微信扫一扫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
| 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
\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
% 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
| 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 |
|--------|---------|--------|---------|
| ± | \pm | ∓ | \mp |
| × | \times | ÷ | \div |
| · | \cdot | ∗ | \ast |
| ⊕ | \oplus | ⊗ | \otimes |
| ∪ | \cup | ∩ | \cap |
| ∨ | \vee | ∧ | \wedge |
| ∘ | \circ | • | \bullet |
| † | \dagger | ‡ | \ddagger |
Arrows
| Symbol | Command | Symbol | Command |
|--------|---------|--------|---------|
| → | \to / \rightarrow | ← | \leftarrow |
| ⇒ | \Rightarrow | ⇐ | \Leftarrow |
| ↔ | \leftrightarrow | ⇔ | \Leftrightarrow |
| ↦ | \mapsto | ⟶ | \longrightarrow |
| ↑ | \uparrow | ↓ | \downarrow |
| ⇑ | \Uparrow | ⇓ | \Downarrow |
| ↗ | \nearrow | ↘ | \searrow |
| ⟹ | \implies | ⟸ | \impliedby |
| ⟺ | \iff | | |
| ↪ | \hookrightarrow | ↠ | \twoheadrightarrow |
Big Operators
| Symbol | Command | Symbol | Command |
|--------|---------|--------|---------|
| ∑ | \sum | ∏ | \prod |
| ∫ | \int | ∮ | \oint |
| ∬ | \iint | ∭ | \iiint |
| ⋃ | \bigcup | ⋂ | \bigcap |
| ⨁ | \bigoplus | ⨂ | \bigotimes |
| ⋁ | \bigvee | ⋀ | \bigwedge |
| ∐ | \coprod | | |
Dots
| Command | Output | Use |
|---------|--------|-----|
| \cdots | ⋯ | between operators: $a + \cdots + z$ |
| \ldots | … | in lists: $a_1, \ldots, a_n$ |
| \vdots | ⋮ | vertical |
| \ddots | ⋱ | diagonal (matrices) |
Misc Symbols (amssymb)
| Symbol | Command | Symbol | Command |
|--------|---------|--------|---------|
| ℝ | \mathbb{R} | ℂ | \mathbb{C} |
| ℤ | \mathbb{Z} | ℕ | \mathbb{N} |
| ℚ | \mathbb{Q} | ∅ | \emptyset / \varnothing |
| ∞ | \infty | ∂ | \partial |
| ∇ | \nabla | ℓ | \ell |
| ℏ | \hbar | ∀ | \forall |
| ∃ | \exists | ¬ | \neg |
| √ | \sqrt{x} | ⁿ√ | \sqrt[n]{x} |
| ∠ | \angle | △ | \triangle |
| ⊤ | \top | ⊥ | \bot |
| ♠ | \spadesuit | ♣ | \clubsuit |
Accents
| Command | Result | Use |
|---------|--------|-----|
| \hat{a} | â | unit vectors |
| \bar{a} | ā | averages, conjugates |
| \vec{a} | a⃗ | vectors |
| \dot{a} | ȧ | time derivative |
| \ddot{a} | ä | second derivative |
| \tilde{a} | ã | approximations |
| \widehat{abc} | wide hat | spanning |
| \widetilde{abc} | wide tilde | spanning |
| \overline{abc} | overline | sets, conjugates |
| \underline{abc} | underline | |
| \overbrace{a+b}^{n} | over-brace | grouping |
| \underbrace{a+b}_{n} | under-brace | grouping |
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
| Style | Body font | Header | Use for |
|-------|-----------|--------|---------|
| plain (default) | italic | bold | theorems, lemmas |
| definition | upright | bold | definitions, examples |
| remark | upright | italic | remarks, notes |
Common Pitfalls
| Problem | Cause | Fix |
|---------|-------|-----|
| $$...$$ | TeX primitive, bad spacing | Use \[...\] or equation* |
| eqnarray | Bad spacing around = | Use align instead (always) |
| Equation number on wrong line | \\ after last line | Remove trailing \\ |
| \left...\right across lines | Can't span \\ | Use \bigl...\bigr manually |
| Bold Greek | \mathbf doesn't work | Use \boldsymbol{\alpha} |
| Missing \displaystyle | Fractions small inline | Use \dfrac (or \displaystyle\frac) |
| := spacing wrong | Colon treated as relation | Use \coloneqq (mathtools) |
| \mid vs \| vs | | Different spacing | \mid for "divides"/"given", \| for norms |
| Overfull hbox in equation | Equation too wide | Use multline, split, or manual breaks |
| Proof box missing | \qed inside environment | Use \qedhere at the end |