\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amsthm,amsfonts,latexsym,amssymb,xcolor}
\usepackage{fancyhdr}
\pagestyle{fancy}
\setlength{\headheight}{50pt}

\begin{document}
\lhead{Course name \\ Assignment 1} 
\rhead{Your name \\ Due date}

\noindent
1. The problem statement goes here.

\bigskip
\bigskip

\noindent
\emph{Proof.}
This is the \color{blue} solution. \color{black}

\begin{enumerate}
\item[(a)]  This 
\item[(b)]  is an 
\item[(iii)]  enumeration 
\item[(4)]  environment.
\end{enumerate}  

\begin{center}
This is centered text.
\end{center}  

\textrm{To} \textsl{display} \texttt{centered} \textbf{math} \textit{text},
\textit{\textbf{try}} \footnote{These fonts, in order, are
  \textrm{roman}, 
  \textsl{slant}, 
  \texttt{teletype}, 
  \textbf{bold}, 
  \textit{italic}, 
  \textit{\textbf{bold italic}}}

\[
(\forall x)(\exists y)(x=y).
\]

Some useful symbols:
\[
\in, \{X, Y\}, \subseteq, \subsetneq, \supseteq,
X\cup Y, X\cap Y, {\mathcal P}(X), 
\forall, \exists, \wedge, \vee, \neg, \to, \leftrightarrow,
\alpha, \beta, \gamma, \delta, 2^{\aleph_0}
\]

If you want to display a line and ``tag'' it with a symbol,
try this:
\begin{equation} \label{eqn1} \tag{$\ddagger$}  
0\to M'\stackrel{\alpha}{\to} M\stackrel{\beta}{\to} M''\to 0.
\end{equation}

Later, to refer to this line, write ``By (\ref{eqn1}), we deduce \ldots''.
\qed

\bigskip

This is one way to write a system of linear equations:
\[
\begin{alignedat}{3}
x&+   &   2y&+  &  3z&=\,1 \\ 
x&-   &   y&+   &  z&=\frac{5}{2} \\ 
3x&-  &   2y&+  &  z&=\,5
\end{alignedat}
\]

Here is the same system written in matrix form:
\[
\begin{bmatrix}
  1 & \hphantom{-}2 & \hphantom{-}3 \\
  1 & -1 & \hphantom{-}1 \\
  3 & \hphantom{-}2 & \hphantom{-}1
\end{bmatrix}
\begin{bmatrix}
x\\y\\z
\end{bmatrix}
=
\begin{bmatrix}
1 \\ \frac{5}{2} \\ 5
\end{bmatrix}
\quad \textrm{or} \quad
\begin{pmatrix}
  1 & \hphantom{-}2 & \hphantom{-}3 \\
  1 & -1 & \hphantom{-}1 \\
  3 & \hphantom{-}2 & \hphantom{-}1
\end{pmatrix}
\begin{pmatrix}
x\\y\\z
\end{pmatrix}
=
\begin{pmatrix}
1 \\ \frac{5}{2} \\ 5
\end{pmatrix}
\]
\end{document}
