%---------change this by adding your uva id into the {}
%%%% PUT YOUR name here
\def\yourname{abhi}
% --- no need to change anything in this section -----------------------------------------------------
\def\homework{1} % 0 for solution, 1 for problem-set only
\def\duedate{wed sep 15, 2016 at 5p}
\def\duelocation{via \href{https://gradescope.com/courses/4095}{gradescope}}
\def\hnumber{0}
\def\prof{abhi shelat}
\def\course{\href{https://shelat.ccis.neu.edu/16f-4800}{cs4800 - algorithms - f'16}}

\documentclass[11pt]{article}
%-------------------------------------------------------------------------------------------------------------

%% ================= no need to edit any of this stuff


%%% ==== standard installations of latex include all of the files that are referenced in this section.  However,
%%% ==== if you are having compile problems, consider commenting some of these commands out 
\usepackage[colorlinks,urlcolor=blue]{hyperref}
\usepackage[osf]{mathpazo}
\usepackage{amsmath,amsfonts,graphicx}
\usepackage{latexsym}
\usepackage[top=1in,bottom=1.4in,left=1.5in,right=1.5in,centering]{geometry}
\usepackage{color}
\definecolor{mdb}{rgb}{0.3,0.02,0.02} 
\definecolor{cit}{rgb}{0.05,0.2,0.45} 
\markboth{\yourname}{\yourname}
%%% ===================================================================


%%% ============ should be no need to edit anything in this section ====================
\newenvironment{proof}{\par\noindent{\it Proof.}\hspace*{1em}}{$\Box$\bigskip}
\newcommand{\qed}{$\Box$}
\newcommand{\alg}[1]{\mathsf{#1}}
\newcommand{\handout}{
   \renewcommand{\thepage}{H\hnumber-\arabic{page}}%
   \noindent%
   \begin{center}%
      \vbox{%
    \hbox to \columnwidth {\sc{\course} --- abhi shelat \hfill}%
    \vspace{-2mm}%
    \hbox to \columnwidth {\sc due \MakeLowercase{\duedate} \duelocation\hfill {\Huge\color{mdb}H\hnumber.\yourname}}%
      }
   \end{center}
   \vspace*{2mm}
}
\newcommand{\solution}[1]{\medskip\noindent\textbf{Solution:}#1}
\newcommand{\bit}[1]{\{0,1\}^{ #1 }}
\newtheorem{problem}{\sc\color{cit}problem}
\newtheorem{lemma}{Lemma}
\newtheorem{definition}{Definition}
%%% ===================================================================
\thispagestyle{empty}

\begin{document}\handout

\noindent You may collaborate with other students on the homework but you must submit your own individually written solution, identify your collaborators, and acknowledge any external sources that you consult.

Please write each answer on a separate page and use \emph{exactly 3 pages} for your submission. You can do this using the \verb=\newpage= command between your answers.  See the template tex file provided on the course website for this assignment.

\begin{problem}Passage\end{problem}

\noindent Typeset your favorite passage from a book.

\newpage

\begin{problem}{Asymptotic notation}\end{problem}

\noindent Let $f$ be a function. Give a formal definition of the set  $\Theta(f)$.

$$\Theta(f) = \left\{\ \parbox{2.5in}{
functions $g$ such that 
...  % put the rest of your answer here
}  \right\}$$
%
Hint: Use the \verb=\exists= command to make the ``there exists'' symbol $\exists$, and the \verb=\forall= command to make the  ``for all'' symbol $\forall$.

\newpage


\begin{problem}{includegraphics command}\end{problem}

\noindent Learn how to include drawings in your documents with the \verb=\includegraphics{file}=
command by submitting a caricature of me.

\end{document}
