% Common Mathematical Notation
% Mort Yao
% 2016-12-18

| Symbols  | Semantics                                         | LaTeX        |
| :------- | :------------------------------------------------ | :----------- |
| $a$, $b$ | (known) variable or element of a set |
| $c$ | constant |
| $e$ | mathematical constant $e$ (Euler's number) |
| $\pi$ | mathematical constant $\pi$ | `\pi`
| $\varepsilon$ | small positive infinitesimal quantity | `\varepsilon`
| $i$ | general integer; subscript or superscript; imaginary unit |
| $j$, $k$, $l$ | general integer; subscript or superscript |
| $n$, $m$ | general natural number; total number |
| $p$ | general prime number; general probability |
| $q$ | general prime number |
| $x$, $y$ | (unknown) variable or element of a set; coordinate |
| $z$, $w$ | general complex number; coordinate |
| $\vert x \vert$, $\vert z \vert$ | absolute value |
| $\bar{z}$ | complex conjugate | `\bar{z}`
| $\Re(z)$; $\operatorname{Re}(z)$ | real part | `\Re{z}`
| $\Im(z)$; $\operatorname{Im}(z)$ | imaginary part | `\Im(z)`
| $\mathcal{E}$ | experiment | `\mathcal{E}`
| $A$, $B$ | (known) set; event |
| $S$, $\Omega$ | set; class of sets; sample space |
| $U$ | universal set |
| $A^\complement$; $\overline{A}$; $\complement_U A$ | complement of set | `A^\complement`
| $\varnothing$ | empty set | `\varnothing`
| $X$, $Y$ | (unknown) set; random variable |
| $\mathcal{X}$, $\mathcal{Y}$ | set with special structure, space | `\mathcal{X}`
| $\mathcal{P}(S)$; $2^S$ | power set | `\mathcal{P}(S)`
| $\vert S \vert$; $\operatorname{Card}(S)$ | cardinality of set |
| $\aleph_0$ | cardinality of natural numbers (Aleph-naught) | `\aleph_0`
| $\mathfrak{c}$ | cardinality of continuum | `\mathfrak{c}`
| $\mathbb{N}$ | set of natural numbers | `\mathbb{N}`
| $\mathbb{Z}^+$ | set of positive integers | `\mathbb{Z}^+`
| $\mathbb{Z}$ | set of integers | `\mathbb{Z}`
| $\mathbb{Q}$ | set of rational numbers | `\mathbb{Q}`
| $\mathbb{R}$ | set of real numbers | `\mathbb{R}`
| $\mathbb{R}^n$ | $n$-dimensional real coordinate space | `\mathbb{R}^n`
| $\mathbb{C}$ | set of complex numbers | `\mathbb{C}`
| $\mathbb{C}^n$ | $n$-dimensional complex coordinate space | `\mathbb{C}^n`
| $\mathbf{A}$, $\mathbf{B}$, $\mathbf{X}$, $\mathbf{Y}$ | matrix | `\mathbf{A}`
| $\boldsymbol{a}$, $\boldsymbol{b}$, $\boldsymbol{x}$, $\boldsymbol{y}$ | vector | `\boldsymbol{a}`
| $\boldsymbol{e}$, $\boldsymbol{i}$, $\boldsymbol{j}$, $\boldsymbol{k}$ | unit vector |
| $\boldsymbol{v}$ | eigenvector |
| $\lambda$ | eigenvalue | `\lambda`
| $\vert\vert \boldsymbol{a} \vert\vert$, $\vert\vert \mathbf{A} \vert\vert$ | norm |
| $\langle \boldsymbol{a},\boldsymbol{b} \rangle$ | inner product of vectors |
| $\mathbf{I}_n$ | identity matrix of size $n$ |
| $\operatorname{diag}(a_1,\dots,a_n)$ | diagonal matrix of size $n$ |
| $\delta_{ij}$ | Kronecker delta | `\delta_{ij}`
| $\mathbf{A}^{\rm T}$ | transpose of matrix | `\mathbf{A}^{\rm T}`
| $\mathbf{A}^{-1}$ | inverse of matrix | `\mathbf{A}^{-1}`
| $\operatorname{rank}(\mathbf{A})$ | rank of matrix |
| $\det(\mathbf{A})$ | determinant of matrix | `\det(\mathbf{A})`
| $f$, $g$, $h$ | function or mapping |
| $\varphi$ | function or mapping with special property | `\varphi`
| $\delta$ | Dirac delta function | `\delta`
| $\eta$ | Dedekind eta function | `\eta`
| $\psi$, $\Psi$ | wave function | `\psi`
| $\wp$ | Weierstrass's elliptic function | `\wp`
| $\operatorname{negl}(x)$ | negligible function |
| $\min(S)$ | minimum | `\min(S)`
| $\max(S)$ | maximum | `\max(S)`
| $\sup(S)$ | supremum | `\sup(S)`
| $\inf(S)$ | infimum | `\inf(S)`
| $\lim(f(x))$; $\lim(a_n)$ | limit | `\lim(f(x))`
| $d{x}$ | differential operator |
| $\partial{x}$ | partial differential operator | `\partial{x}`
| $\Delta$ | forward difference; Laplace operator | `\Delta`
| $\nabla$ | backward difference; gradient | `\nabla`
| $e^{x}$; $\exp(x)$ | exponential function |
| $\ln(x)$ | natural logarithm | `\ln(x)`
| $\log(x)$ | logarithm | `\log(x)`
| $\mathcal{A}$ | algorithm | `\mathcal{A}`
| $\mathcal{O}(f(n))$ | big-O notation | `\mathcal{O}(f(n))`
| $\Omega(f(n))$ | big-Omega notation | `\Omega(f(n))`
| $\Theta(f(n))$ | big-Theta notation | `\Theta(f(n))`
| $p_X \left({x}\right)$ | probability mass function (pmf) | `p_X(x)`
| $\Pr[X=x]$ | probability measure | `\Pr[X=x]`
| $\operatorname{E}[X]$; $\mu$ | expectation | `\operatorname{E}[X]`
| $\operatorname{Cov}(X,Y)$ | covariance | `\operatorname{Cov}(X,Y)`
| $\operatorname{Var}(X)$ | variance | `\operatorname{Var}(X)`
| $\sigma$ | standard deviation | `\sigma`
| $s$ | (unbiased) sample standard deviation |
| $\bar{X}$ | sample mean | `\bar{X}`
| $X \sim \operatorname{Pois}(\lambda)$ | random variable that satisfies a probability distribution | `\sim`