**Learn to typeset and align equations, matrices and fractions in LaTeX. Overview of basic math features, with live-rendering.**

There are two major modes of typesetting math in LaTeX one is embedding the math directly into your text by *encapsulating* your formula in *dollar signs* and the other is using a predefined *math environment. *You can follow along and try the code in your computer or online using overleaf. I also prepared a quick reference of

## Using inline math – embed formulas in your text

To make use of the inline math feature, simply write your text and if you need to typeset a single math symbol or formula, surround it with dollar signs:

... This formula $f(x) = x^2$ is an example. ...

Output equation: \(\text{This formula }f(x) = x^2\text{ is an example.}\)

## The equation and align environment

The most useful *math envorinments *are the *equation environment* for typesetting single equations and the *align *environment for multiple equations and automatic alignment:

\documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation*} 1 + 2 = 3 \end{equation*} \begin{equation*} 1 = 3 - 2 \end{equation*} \begin{align*} 1 + 2 &= 3\\ 1 &= 3 - 2 \end{align*} \end{document}

Output Equation:

\(\begin{equation}1 + 2 = 3\end{equation}\)

\(\begin{equation}1 = 3 – 2\end{equation}\)

Output Align:

\(\begin{align} 1 + 2 & = 3\\ 1 & = 3 – 2 \end{align}\)

The *align *environment will align the equations at the *ampersand &*. Single equations have to be* seperated *by a *linebreak \\*. There is no alignment when using the simple* equation *environment. Furthermore it is not even possible to enter two equations in that environment, it will result in a *compilation error*. The asterisk (e.g. equation*) only indicates, that I don’t want the equations to be numbered.

## Fractions and more

LaTeX is capable of displaying any mathematical notation. It’s possible to typeset integrals, fractions and more. Every command has a specific syntax to use. I will demonstrate some of the most common LaTeX math features:

\documentclass{article} \usepackage{amsmath} \begin{document} \begin{align*} f(x) &= x^2\\ g(x) &= \frac{1}{x}\\ F(x) &= \int^a_b \frac{1}{3}x^3 \end{align*} \end{document}

Output:

\(\begin{align*} f(x) &= x^2\\ g(x) &= \frac{1}{x}\\ F(x) &= \int^a_b \frac{1}{3}x^3 \end{align*}\)

It is also possible to combine various commands to create more sophisticated expressions such as:

\frac{1}{\sqrt{x}}

Output: \(\frac{1}{\sqrt{x}}\)

The more complex the expression, the more error prone this is, it’s important to take care of opening and closing the braces* {}*. It can take a long time to debug such errors. The *Lyx* program offers a great formula editor, which can ease this work a bit. Personally, I write all code by hand though, since it’s faster than messing around with the formula editor.

## Matrices

Furthermore it’s possible to display matrices in LaTeX. There is a special matrix environment for this purpose, please keep in mind that the matrices only work within math environments as described above:

\begin{matrix} 1 & 0\\ 0 & 1 \end{matrix}

Output: \(\begin{matrix} 1 & 0\\ 0 & 1 \end{matrix}\)

## Brackets in math mode – Scaling

To surround the matrix by brackets, it’s necessary to use special statements, because the plain [ ] symbols do not scale as the matrix grows. The following code will result in wrong brackets:

[ \begin{matrix} 1 & 0\\ 0 & 1 \end{matrix} ]

Output: \([ \begin{matrix} 1 & 0\\ 0 & 1 \end{matrix} ]\)

To scale them up, we must use the following code:

\left[ \begin{matrix} 1 & 0\\ 0 & 1 \end{matrix} \right]

Output: \( \left[ \begin{matrix} 1 & 0\\ 0 & 1 \end{matrix} \right] \)

This does also work for parentheses and braces and is not limited to matrices. It can be used to scale for fractions and other expressions as well:

\left(\frac{1}{\sqrt{x}}\right)

Output: \(\left(\frac{1}{\sqrt{x}}\right)\)

## Summary

- LaTeX is a
*powerful*tool to typeset math *Embed formulas*in your text by*surrounding*them with*dollar signs $*- The
*equation environment*is used to typeset*one*formula - The
*align environment*will align formulas at the*ampersand & symbol* - Single formulas
*must*be seperated with*two backslashes \\* - Use the
*matrix environment*to typeset matrices - Scale parentheses with
*\left( \right)*automatically - All mathematical expressions have a unique command with unique syntax
- Notable examples are:
- \int^a_b for integral symbol
- \frac{u}{v} for fractions
- \sqrt{x} for square roots

- Characters for the
*greek alphabet*and other*mathematical symbols*such as*\lambda*

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