Solutions

Listing Things

In [1]:
%%pdflatex
Okay, lets start with a list of my favourite things:
\begin{itemize}
    \item Raindrops on \textit{roses}
    \item Whiskers on \textit{kittens}
    \item Bright copper \textit{kettles}
    \item Warm woolen \textit{mittens}
    \item Brown paper \textit{packages} tied up with string
\end{itemize}
How to make scones:
\begin{enumerate}
    \item Heat the oven to 220C/425F/Gas 7. Lightly grease a baking sheet.
    \item \begin{enumerate}
            \item Mix together the \textbf{flour \& salt} and rub in the \textbf{butter}.
            \item Stir in the \textbf{sugar} \& then the \textbf{milk} to get a soft dough.
          \end{enumerate}
    \item Turn on to a floured work surface and knead very lightly. Pat out to a round 2cm/(3/4)in thick. 
    Use a 5cm/2in cutter to stamp out rounds and place on a baking sheet. 
    Lightly knead together the rest of the dough and stamp out more scones to use it all up.
    \item Brush the tops of the scones with the beaten egg. Bake for 12-15 minutes until well risen and golden.
    \item Cool on a wire rack and serve with butter and good \textbf{jam} and maybe some clotted cream.
\end{enumerate}
Out[1]:

Writing Maths

In [2]:
%%pdflatex
A Quadratic equation: $ ax^2 + bx + c = 0 $.
The quadratic formula:
$$ x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}. $$
A matrix equation
$$
\begin{pmatrix}
    a & \log{b}\\
    c & d
\end{pmatrix}
\begin{pmatrix}
x\\
y
\end{pmatrix}
=\begin{pmatrix}
0\\
0
\end{pmatrix}
$$
can be rewritten as a system of linear equations
\begin{align}
ax + \log(b)y & = 0 \\
cx + dy & = 0.
\end{align}
The Riemann zeta function
$$ \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} $$
can be rewritten as
$$ \zeta(s) = \frac{1}{\Gamma(s)} \int_0^\infty \frac{x^{s-1}}{e^x - 1}\ dx, $$
where
$$ \Gamma(s) = \int_0^\infty e^{-x}x^{s-1}\ dx. $$
Out[2]:

Time for a table

In [3]:
%%pdflatex
\begin{tabular}{ccc}
\textbf{Time} & \textbf{Activity} & \textbf{Energy Levels} \\
\hline
 0730 & Get Up & 15\% \\
 0745 & Eat Breakfast & 100\% \\
 0815 & Go to Office & 80\% \\
 0900 & Do Research & 20\% \\
 1230 & Have Lunch & 100\% \\
 1330 & More Research & 0\% \\
 1730 & Go Home & -10\% \\
 2000 & Make Tea & 50\% \\
 2330 & Sleep & 40\% \\
\end{tabular}
Out[3]:

Ooh, what a picture!

In [4]:
%%pdflatex
A picture of Donald Knuth, creator of \LaTeX, playing the organ.
\begin{figure}
    \centering
    \includegraphics[scale=0.25]{./images/knuth.jpg}
    \caption{This image was taken by Peter Badge, and can be found 
             at https://cs.stanford.edu/~knuth/dek-badge-20120614.jpg}
\end{figure}
Out[4]: