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$\mathrm{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}$

$A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z$

$\mathrm{a\,b\,c\,d\,e\,f\,g\,h\,i\,j\,k\,l\,m\,n\,o\,p\,q\,r\,s\,t\,u\,v\,w\,x\,y\,z}$

$a\,b\,c\,d\,e\,f\,g\,h\,i\,j\,k\,l\,m\,n\,o\,p\,q\,r\,s\,t\,u\,v\,w\,x\,y\,z$

$0\;1\;2\;3\;4\;5\;6\;7\;8\;9$

$\Gamma\;\Delta\;\Theta\;\Lambda\;\Xi\;\Pi\;\Sigma\;\Upsilon\;\Phi\;\Psi\;\Omega$

$\alpha\;\beta\;\gamma\;\delta\;\epsilon\;\zeta\;\eta\;\theta\;\iota\;\kappa\;\lambda\;\mu\;\nu\;\xi\;\pi\;\rho\;\sigma\;\tau\;\upsilon\;\phi\;\chi\;\psi\;\omega$

$\varepsilon\;\vartheta\;\varkappa\;\varpi\;\varrho\;\varsigma\;\varphi$

$\mathbb{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}$

$\mathcal{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}$

$\mathfrak{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}$

$+ \;-\; \times\; \div\; \pm\; \mp\; \cdot\; \circ\; \star\; \ast\; \bullet\; \oplus\; \otimes\; \odot$

$= \;\neq\; <\; >\; \leq\; \geq\; \ll\; \gg\; \approx\; \sim\; \simeq\; \cong\; \equiv\; \propto$

$\in\; \notin\; \ni\; \subset\; \supset\; \subseteq\; \supseteq\; \cap\; \cup\; \setminus\; \emptyset$

$\forall\; \exists\; \nexists\; \neg\; \land\; \lor\; \Rightarrow\; \Leftrightarrow\; \vdash\; \models\; \top\; \bot$

$\infty\; \partial\; \nabla\; \triangle\; \square\; \hbar\; \ell\; \wp\; \Re\; \Im\; \aleph$

$b\beta p\beta a\beta f\beta$   $\mathrm{b\beta p\beta a\beta f\beta}$   $\mathbf{b}\boldsymbol{\beta}\mathbf{p}\boldsymbol{\beta}\mathbf{a}\boldsymbol{\beta}\mathbf{f}\boldsymbol{\beta}$

$\alpha\boldsymbol{\alpha}$   $\beta\boldsymbol{\beta}$   $\gamma\boldsymbol{\gamma}$   $\theta\boldsymbol{\theta}$   $\sigma\boldsymbol{\sigma}$   $\Sigma\boldsymbol{\Sigma}$   $\Gamma\boldsymbol{\Gamma}$   $\Omega\boldsymbol{\Omega}$

$A\Sigma B\Gamma C\Omega$   $\mathbf{A}\boldsymbol{\Sigma}\mathbf{B}\boldsymbol{\Gamma}\mathbf{C}\boldsymbol{\Omega}$   $x\alpha y\beta z\gamma$   $\mathbf{x}\boldsymbol{\alpha}\mathbf{y}\boldsymbol{\beta}\mathbf{z}\boldsymbol{\gamma}$

$\int_a^b f(x)\,dx$   $\int_0^1 g(t)\,dt$   $\int_\Omega \nabla u \cdot \nabla v\,dx$   $\int_{-\infty}^{\infty} e^{-x^2}\,dx$   $\oint_\gamma f(z)\,dz$

$\iint_\Omega f\,dA$   $\iiint_V \rho\,dV$   $\int_0^\pi \sin\theta\,d\theta$   $\int_a^b \int_c^d f(x,y)\,dy\,dx$

The fundamental theorem of calculus states that if $F$ is an antiderivative of $f$, then $\int_a^b f(x)\,dx = F(b) - F(a)$. For instance, $\int_0^1 x^2\,dx = \frac{1}{3}$ and $\int_0^\pi \sin\theta\,d\theta = 2$. The Gaussian integral $\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}$ appears throughout probability and physics.

In complex analysis, the residue theorem gives $\oint_\gamma f(z)\,dz = 2\pi i \sum_k \operatorname{Res}(f, z_k)$, where the integral is taken over a closed contour $\gamma$. For multivariable calculus, the divergence theorem relates $\iiint_V \nabla \cdot \mathbf{F}\,dV = \iint_{\partial V} \mathbf{F}\cdot\mathbf{n}\,dS$. The energy of a signal $f$ is $E = \int_0^T |f(t)|^2\,dt$, and the Fourier transform is $\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\,e^{-2\pi i x \xi}\,dx$.

$\sum_{i=1}^n a_i$   $\prod_{j=1}^m b_j$   $\coprod_{k \in K} G_k$   $\bigcup_{i=1}^n A_i$   $\bigcap_{i=1}^n A_i$

$\int_a^b$   $\int_0^1$   $\int_\Omega$   $\oint_\gamma$   $\iint_D$   $\iiint_V$

$\sum_{i=1}^n$   $\prod_{j=1}^m$   $\bigcup_{k}^{}$   $\bigcap_{k}^{}$

The matrix $A$ has eigenvalues $\lambda_1, \ldots, \lambda_n$. Let $X$ be a topological space and $L$ a line bundle. The function $f(x) = e^{-x^2}$ is in $L^2(\mathbb{R})$. We define $T : V \to W$ where $V$ and $W$ are Banach spaces.

A $A$ B $B$ C $C$ D $D$ E $E$ F $F$ G $G$ H $H$ I $I$ J $J$ K $K$ L $L$ M $M$ N $N$ O $O$ P $P$ Q $Q$ R $R$ S $S$ T $T$ U $U$ V $V$ W $W$ X $X$ Y $Y$ Z $Z$

A $\mathbf{A}$ B $\mathbf{B}$ C $\mathbf{C}$ D $\mathbf{D}$ E $\mathbf{E}$ F $\mathbf{F}$ G $\mathbf{G}$ H $\mathbf{H}$ I $\mathbf{I}$ J $\mathbf{J}$ K $\mathbf{K}$ L $\mathbf{L}$ M $\mathbf{M}$

a $a$ b $b$ c $c$ d $d$ e $e$ f $f$ g $g$ h $h$ i $i$ j $j$ k $k$ l $l$ m $m$ n $n$ o $o$ p $p$ q $q$ r $r$ s $s$ t $t$ u $u$ v $v$ w $w$ x $x$ y $y$ z $z$

0 $0$ 1 $1$ 2 $2$ 3 $3$ 4 $4$ 5 $5$ 6 $6$ 7 $7$ 8 $8$ 9 $9$

If $n \geq 3$ then the group $G$ acts on $X$ with $|G| = 12$. The constant $C > 0$ satisfies $C \leq M$ for all $M$ in the set $S$. Theorem 3.1 states that $\|Tx\| \leq K\|x\|$ for every $x \in H$.

Let $V$ be a finite-dimensional vector space over $\F$ with basis $\{e_1, \ldots, e_n\}$. A linear map $T : V \to W$ is represented by a matrix $\mathbf{A} \in \F^{m \times n}$ whose entries are $a_{ij} = \langle w_i^*, T(e_j) \rangle$.

The eigenvalue problem seeks $\lambda \in \C$ and $\mathbf{v} \neq \mathbf{0}$ such that $\mathbf{A}\mathbf{v} = \lambda\mathbf{v}$, equivalently $\det(\mathbf{A} - \lambda \mathbf{I}) = 0$. The characteristic polynomial is

where $e_k(\mathbf{A})$ is the $k$-th elementary symmetric polynomial of the eigenvalues. By the Cayley–Hamilton theorem, $p(\mathbf{A}) = \mathbf{0}$.

The singular value decomposition factors any $\mathbf{A} \in \R^{m \times n}$ as

where $\mathbf{U} \in \R^{m \times m}$ and $\mathbf{V} \in \R^{n \times n}$ are orthogonal, $\sigma_1 \geq \cdots \geq \sigma_r > 0$, and $r = \rank(\mathbf{A})$. The Neumann series $(I - \lambda \mathbf{A})^{-1} = \sum_{k=0}^{\infty} \lambda^k \mathbf{A}^k$ converges when $|\lambda| \cdot \|\mathbf{A}\| < 1$.

