AMS- LATEX Q u i c k R e f e rence
Packages
Mathematical font
Braces
The main package to load is amsmath. More symbols
are included in amssymb.
ABCDEFGHIJKLMNOPQRSTUVWXYZ
\mathcal{ letter }
\overbrace{ . . . }^{ text over brace }
\underbrace{ . . . }_{ text under brace }
Typeset
Superscript & Subscript
Accents
For text style (inline) math, use: $ . . . $
For display style math, which breaks the paragraph:
\begin{equation} . . . \end{equation} (numbered) or
\[ . . . \] (non-numbered).
xy
xy
â
ǎ
ã
Greek letters
α
δ
ζ
ϑ
λ
ξ
ρ
τ
ϕ
ω
Γ
Λ
Σ
Ψ
\alpha
\delta
\zeta
\vartheta
\lambda
\xi
\rho
\tau
\varphi
\omega
\Gamma
\Lambda
\Sigma
\Psi
β
η
ι
µ
π
ρ
υ
χ
∆
Ξ
Υ
Ω
\beta
\epsilon
\eta
\iota
\mu
\pi
\varrho
\upsilon
\chi
\Delta
\Xi
\Upsilon
\Omega
γ
ε
θ
κ
ν
$
σ
φ
ψ
Θ
Π
Φ
\gamma
\varepsilon
\theta
\kappa
\nu
\varpi
\sigma
\phi
\psi
\Theta
\Pi
\Phi
To ensure a consistent style throughout the document:
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\theta}{\vartheta}
\renewcommand{\rho}{\varrho}
\renewcommand{\phi}{\varphi}
xa+b
xa+b
x^y
x_y
x^{a+b}
x_{a+b}
Root
Square root
N-th root
√
x
√
N
x
ā
ȧ
ä
\hat{a}
\check{a}
\tilde{a}
\bar{a}
\dot{a}
\ddot{a}
å
a
~
[
AAA
\mathring{a}
\vec{a}
\widehat{AAA}
Operators
\sqrt{x}
\sqrt[N]{x}
Dots
Multiplication dot
Three centered dots
Three baseline dots
·
···
...
\cdot
\cdots
\ldots
Three diagonal dots
..
\ddots
Three vertical dots
..
.
.
\vdots
\sin
\cosh
\max
\cot
\cos
\tan
\min
\sec
\arcsin
\arctan
\sup
\csc
\arccos
\log
\inf
\det
\sinh
\ln
\tanh
To define a custom operator:
\DeclareMathOperator{\argmax}{argmax}
Modulo
a mod b
a ≡ b (mod m)
a \bmod b
a \equiv b \pmod{m}
Spaces
Fractions
Negative space
Thinnest space
Thin space
Medium space
1em space
2em space
\!
\,
\:
\;
\quad
\qquad
\frac{ . . . }{ . . . }
Symbol stacking
\overset{ . . . }{ . . . }
\underset{ . . . }{ . . . }
First argument is the main symbol, second argument
is the symbol to put over or under the main symbol.
Big operators
Arrows
Zb
n
X
\int_{a}^{b}
\sum_{k=0}^{n}
a
k=0
n
Y
lim
\prod_{k=0}^{n}
x→0
k=0
RR
For multiple integrals:H \iint
Closed path integral: \oint
\lim_{x \to 0}
RRR
\iiint etc.
Delimiter size
Change the delimiter size by adding one of these
modifiers immediately before the delimiter itself:
Logic symbols
↑ \uparrow ↓ \downarrow l \updownarrow
⇑ \Uparrow ⇓ \Downarrow m \Updownarrow
← \leftarrow or \gets → \rightarrow or \to
↔ \leftrightarrow
⇐ \Leftarrow
⇒ \Rightarrow
⇔ \Leftrightarrow
7→ \mapsto
←− \longleftarrow
−→ \longrightarrow
←→ \longleftrightarrow
⇐= \Longleftarrow
=⇒ \Longrightarrow
⇐⇒ \Longleftrightarrow
7−→ \longmapsto
\big \Big \bigg \Bigg
Let LATEX determine the correct size using \left and
\right immediately before the opening and closing
Binary relations
delimiters, respectively.
6=
≡
.
=
⊂
⊆
∈
|
Absolute value & Norm
|x|
kxk
\lvert x \rvert
\lVert x \rVert
The same can be achieved by defining:
\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
Use starred variants \abs* and \norm* to produce the
correct delimiter height for any kind of equation.
|x|
\abs{x}
kxk
\norm{x}
a
b
a
b
\abs*{\frac{a}{b}}
\norm*{\frac{a}{b}}
\le
\ll
\sim
\supset
\supseteq
\ni
\parallel
⩾
≃
≈
∼
=
∝
⊥
\ge
\gg
\simeq
\approx
\cong
\propto
\perp
It’s possible to negate these symbols by prefixing
them with \not (for example: 6≡ \not\equiv)
Binary operators
±
÷
?
∗
⊕
\pm
\div
\star
\ast
\oplus
\oslash
∓
×
∪
◦
⊗
\lor
\exists
\implies
∧
@
⇐⇒
\land
\nexists
\iff
¬
∀
|=
∞
∂
∅
∇
hxi
\infty
\partial
\emptyset
\nabla
\langle x \rangle
\neg
\forall
\models
Other symbols
Infinity
Partial derivative
Empty set
Nabla
Angle brackets
Multi line equations
Use the multline environment:
\begin{multline} . . . \end{multline}
⩽
∼
⊃
⊇
3
k
\ne
\equiv
\doteq
\subset
\subseteq
\in
\mid
∨
∃
=⇒
\mp
\times
\cup
\circ
\ominus
\otimes
To align equations, use the align environment.
Specify the alignment position with & and separate
equations with \\:
\begin{align}
. . . &= . . . \\
. . . &= . . .
\end{align}
Vectors
~x
x
·
\
∩
•
r
\cdot
\setminus
\cap
\bullet
\odot
\smallsetminus
\vec{x}
\bm{x} (needs bm package)
Best practice to easily switch between types:
\usepackage{bm}
\renewcommand{\vec}{\bm}
Arrays
Matrices
Use the array environment. Use \\ to separate rows,
and & to separate elements of each row. To produce
large delimiters around the array, use \left and
\right followed by the desired delimiter.
Use one of the following environments:

a
 d
g
b
e
h

c
f 
i
\left(
\begin{array}{lcr}
a & b & c \\
d & e & f \\
g & h & i
\end{array}
\right)
Each letter in the argument of the array represents a
column:
left aligned text
centered text
right aligned text
l
c
r
Use the cases environment. Use \\ to separate
different cases, and & for correct alignment.
x
0
Use \\ to separate different rows, and & to separate
elements of each row.
1
4
2
5
3
6
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6
\end{bmatrix}
To produce a small matrix, useful
bfor
inline math, use
the smallmatrix environment: ac d
.
Blackboard bold
Cases
No delimiter
( delimiter
[ delimiter
{ delimiter
| delimiter
k delimiter
matrix
pmatrix
bmatrix
Bmatrix
vmatrix
Vmatrix
if x > 0
if x ⩽ 0
\begin{cases}
x & \text{if } x > 0 \\
0 & \text{if } x \le 0
\end{cases}
Include the package bbm for these symbols.
Blackboard 1
Blackboard R
All letters are supported.
1
R
\mathbb{1}
\mathbb{R}