Mathematics

The great power of LaTeX lies in it's ability to easily render mathematics. There are two types of mathematics. Inline and display.

Cheat Sheet

Many useful mathematical features require the American Mathematical Society package. Include \usepackage{amsmath} in your preamble

Inline Mathematics

Inline mathematics form part of a sentence and start and end with a single $. Eg.

To differentiate $x^n$ we multiply by the power and decrease it by 1 to get $nx^{n-1}$.

Display Mathematics

Display mathematics has it's own line and starts and end with a double $$. You can choose to make your code neater by putting in on it's own line but this is not required. Eg.

To differentiate $x^n$ we multiple by the power and decrease it by 1 to get \[nx^{n-1}\].

Aligned Mathematics

Sometimes we want to align the equals sign on multiple mathematical steps. To do this we need to use the amsmath package by including the line

\usepackage{amsmath} 

at the top of our document.

We can then use the align environment with a & sign before the symbol we want aligned to and \\ to signify the end of a line. For example:

\begin{align}
    (x+2)(x-2) &= x^2 + 2x - 2x -4 \\
    &= x^2 -4
\end{align}

If we don't want our equations to be numbers, we can use the align* environment:

\begin{align*}
    (x+2)(x-2) &= x^2 + 2x - 2x -4 \\
    &= x^2 -4
\end{align*}

Symbols

Powers

Roots

Fractions

Inequalities

The basic less than / more than inequalities are just represented by < and >. We can use \leq for less than or equal to and \geq for greater than or equal to

\begin{align*}
    3 &> 2 \\
    2 &< 3 \\
    x &\leq 2 \\
    x &\geq 2
\end{align*}

Limits

Sums

Calculus

Sets