Let $\Omega \subset \R^n$ be a bounded domain with smooth boundary $\partial\Omega$. Consider the Dirichlet problem for the Laplacian:

where $\Delta u = \sum_{i=1}^{n} \dfrac{\partial^2 u}{\partial x_i^2}$ is the Laplacian. A weak solution $u \in H^1(\Omega)$ satisfies

By the Lax–Milgram theorem, existence and uniqueness follow from the coercivity $\|\nabla u\|_{L^2}^2 \geq C \|u\|_{H^1}^2$ (Poincaré inequality).

The heat equation $\partial_t u - \Delta u = 0$ on $\R^n \times (0,\infty)$ has fundamental solution

The Fourier transform $\hat{f}(\xi) = \int_{\R^n} f(x)\, e^{-2\pi i \langle x, \xi\rangle}\, dx$ satisfies Parseval's identity $\|\hat{f}\|_{L^2} = \|f\|_{L^2}$ and the convolution theorem $\widehat{f * g} = \hat{f} \cdot \hat{g}$.

Let $(X, \tau)$ be a topological space. A sequence of covers $\mathcal{U}_1 \succ \mathcal{U}_2 \succ \cdots$ refining each other gives rise to the Čech cohomology groups

where $\mathcal{F}$ is a sheaf on $X$. For a compact oriented $n$-manifold $M$ without boundary, Poincaré duality gives an isomorphism

and the Euler characteristic satisfies $\chi(M) = \sum_{k=0}^{n} (-1)^k \, b_k$ where $b_k = \rank H_k(M; \, \Z)$ are the Betti numbers.

The Gauss–Bonnet theorem for a compact surface $\Sigma$ states

where $K$ is the Gaussian curvature and $\kappa_g$ is the geodesic curvature of the boundary. For a closed surface, this reduces to $\int_\Sigma K \, dA = 2\pi\,\chi(\Sigma)$.

The long exact sequence of a fibration $F \hookrightarrow E \twoheadrightarrow B$ is

The number of ways to partition a set of $n$ elements into $k$ non-empty subsets is the Stirling number of the second kind, given by

The exponential generating function is $\sum_{n \geq k} S(n,k)\, \frac{x^n}{n!} = \frac{(e^x - 1)^k}{k!}$.

The Catalan numbers $C_n = \frac{1}{n+1}\binom{2n}{n}$ count the number of Dyck paths from $(0,0)$ to $(2n,0)$. Their generating function satisfies

By the matrix-tree theorem, the number of spanning trees of a graph $G$ on $n$ vertices equals any cofactor of the Laplacian $\mathbf{L} = \mathbf{D} - \mathbf{A}$:

where $0 = \lambda_0 \leq \lambda_1 \leq \cdots \leq \lambda_{n-1}$ are the eigenvalues of $\mathbf{L}$. The chromatic polynomial $\chi_G(k)$ counts proper $k$-colorings and satisfies the deletion–contraction recurrence $\chi_G(k) = \chi_{G-e}(k) - \chi_{G/e}(k)$.

Let $X_1, X_2, \ldots$ be i.i.d. random variables with $\E[X_i] = \mu$ and $\operatorname{Var}(X_i) = \sigma^2 < \infty$. The central limit theorem states

where $\bar{X}_n = \frac{1}{n}\sum_{i=1}^n X_i$. The density of $\mathcal{N}(\mu, \sigma^2)$ is

For a Markov chain with transition matrix $\mathbf{P} = (p_{ij})$, the stationary distribution $\boldsymbol{\pi}$ satisfies $\boldsymbol{\pi}^\top \mathbf{P} = \boldsymbol{\pi}^\top$ and $\sum_i \pi_i = 1$. The ergodic theorem gives

Bayes' theorem: $\P(A \mid B) = \dfrac{\P(B \mid A)\,\P(A)}{\P(B)}$, or in density form, $f_{\Theta|X}(\theta \mid x) \propto f_{X|\Theta}(x \mid \theta) \, f_\Theta(\theta)$.

