\documentclass{article}
\usepackage[a4paper]{geometry} 
\usepackage[english]{babel}
\usepackage{amsmath, amssymb, textcomp}

\begin{document}
	\title{\LaTeX course week 2, exercises}
	\author{\TeX niCie\\ A--Eskwadraatcommittee}
	\maketitle
Please make the following mathematical formulas. It could be useful to look into the tex-code of the manual.
\section{Mathmode}
\begin{equation}
n! = \prod_{i=1}^{n}i
\end{equation}

\begin{equation}
\sum_{n=1}^{\infty}z^n = \frac{1}{1-z}, \; |z|<1
\end{equation}


\begin{equation}
\int_a^b\!x^2 \mathrm{d} x = \frac{1}{3}(b^3 - a^3)
\end{equation}


\begin{equation}
\oint \nabla f \mathrm{d} t = 0
\end{equation}

\begin{align}
(\alpha + \beta)^2 & = (\alpha + \beta)(\alpha + \beta)\\
					& = \alpha \alpha + \alpha \beta + \beta \alpha + \beta \beta\\
					& = \alpha^2 + 2 \alpha\beta + \beta^2
\end{align}

The same formulas, but without references:

$\begin{array}{rl}
(\alpha + \beta)^2 & = (\alpha + \beta)(\alpha + \beta)\\
& = \alpha \alpha + \alpha \beta + \beta \alpha + \beta \beta\\
& = \alpha^2 + 2 \alpha\beta + \beta^2
\end{array}$

If you find the above really easy, you could try the line below.
\begin{equation}
\int\! \cosh^{-1}\frac{x}{a} \mathrm{d}x = \begin{cases}
x \cosh^{-1} \frac{x}{a} - \sqrt{x^2-a^2} \; \left[ \cosh^{-1}(\frac{x}{a})> 0, a > 0 \right]\\
x \cosh^{-1} \frac{x}{a} + \sqrt{x^2-a^2} \; \left[ \cosh^{-1}(\frac{x}{a}) < 0, a > 0 \right]\\
\end{cases}
\end{equation}


\section{Matrices}

$A_{3,3} = \begin{pmatrix}
a_{11} & a_{12} & a_{13}\\
a_{21} & a_{22} & a_{23}\\
a_{31} & a_{32} & a_{33}\\
\end{pmatrix}$


\section{Tables}
Try to make the table below. You can look into the manual to see how it is done there. Do you understand every command and sign?
\begin{table}[h]
	\begin{tabular}[width=\textwidth]{|l||llp{5cm}|}
		\hline
		\textbf{A--Eskwadraat activities} & \textbf{Date} & \textbf{Time} & \textbf{Description}\\
		\hline
		Bake-a-cake-contest & November $19^{th}$ & 12:45-13:15 & You can hand in your homemade cake until 12:50h. At 1pm the price will be given to the best cook. Afterwards you can buy a piece of cake. The money will go to charity.\\
		Kickboxing & November $19^{th}$ & 16-17.30& Kickboxing at Olympos, 1.5 hours for just 5 euros. You can buy your ticket at A-Eskwadraat, BBG 269.\\
		Paint your mug & November $24^{th}$ & 12-16 & This is your chance to customize your own mug and place it in the A-Eskwadraat room.\\

		\hline
	\end{tabular}
\caption{Table of \mbox{A--Es}kwadraat activity's}
\end{table}

\end{document}
