amsmath

Extends LaTeX's mathematical typesetting capabilities with advanced environments, commands, and tools for formatting complex mathematical expressions.

Overview

Serves as the foundation for serious mathematical typesetting in LaTeX, providing comprehensive facilities for creating professional-quality mathematical documents. The package significantly enhances LaTeX's native math capabilities and is considered essential for academic and scientific writing.

Offers sophisticated environments like align, gather, and multline for precise equation alignment and multi-line mathematical expressions
Includes specialized tools for matrices, fractions, operator names, and bold mathematical symbols
Automatically loads complementary packages for bold symbols, operator names, and text within mathematics
Widely adopted in academic journals, research papers, mathematical textbooks, and scientific documentation
Compatible with numerous extension packages that add specialized mathematical formatting features

Getting Started

To use amsmath, include it in your document preamble:

\documentclass{article}
\usepackage{amsmath}

The package automatically loads amsbsy, amsopn, and amstext packages, so you don't need to include them separately.

Examples

Using the align environment for multiple equations with alignment.

We can align multiple equations at the equals sign:
\begin{align}
  x^2 + y^2 &= z^2 \\
  x^3 + y^3 &= z^3 + 1 \\
  x^4 + y^4 &= z^4 + 2
\end{align}

Creating a piecewise function with the cases environment.

The absolute value function can be defined as:
\[
|x| = \begin{cases}
  x, & \text{if } x \geq 0 \\
  -x, & \text{if } x < 0
\end{cases}
\]

Using matrices and equation numbering with tags.

The matrix multiplication is given by:
\begin{equation}\label{eq:matrix-mult}
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
\begin{pmatrix} e & f \\ g & h \end{pmatrix} =
\begin{pmatrix} ae+bg & af+bh \\ ce+dg & cf+dh \end{pmatrix}
\end{equation}

We can also create a custom tag for an equation:
\begin{equation}\tag{Euler's Identity}
 e^{i\pi} + 1 = 0
\end{equation}