Let $G$ be a finite group acting on a set $S$. By Burnside's lemma, the number of distinct orbits is

where $S^g = \{s \in S : g \cdot s = s\}$ is the fixed-point set of $g$.

For a Galois extension $L/K$ with $\Gal(L/K) \cong G$, the fundamental theorem of Galois theory establishes a bijection

given by $E \mapsto \Gal(L/E)$ and $H \mapsto L^H$, where $[E : K] = [G : H]$.

In a principal ideal domain $R$, every finitely generated module $M$ decomposes as

where $r = \rank(M)$ and $p_1^{a_1}, \ldots, p_s^{a_s}$ are the elementary divisors. For $R = \Z$, this gives the classification of finitely generated abelian groups.

Maxwell's equations in differential form (Gaussian units):

The Schrödinger equation for a particle of mass $m$ in potential $V$ is

and the time-independent version $\hat{H}\psi = E\psi$ with Hamiltonian $\hat{H} = -\frac{\hbar^2}{2m}\nabla^2 + V$ has eigenvalues $E_n$ forming the energy spectrum.

Einstein's field equations of general relativity:

where $R_{\mu\nu}$ is the Ricci tensor, $R = g^{\mu\nu}R_{\mu\nu}$ is the scalar curvature, $g_{\mu\nu}$ is the metric tensor, $\Lambda$ is the cosmological constant, and $T_{\mu\nu}$ is the stress–energy tensor.

A function $f : \C \to \C$ is holomorphic on a domain $\Omega$ if $\bar{\partial} f = 0$, where $\bar{\partial} = \frac{1}{2}\left(\frac{\partial}{\partial x} + i\frac{\partial}{\partial y}\right)$. Equivalently, $f$ satisfies the Cauchy–Riemann equations:

where $f = u + iv$. Cauchy's integral formula gives the value of $f$ at any point $z_0$ inside a simple closed contour $\gamma$:

and its $n$-th derivative is $f^{(n)}(z_0) = \frac{n!}{2\pi i} \oint_\gamma \frac{f(z)}{(z - z_0)^{n+1}}\,dz$. A function with an isolated singularity at $z_0$ has a Laurent expansion

The coefficient $a_{-1} = \operatorname{Res}(f, z_0)$ is the residue, and the residue theorem states $\oint_\gamma f(z)\,dz = 2\pi i \sum_k \operatorname{Res}(f, z_k)$. A useful application: $\int_0^\infty \frac{\sin x}{x}\,dx = \frac{\pi}{2}$, proved via the contour integral $\oint_\gamma \frac{e^{iz}}{z}\,dz$ over an indented semicircle.

The Riemann mapping theorem states that any simply connected domain $\Omega \subsetneq \C$ is biholomorphic to the unit disk $\mathbb{D} = \{z : |z| < 1\}$. The Schwarz–Christoffel formula maps $\mathbb{H} \to P$:

The number of subsets of $\{1, 2, \ldots, n\}$ of size $k$ is the binomial coefficient $\binom{n}{k} = \frac{n!}{k!(n-k)!}$. The binomial theorem gives

A graph $G = (V, E)$ has adjacency matrix $\mathbf{A} \in \{0,1\}^{n \times n}$ where $A_{ij} = 1$ iff $\{i, j\} \in E$. The number of walks of length $k$ from $i$ to $j$ is $(\mathbf{A}^k)_{ij}$. The chromatic polynomial $P(G, k)$ counts the number of proper $k$-colorings; for a tree on $n$ vertices, $P(T_n, k) = k(k-1)^{n-1}$.

The Master theorem for divide-and-conquer recurrences: if $T(n) = aT(n/b) + \Theta(n^c)$, then

For instance, merge sort has $T(n) = 2T(n/2) + \Theta(n)$, so $a = b = 2$, $c = 1$, $\log_2 2 = 1 = c$, giving $T(n) = \Theta(n \log n)$. Strassen's matrix multiplication achieves $T(n) = 7T(n/2) + \Theta(n^2)$, yielding $T(n) = \Theta(n^{\log_2 7}) \approx \Theta(n^{2.807})$.

