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\usepackage{amsthm, amssymb, amsmath}
\usepackage[colorlinks=true]{hyperref}
\usepackage{enumitem}
\usepackage[margin=1in]{geometry}
\def\hhref#1#2{\href{#1}{#2} [\texttt{#1}]}

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\newtheorem{question}{Question}
\newtheorem{theorem}{Theorem}
\newtheorem{definition}{Definition}

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\newcommand{\ZZ}{\mathbb{Z}}

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\begin{document}

% This sets up the title and author
\title{\LaTeX\ tutorial}
\author{Your name here}
\date{\today}
\maketitle


\begin{enumerate}
\item 
Use summation notation (i.e. $\sum_{i = 1}^n$) to rewrite the following expression without ellipses:
\begin{equation*}
1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \cdots = 
\end{equation*}
(Does this sum converge, and if so, do you know what the value of the sum?)

\item
        For each of the following sets (their names are $A$, $B$ and $C$), correct the poorly-formed set builder notation:
   $$A = \{ x in \mathbb{Z} : x \}$$
   $$B = { x \in : x > 1 } $$
   $$ C = \{ \mathbb{Z} : x <= 1 $$

Hint: \hhref{http://detexify.kirelabs.org/}{detexify} could help you find the \LaTeX code for any particular symbols you may want, like `is less than or equal to'.

\item
If $A=\{0,\emptyset\}$, then $\mathcal{P}(A) =$ 

\item 
The quadratic formula gives an explicit expression for the solutions to an equation $ax^2 + bx + c = 0$. 
Typeset the quadratic formula below.

\item
Here's a definition of an odd number:
\begin{definition}
   An integer $n$ is \emph{odd} if $n = 2a+1$ for some integer $a \in \mathbb{Z}$.
\end{definition}
Notice how I have typset the word we are defining (`odd') to emphasize it.

Typeset the definition of subset below:


\item
        In Chapter 2 we will learn about truth tables. When we get to that topic, you can use the example below as a reference. This is the \emph{truth table} for $P \wedge Q$ (this is the symbolic way to write `$P$ and $Q$'):

\begin{center}
\begin{tabular}{c|c|c|c}
$P$ & $Q$ & $P \wedge Q$ \\
\hline
T & T &  T\\
T & F &  F\\
F & T &  F\\
F & F &  F
\end{tabular}
\end{center}
In this example, in the first row, we see that if $P$ is true, and $Q$ is true, then `$P$ and $Q$' is also true. Typeset the truth table for $P \vee Q$ (this is the symbolic way to write `$P$ or $Q$')

\item
Compute a few of the sums in the following sequence:
$$
1,\; 1 + 3,\; 1 + 3 + 5,\; 1 + 3 + 5 + 7,\; 1 + 3 + 5 + 7 + 9,\; \ldots
$$

Do you see a pattern?  Write a formula expressing the pattern you found.

\end{enumerate}

\end{document}