of \LaTeX\ is its math mode.
Mathematical symbols should look like $a$ or $X_5$ or $A_{ij}^*$;
never write something like x in ordinary text mode---it looks bad, 
might be confused with ordinary English text, and 
a mathematician will likely assume that 
x, \texttt{x}, $x$, $X$, and $\cal X$ are all intended to mean different things.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section*{Problem 3} 

To produce an offset formula you can write things like:
\begin{eqnarray*}
    \sum_{i=1}^n i  &=&   \frac{n(n+1)}{2} \\
                    &\in& O(n^2)
\end{eqnarray*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section*{Problem 4} 
I won't suggest that becoming good with \LaTeX\ is easy; it isn't.
But CS researchers, grad students, and serious undergrads all use this program---and lots
of other scientists and non-scientists do, too.
I would even say that LaTeX is the program of choice for all your college 
essays; the quality of output is a world apart from that you'll get from Word,
even when there's not a formula in sight.



\end{document}