The generating function for the Fibonacci numbers $F_n$ is

and the closed form is $F_n = \frac{\varphi^n - \hat{\varphi}^n}{\sqrt{5}}$ where $\varphi = \frac{1 + \sqrt{5}}{2}$ and $\hat{\varphi} = \frac{1 - \sqrt{5}}{2}$. The number of binary trees with $n$ internal nodes is the Catalan number $C_n = \frac{1}{n+1}\binom{2n}{n} = \frac{(2n)!}{(n+1)!\,n!}$.

$\hat{a}\;\hat{f}\;\hat{x}\;\hat{y}\;\hat{A}\;\hat{F}$   $\tilde{a}\;\tilde{f}\;\tilde{x}\;\tilde{y}\;\tilde{A}\;\tilde{F}$   $\bar{a}\;\bar{f}\;\bar{x}\;\bar{y}\;\bar{A}\;\bar{F}$

$\dot{a}\;\dot{f}\;\dot{x}\;\dot{y}\;\dot{A}\;\dot{F}$   $\ddot{a}\;\ddot{f}\;\ddot{x}\;\ddot{y}\;\ddot{A}\;\ddot{F}$   $\vec{a}\;\vec{f}\;\vec{x}\;\vec{y}\;\vec{A}\;\vec{F}$

$\check{a}\;\check{f}\;\check{x}\;\check{y}\;\check{A}\;\check{F}$   $\breve{a}\;\breve{f}\;\breve{x}\;\breve{y}\;\breve{A}\;\breve{F}$   $\acute{a}\;\acute{f}\;\acute{x}\;\acute{y}\;\acute{A}\;\acute{F}$

$\grave{a}\;\grave{f}\;\grave{x}\;\grave{y}\;\grave{A}\;\grave{F}$

$\widehat{x}\quad \widehat{xy}\quad \widehat{xyz}\quad \widehat{xyzw}\quad \widehat{xyzwv}$

$\widetilde{x}\quad \widetilde{xy}\quad \widetilde{xyz}\quad \widetilde{xyzw}\quad \widetilde{xyzwv}$

$\overline{x}\quad \overline{xy}\quad \overline{xyz}\quad \overline{xyzw}\quad \overline{x+y+z+w+v}$

$\hat{\alpha}\;\hat{\beta}\;\hat{\lambda}$   $\tilde{\sigma}\;\tilde{\omega}$   $\bar{\mu}\;\dot{\theta}\;\vec{\rho}$

$\mathrm{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$\mathrm{a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z}$

$\mathrm{0\;1\;2\;3\;4\;5\;6\;7\;8\;9}$

$A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z$

$a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z$

$0\;1\;2\;3\;4\;5\;6\;7\;8\;9$

$\mathbf{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$\mathbf{a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z}$

$\mathbf{0\;1\;2\;3\;4\;5\;6\;7\;8\;9}$

$\boldsymbol{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$\boldsymbol{a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z}$

$\boldsymbol{0\;1\;2\;3\;4\;5\;6\;7\;8\;9}$

$\Gamma\;\Delta\;\Theta\;\Lambda\;\Xi\;\Pi\;\Sigma\;\Upsilon\;\Phi\;\Psi\;\Omega$

$\boldsymbol{\Gamma}\;\boldsymbol{\Delta}\;\boldsymbol{\Theta}\;\boldsymbol{\Lambda}\;\boldsymbol{\Xi}\;\boldsymbol{\Pi}\;\boldsymbol{\Sigma}\;\boldsymbol{\Upsilon}\;\boldsymbol{\Phi}\;\boldsymbol{\Psi}\;\boldsymbol{\Omega}$

$\alpha\;\beta\;\gamma\;\delta\;\epsilon\;\zeta\;\eta\;\theta\;\iota\;\kappa\;\lambda\;\mu\;\nu\;\xi\;\pi\;\rho\;\sigma\;\tau\;\upsilon\;\phi\;\chi\;\psi\;\omega$

