## 2.1 Using LaTeX

LaTeX is a powerful typesetting language with primary use in academia for the publication of scientific papers and presentation slides as well as book publication. It is also used in RMarkdown, when compiling a notebook to a .pdf format.

### 2.1.1 LaTeX setup

You can download LaTeX by going to the following website:

and selecting a version for your operating system:

For windows, you can get the proTeXt distribution:

Extract the installation folder:

and open the installation:

Install the distribution:

and make sure that it is the complete package set:

Finally, test if your LaTeX installation is working as intended. You can either open TeXWorks, or download any other TeX editor like TEXMaker and create (and save) the following code:

\documentclass[12pt]{article}

\usepackage{amsmath}

\begin{document}

\sqrt{\pi}

$$\mathbf{E} (Y) = \alpha + \beta X$$

\begin{align*}
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix} &=
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix} + \begin{pmatrix}
a & b \\
c & d
\end{pmatrix} \\
&- \begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\end{align*}

\end{document}

To compile the .tex document into a .pdf, click the arrow button:

If everything works, a separate window should open with the generated formula file.

### 2.1.2 Formula examples

Formulas in Markdown (and in LaTeX) are written between the \$ symbols for inline formulas, and between $$ symbols for centered formulas. For example, writing X_t = \sum_{j = 1}^t \epsilon_j produces the following output: $$X_t = \sum_{j = 1}^t \epsilon_j$$. Writing $$X_t = \sum_{j = 1}^t \epsilon_j$$ produces: $X_t = \sum_{j = 1}^t \epsilon_j$ #### 2.1.2.2 Matrices If we want to write a matrix, we use (either with  or $$, and using \quad to separate the different matrices)::

$$\begin{bmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{bmatrix} \quad \begin{pmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{pmatrix}$$

which produces the following output: $\begin{bmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{bmatrix}, \quad \begin{pmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{pmatrix}$

#### 2.1.2.3 Equation aligning

Using the align environment and writing & next to the symbols we want to align in each row lets us specify multiple equations aligned by the same symbol, for example:

\begin{aligned} Y_{1,t} &= \alpha_1 + \beta_1 X_{1,t} + \epsilon_{1,t} \\ Y_{2,t} &= \alpha_1 + \beta_1 X_{1,t} + \epsilon_{1,t} \end{aligned}

Produces:

\begin{aligned} Y_{1,t} &= \alpha_1 + \beta_1 X_{1,t} + \epsilon_{1,t} \\ Y_{2,t} &= \alpha_1 + \beta_1 X_{1,t} + \epsilon_{1,t} \end{aligned}

Or if we need to write our equation in a different form:

\begin{aligned} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \end{aligned}

\begin{aligned} f(x) &= (a+b)^2 \\ &= a^2+2ab+b^2 \end{aligned}

Or if we simply have longer names for our variables:

\begin{aligned}
Population_t &= \alpha_1 + \gamma_1 X_{1,t} + \gamma_2 X_{1,t-1} \\
Price_t &= \alpha_2 + \beta_1 Z_{1,t}
\end{aligned}

\begin{aligned} Population_t &= \alpha_1 + \gamma_1 X_{1,t} + \gamma_2 X_{1,t-1} \\ Price_t &= \alpha_2 + \beta_1 Z_{1,t} \end{aligned}

#### 2.1.2.4 Writing equation systems

We can write the equation systems using the cases environment (note - we are also using the & symbol to align our equations):

$$f(n) = \begin{cases} n/2 &\mbox{if } n \equiv 0 \\ (3n +1)/2 & \mbox{if } n \equiv 1. \end{cases} \pmod{2}$$

$f(n) = \begin{cases} n/2 &\mbox{if } n \equiv 0 \\ (3n +1)/2 & \mbox{if } n \equiv 1. \end{cases} \pmod{2}$