amsmath

# amsmath + amssymb + mathtools — Math Typesetting **CTAN:** https://ctan.org/pkg/amsmath | https://ctan.org/pkg/mathtools **Manual:** `texdoc amsmath`, `texdoc mathtools` ## Setup ```latex \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 ```latex % 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 ```latex \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 ```latex \begin{gather} x + y = 1 \\ x - y = 3 \end{gather} ``` ### multline — Long Single Equation ```latex \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 ```latex \begin{equation} \begin{split} f(x) &= a + b + c \\ &\quad + d + e \end{split} \end{equation} ``` Single equation number for the group. ### cases ```latex \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 ```latex % Use inside equation or \[ \] for sub-alignment \begin{equation} \left\{ \begin{aligned} 2x + 3y &= 7 \\ x - y &= 1 \end{aligned} \right. \end{equation} ``` ### subequations ```latex \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 | Environment | Alignment | Numbering | Use for | |-------------|-----------|-----------|---------| | `equation` | centered | one number | single equation | | `align` | `&` columns | per line | aligned equations | | `gather` | centered | per line | unrelated equations | | `multline` | first L, last R | one number | long equation | | `split` | `&` columns | one number (parent) | sub-align in equation | | `cases` | `&` columns | none (in equation) | piecewise functions | | `aligned` | `&` columns | none (in equation) | inline sub-alignment | | `flalign` | `&` columns | per line | full-width alignment | Add `*` for unnumbered variants (except `split`, `aligned`, `gathered`). ## Text in Math ```latex \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 | Command | Width | Example | |---------|-------|---------| | `\,` | 3/18 em (thin) | `\int f(x)\, dx` | | `\:` or `\>` | 4/18 em (medium) | | | `\;` | 5/18 em (thick) | | | `\!` | −3/18 em (negative thin) | `\!\!` to tighten | | `\quad` | 1 em | `x \quad y` | | `\qquad` | 2 em | | | `\phantom{x}` | space of "x" | alignment trick | | `\hphantom{x}` | horizontal only | | | `\vphantom{x}` | vertical only | | ## Operators ```latex % 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 ```latex \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 ```latex % 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 ```latex % 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 | Lower | Upper | Lower | Upper | |-------|-------|-------|-------| | `\alpha` α | — | `\nu` ν | — | | `\beta` β | — | `\xi` ξ | `\Xi` Ξ | | `\gamma` γ | `\Gamma` Γ | `\pi` π | `\Pi` Π | | `\delta` δ | `\Delta` Δ | `\rho` ρ | — | | `\epsilon` ε | — | `\sigma` σ | `\Sigma` Σ | | `\varepsilon` ε | — | `\tau` τ | — | | `\zeta` ζ | — | `\upsilon` υ | `\Upsilon` Υ | | `\eta` η | — | `\phi` ϕ | `\Phi` Φ | | `\theta` θ | `\Theta` Θ | `\varphi` φ | — | | `\iota` ι | — | `\chi` χ | — | | `\kappa` κ | — | `\psi` ψ | `\Psi` Ψ | | `\lambda` λ | `\Lambda` Λ | `\omega` ω | `\Omega` Ω | | `\mu` μ | — | | | Variants: `\varepsilon`, `\vartheta`, `\varphi`, `\varrho`, `\varsigma` ### Relations | Symbol | Command | Symbol | Command | |--------|---------|--------|---------| | ≤ | `\leq` | ≥ | `\geq` | | ≪ | `\ll` | ≫ | `\gg` | | ≠ | `\neq` | ≈ | `\approx` | | ∼ | `\sim` | ≃ | `\simeq` | | ≡ | `\equiv` | ≅ | `\cong` | | ∝ | `\propto` | ∈ | `\in` | | ∉ | `\notin` | ⊂ | `\subset` | | ⊆ | `\subseteq` | ⊃ | `\supset` | | ⊇ | `\supseteq` | ⊄ | `\not\subset` | | ≺ | `\prec` | ≻ | `\succ` | | ⊥ | `\perp` | ∥ | `\parallel` | | ⊢ | `\vdash` | ⊣ | `\dashv` | | ⊨ | `\models` | | | ### Binary Operators | Symbol | Command | Symbol | Command |