igbuend/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

| 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 |