\documentclass[12pt]{article}

% import a set of useful packages for math
\usepackage{amsmath, amsfonts, amssymb}

% this package makes margins smaller
\usepackage{fullpage}

% for importing images
\usepackage{graphicx}

%%%% import any other packages here

%%%% make any other definitions here


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\begin{document}

\title{Homework NUMBER \\
       Colorado CSCI 5454}
\author{STUDENT NAME}
\date{\today}
\maketitle

People I studied with for this homework:

Other external resources used:


%%%%%%%%%%%%%%%%
\section*{Problem 1}
I can use math like so: $f(x) = 42$.


%%%%%%%%%%%%%%%%
\section*{Problem 2}
I \emph{can} use \textbf{math} with spacing:
  \[ x + 1 = 43 \]


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

%%%%%%%%
\subsection*{Part a}
I can use multiple steps of math, aligned at the equals sign:
\begin{align*}
  f(x) &= 3^4 - 3^3 - 3^2 - 3^1  \\
       &= 81 - 27 - 9 - 3  \\
       &= 42
\end{align*}

%%%%%%%%
\subsection*{Part b}
I can include a picture scaled to a certain fraction of the page width (if I uncomment these lines):
%\includegraphics[width=0.5\textwidth]{filename.jpg}
%\includegraphics[width=0.25\textwidth]{filename.pdf}

%%%%%%%%
\subsection*{Part c}
I can use parentheses and brackets that scale or don't scale.
\begin{align*}
  Z  &= \Pr [ 2 (\frac{a}{b}) = 42]  \\
     &= \Pr \left[ 2 \left( \frac{a}{b} \right) = 42 \right]
\end{align*}


%%%%%%%%%%%%%%%%
\section*{Problem 4}
I can do other interesting math.
  \[
     f(x) = \begin{cases}
            42    & x \leq 0  \\
            41.5  & x > 0
            \end{cases}
  \]

I can make a table with two colums and three rows.
Each column is left-aligned (``l'').

\begin{tabular}{ll}
  a   & b  \\
  $a$ & $b$ \\
  $6$ & $7$
\end{tabular}

\vskip2em

I can leave some space.

\vskip2em

I can make a table with three columns, each centered (``c'') and with vertical lines between the columns, and with a horizontal line.

\vskip1em

\begin{tabular}{c|c|c}
  a   & b   & c    \\
  $a$ & $b$ & $c$  \\
  \hline
  $6$ & $7$ & $8$  \\
  red & blue & yellow
\end{tabular}


\end{document}
