# Common Mathematical Notation

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