math.Rmd

# Math

Want to include equations in your writing?
Easy.
R Markdown supports LaTeX style equation writing.
This section introduces the two types equations, inline, and display form, and how to number equations.

## Overview

* **Teaching**: 10 minutes
* **Exercises**: 10 minutes

## Questions

- How to I create an equation?
- LaTeX is funky, what are the basic math commands?

## Objectives

## Some history {.history}

Equation editing was first made available in TeX, which later become LaTeX, named after Leslie Lamport.

## Anatomy of Equations

This section shows you some basic equations types that you want to be familiar with.

Inline equations are referenced by a pair of dollar signs: `$`.

```
So this text would have an equation here $ E = mc^2$
```

Generates:

So this text would have an equation here $ E = mc^2$

Display equations are referenced by two pairs of dollar signs:

```
$$
E = mc^2
$$
```

<!-- TODO: will need to display the unevaluated LaTeX code? -->

$$
E = mc^2
$$

#### Viewing equations

Understanding whether or not you have created the right equation can be difficult. RStudio provides previews of your equations in text (**demo**).

## Example math commands

LaTeX is an amazing language, but understanding how to create the equations can be (more than) a bit confusing at times.
This section demonstrates some example equations that you might be familiar with.


#### Fractions

$$
\frac{1}{2}
$$

#### Sub and Super Scripts

$$
Y = X_1 + X_2
$$

$$
a^2 + b^2 = c^2
$$

#### Square roots

$$
\sqrt{p}
$$
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

#### Summations

$$
\sum_{i = 1}^{n}{(\bar{x} - x_i)^2}
$$
#### Bayes Rule

$$
Pr(\theta | y) = \frac{Pr(y | \theta) Pr(\theta)}{Pr(y)}
$$

$$
Pr(\theta | y) \propto Pr(y | \theta) Pr(\theta)
$$

#### Linear Model

$$
Y \sim X\beta_0 + X\beta_1 + \epsilon
$$

$$
\epsilon \sim N(0,\sigma^2)
$$


## Exercise

1. Add some math to your example document

## Further Reading:

https://bookdown.org/yihui/bookdown/markdown-extensions-by-bookdown.html#equations
https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols