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\documentclass{article}
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\usepackage{amsthm, amssymb, amsmath}
\usepackage[colorlinks=true]{hyperref}
\def\hhref#1#2{\href{#1}{#2} [\texttt{#1}]}
\usepackage{enumitem}
\usepackage[margin=1in]{geometry}
% This sets up personal environments, like theorems
\newtheorem{question}{Question}
\newtheorem{theorem}{Theorem}
\newtheorem{definition}{Definition}
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\newcommand{\ZZ}{\mathbb{Z}}
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\begin{document}
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\title{\LaTeX\ tutorial}
\author{Your name here}
\date{\today}
\maketitle
\begin{enumerate}[label=(\alph{*})]
\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*}
Do you know what the value of this sum is?
\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
For each of the following sets (their names are $A$, $B$ and $C$), correct the poorly-formed set builder notation:
\begin{align*}
A &= \{ x in \mathbb{Z} : x \} \\
B &= { x \in : x > 1 } \\
C = \{ \mathbb{Z} &: x <= 1
\end{align*}
Can you also correct the weird alignment so it looks better? Notice the \texttt{align} environment and the $\&$ symbols in the code.
Hint: \hhref{http://detexify.kirelabs.org/}{detexify} could help you find the \LaTeX code for any particular symbols you may want, like `less-than-or-equals'.
\item
Here's a definition of an odd number:
\begin{definition}
An integer $n$ is \emph{odd} if it has the form $n = 2k+1$ for some integer $k$.
\end{definition}
Notice how I have typset the word we are defining (`odd') to emphasize it.
Use the \texttt{theorem} environment to typeset a nicely stated theorem which says what the parity of a sum of two odd numbers will be. Hint: check your statement with me.
\item
Use the \texttt{proof} environment to typeset a proof of your theorem. Hint: check your proof with me.
\item
Fill in the third column of this \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 & F & \\
F & T & \\
F & F &
\end{tabular}
\end{center}
In other words, for the first row, if $P$ is true, and $Q$ is true, is it true or false that `$P$ and $Q$'?
\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.
\item
Thinking back to the first-day activity, can you typset a conjecture you made about the edges, vertices and faces of polyhedra?
\end{enumerate}
\end{document}