$\boldsymbol{\alpha}\;\boldsymbol{\beta}\;\boldsymbol{\gamma}\;\boldsymbol{\delta}\;\boldsymbol{\epsilon}\;\boldsymbol{\zeta}\;\boldsymbol{\eta}\;\boldsymbol{\theta}\;\boldsymbol{\iota}\;\boldsymbol{\kappa}\;\boldsymbol{\lambda}\;\boldsymbol{\mu}\;\boldsymbol{\nu}\;\boldsymbol{\xi}\;\boldsymbol{\pi}\;\boldsymbol{\rho}\;\boldsymbol{\sigma}\;\boldsymbol{\tau}\;\boldsymbol{\upsilon}\;\boldsymbol{\phi}\;\boldsymbol{\chi}\;\boldsymbol{\psi}\;\boldsymbol{\omega}$

$\varepsilon\;\vartheta\;\varkappa\;\varpi\;\varrho\;\varsigma\;\varphi$

$\boldsymbol{\varepsilon}\;\boldsymbol{\vartheta}\;\boldsymbol{\varkappa}\;\boldsymbol{\varpi}\;\boldsymbol{\varrho}\;\boldsymbol{\varsigma}\;\boldsymbol{\varphi}$

$\mathbb{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$\mathbb{a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z}$

$\mathcal{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$\mathfrak{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$\mathfrak{a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z}$

$\mathscr{A\;B\;C\;D\;E\;F\;G\;H\;I\;J\;K\;L\;M\;N\;O\;P\;Q\;R\;S\;T\;U\;V\;W\;X\;Y\;Z}$

$+\;\; -\;\; \times\;\; \div\;\; \pm\;\; \mp\;\; \cdot\;\; \circ\;\; \star\;\; \ast\;\; \bullet$

$\oplus\;\; \otimes\;\; \odot\;\; \ominus\;\; \oslash\;\; \wedge\;\; \vee\;\; \cap\;\; \cup$

$=\;\; \neq\;\; <\;\; >\;\; \leq\;\; \geq\;\; \ll\;\; \gg\;\; \approx\;\; \sim\;\; \simeq\;\; \cong\;\; \equiv\;\; \propto$

$\prec\;\; \succ\;\; \preceq\;\; \succeq$

$\in\;\; \notin\;\; \ni\;\; \subset\;\; \supset\;\; \subseteq\;\; \supseteq$

$\sqsubset\;\; \sqsupset\;\; \sqsubseteq\;\; \sqsupseteq$

$\rightarrow\;\; \leftarrow\;\; \Rightarrow\;\; \Leftarrow\;\; \leftrightarrow\;\; \Leftrightarrow\;\; \mapsto$

$\hookrightarrow\;\; \hookleftarrow\;\; \uparrow\;\; \downarrow\;\; \updownarrow$

$\nearrow\;\; \searrow\;\; \nwarrow\;\; \swarrow$

$\longrightarrow\;\; \longleftarrow\;\; \Longrightarrow\;\; \Longleftarrow$

$\forall\;\; \exists\;\; \nexists\;\; \neg\;\; \land\;\; \lor\;\; \vdash\;\; \models\;\; \top\;\; \bot\;\; \vDash\;\; \Vdash$

$\infty\;\; \partial\;\; \nabla\;\; \triangle\;\; \square\;\; \diamond\;\; \hbar\;\; \ell\;\; \wp\;\; \Re\;\; \Im\;\; \aleph\;\; \beth$

$a_1, a_2, \ldots, a_n \qquad a_1 + a_2 + \cdots + a_n$

1x: $( ) \quad [ ] \quad \{ \} \quad \langle \rangle \quad | \quad \|$

Display style: $\displaystyle \sum_{k=0}^{\infty} \frac{x^k}{k!} = e^x$

Text style: $\textstyle \sum_{k=0}^{\infty} \frac{x^k}{k!} = e^x$

Script style: $\scriptstyle \sum_{k=0}^{\infty} \frac{x^k}{k!} = e^x$

Scriptscript style: $\scriptscriptstyle \sum_{k=0}^{\infty} \frac{x^k}{k!} = e^x$