\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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}