Writing Mathematical Notation in LaTeX

As is well known, $\TeX$ was designed to produce beautiful books, especially books containing a lot of mathematics. Because of that, $\LaTeX$ is very strong for preparing documents with mathematical notation. To write mathematical symbols and formulas, we need to use the mathematical environment.

Displaying Mathematical Formulas

Mathematical formulas in $\TeX$ can be written between $...$ or $$...$$.

The difference is:

1. Formulas between $...$ or \(...\) appear as part of a sentence. This is called an inline equation.
2. Formulas between $$...$$ or \[...\] appear as stand-alone formulas. This is called a displayed equation.

If you want numbered equations, use the equation environment.

Example:

Inline formula: $a^2+b^2=c^2$

\[
\int_0^1 x^2 \, dx
\]

\begin{equation}
E = mc^2
\end{equation}

The output can be seen in the following image.

Subscript and Superscript

A subscript is written below a symbol and usually uses _.
A superscript is written above a symbol and usually uses ^.

Example:

$x_1,\ a_n,\ y^2,\ x^{n+1}$

The output:

Binomial and Division-Style Notation

To write binomial notation, use \binom{...}{...}.

Example:

\[
\binom{n}{r}
\]

The output:

Integrals, Roots, and Fractions

To write:

• integrals, use \int
• roots, use \sqrt{...}
• fractions, use \frac{...}{...}

Example:

\[
\int x^2 \, dx,\qquad
\sqrt{x+1},\qquad
\frac{a+b}{c+d}
\]

The output:

Matrix

To write matrices, we can use parentheses or square brackets.

Example:

\[
\begin{pmatrix}
1 & 2 \\
3 & 4
\end{pmatrix}
\qquad
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
\]

The output:

Limit

To write limits, use \lim.

Example:

\[
\lim_{x \to 0}\frac{\sin x}{x}
\]

The output:

Sigma

To write sigma notation, use \sum.

Example:

\[
\sum_{i=1}^{n} i^2
\]

The output:

Systems of Equations

Systems of equations are commonly written with curly brackets. For this, we can use the amsmath or systeme package.

Example:

\[
\begin{cases}
x+y=5 \\
2x-y=1
\end{cases}
\]

The output:

Brackets

In mathematical formulas, brackets are often used to separate expressions.

Example:

\[
\left( \frac{a+b}{c+d} \right),
\quad
\left[ x^2+y^2 \right],
\quad
\left\{ \frac{x}{y} \right\}
\]

The output:

Besides the examples above, there are many more techniques for writing mathematics in $\LaTeX$. If you want to study the symbols in more detail, the documentation can be downloaded here.

Closing

That is a short guide to writing mathematical notation in LaTeX. If you have suggestions or corrections, please leave them in the comments.