Amsmath

amsmath + amssymb + mathtools — Math Typesetting

CTAN: https://ctan.org/pkg/amsmath | https://ctan.org/pkg/mathtools
Manual: texdoc amsmath, texdoc mathtools

Setup

\usepackage{amsmath}    % core math environments
\usepackage{amssymb}    % extra symbols (loads amsfonts)
\usepackage{mathtools}  % fixes + extensions for amsmath (loads amsmath)
\usepackage{amsthm}     % theorem environments

% mathtools loads amsmath, so you can just use:
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{amsthm}

Equation Environments

Single Equations

% Numbered
\begin{equation}
  E = mc^2
  \label{eq:einstein}
\end{equation}

% Unnumbered
\begin{equation*}
  E = mc^2
\end{equation*}
% or: \[ E = mc^2 \]

align — Multiple Aligned Equations

\begin{align}
  f(x) &= x^2 + 2x + 1 \label{eq:f} \\
       &= (x+1)^2       \label{eq:f2}
\end{align}

% Unnumbered: align*
% Suppress single number: \nonumber or \notag before \\

gather — Centered, No Alignment

\begin{gather}
  x + y = 1 \\
  x - y = 3
\end{gather}

multline — Long Single Equation

\begin{multline}
  f(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 \\
    + a_4 x^4 + a_5 x^5 + a_6 x^6
\end{multline}

First line left-aligned, last line right-aligned, middle centered.

split — Sub-alignment Inside equation

\begin{equation}
\begin{split}
  f(x) &= a + b + c \\
       &\quad + d + e
\end{split}
\end{equation}

Single equation number for the group.

cases

\begin{equation}
  |x| = \begin{cases}
    x  & \text{if } x \geq 0 \\
    -x & \text{if } x < 0
  \end{cases}
\end{equation}

% mathtools: dcases (displaystyle), rcases (right brace)
\begin{dcases}
  \frac{x}{2} & x > 0 \\
  0            & x = 0
\end{dcases}

aligned / gathered — Inline Sub-environments

% Use inside equation or \[ \] for sub-alignment
\begin{equation}
  \left\{
  \begin{aligned}
    2x + 3y &= 7 \\
    x - y   &= 1
  \end{aligned}
  \right.
\end{equation}

subequations

\begin{subequations} \label{eq:system}
\begin{align}
  x + y &= 1 \label{eq:system_a} \\
  x - y &= 3 \label{eq:system_b}
\end{align}
\end{subequations}
% Produces (1a), (1b)

Environment Summary

Add * for unnumbered variants (except split, aligned, gathered).

Text in Math

\text{if }           % normal text (respects surrounding font)
\mathrm{const}       % upright roman
\textit{word}        % italic text
\mathit{diff}        % math italic (different spacing than default)
\mathbf{v}           % bold (not for Greek — use \boldsymbol)
\boldsymbol{\alpha}  % bold Greek
\mathbb{R}           % blackboard bold: ℝ (amssymb)
\mathcal{L}          % calligraphic: ℒ
\mathfrak{g}         % Fraktur (amssymb)
\mathsf{X}           % sans-serif
\mathtt{code}        % monospace
\operatorname{span}  % upright operator (one-off)

Spacing in Math

Operators

% Built-in: \sin, \cos, \tan, \log, \ln, \exp, \min, \max,
%   \sup, \inf, \lim, \det, \dim, \ker, \gcd, \Pr, \hom, ...

% Custom operator (preamble)
\DeclareMathOperator{\tr}{tr}       % like \sin
\DeclareMathOperator*{\argmax}{arg\,max}  % limits below in display

% Usage
\tr(A) = \sum_i a_{ii} \qquad x^* = \argmax_x f(x)

Matrices

\begin{pmatrix} a & b \\ c & d \end{pmatrix}   % ( )
\begin{bmatrix} a & b \\ c & d \end{bmatrix}   % [ ]
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}   % { }
\begin{vmatrix} a & b \\ c & d \end{vmatrix}   % | |  (determinant)
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}   % ‖ ‖
\begin{matrix}  a & b \\ c & d \end{matrix}    % no delimiters

% Small inline matrix
$\bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\bigr)$

Max columns default = 10. For more: \setcounter{MaxMatrixCols}{20}

Delimiters

% Auto-sizing (use sparingly — can oversize)
\left( \frac{a}{b} \right)
\left[ \sum_i x_i \right]
\left\{ x \in \mathbb{R} \mid x > 0 \right\}
\left. \frac{df}{dx} \right|_{x=0}   % \left. = invisible delimiter

% Manual sizing (preferred for control)
\bigl(  \bigr)    % slightly bigger
\Bigl(  \Bigr)    % bigger
\biggl( \biggr)   % even bigger
\Biggl( \Biggr)   % biggest

% mathtools paired delimiters (best approach)
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
\DeclarePairedDelimiter\set{\{}{\}}

% Usage:
\abs{x}       % |x|  (no sizing)
\abs*{x}      % \left|x\right|  (auto-sizing)
\abs[\big]{x} % \bigl|x\bigr|  (manual)

mathtools Additions

% Colon equals
\coloneqq   % :=
\eqqcolon   % =:

% dcases (displaystyle fractions in cases)
\begin{dcases} ... \end{dcases}

% rcases (right brace)
\begin{rcases} ... \end{rcases}

% Short intertext (less vertical space than \intertext)
\begin{align}
  f(x) &= x^2 \\
  \shortintertext{where}
  x &> 0
\end{align}

% Prescript (left sub/superscript)
\prescript{14}{6}{\mathrm{C}}   % ¹⁴₆C

% Cramped styles
\cramped{x^{x^x}}  % reduces height

% Smashed operator limits
\smashoperator{\sum_{i=1}^{n}}

Symbol Reference

Greek Letters

Variants: \varepsilon, \vartheta, \varphi, \varrho, \varsigma

Relations

Binary Operators

Arrows

Big Operators

Dots

Misc Symbols (amssymb)

Accents

Theorem Environments (amsthm)

\usepackage{amsthm}

% Define theorem types (preamble)
\newtheorem{theorem}{Theorem}[section]     % numbered by section
\newtheorem{lemma}[theorem]{Lemma}         % shares theorem counter
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}

\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}

% Usage
\begin{theorem}[Pythagoras]
  For a right triangle: $a^2 + b^2 = c^2$.
\end{theorem}

\begin{proof}
  Obvious. % ends with □ automatically
  % Use \qedhere to place □ at end of equation:
  % \[ a^2 + b^2 = c^2 \qedhere \]
\end{proof}

Theorem Styles

Common Pitfalls