## B.2 Math Expresssion/ Syntax

Full list

Aligning equations

\begin{aligned}
a & = b \\
X &\sim {\sf Norm}(10, 3) \\
5 & \le 10
\end{aligned}

\begin{aligned} a & = b \\ X &\sim {\sf Norm}(10, 3) \\ 5 & \le 10 \end{aligned}

Syntax Notation
Math
$\pm$ $$\pm$$
$\ge$ $$\ge$$
$\le$ $$\le$$
$\neq$ $$\neq$$
$\equiv$ $$\equiv$$
$^\circ$ $$^\circ$$
$\times$ $$\times$$
$\cdot$ $$\cdot$$
$\leq$ $$\leq$$
$\geq$ $$\geq$$
\propto $$\propto$$
$\subset$ $$\subset$$
$\subseteq$ $$\subseteq$$
$\leftarrow$ $$\leftarrow$$
$\rightarrow$ $$\rightarrow$$
$\Leftarrow$ $$\Leftarrow$$
$\Rightarrow$ $$\Rightarrow$$
$\approx$ $$\approx$$
$\mathbb{R}$ $$\mathbb{R}$$
$\sum_{n=1}^{10} n^2$ $$\sum_{n=1}^{10} n^2$$
$$\sum_{n=1}^{10} n^2$$ $\sum_{n=1}^{10} n^2$
$x^{n}$ $$x^{n}$$
$x_{n}$ $$x_{n}$$
$\overline{x}$ $$\overline{x}$$
$\hat{x}$ $$\hat{x}$$
$\tilde{x}$ $$\tilde{x}$$
\check{} $$\check{}$$
\underset{\gamma}{\operatorname{argmin}} $$\underset{\gamma}{\operatorname{argmin}}$$
$\frac{a}{b}$ $$\frac{a}{b}$$
$\frac{a}{b}$ $$\frac{a}{b}$$
$\displaystyle \frac{a}{b}$ $$\displaystyle \frac{a}{b}$$
$\binom{n}{k}$ $$\binom{n}{k}$$
$x_{1} + x_{2} + \cdots + x_{n}$ $$x_{1} + x_{2} + \cdots + x_{n}$$
$x_{1}, x_{2}, \dots, x_{n}$ $$x_{1}, x_{2}, \dots, x_{n}$$
\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$ $$\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$$ $x \in A$ $$x \in A$$ $|A|$ $$|A|$$ $x \in A$ $$x \in A$$ $x \subset B$ $$x \subset B$$ $x \subseteq B$ $$x \subseteq B$$ $A \cup B$ $$A \cup B$$ $A \cap B$ $$A \cap B$$ $X \sim {\sf Binom}(n, \pi)$ $$X \sim {\sf Binom}(n, \pi)$$ $\mathrm{P}(X \le x) = {\tt pbinom}(x, n, \pi)$ $$\mathrm{P}(X \le x) = {\tt pbinom}(x, n, \pi)$$ $P(A \mid B)$ $$P(A \mid B)$$ $\mathrm{P}(A \mid B)$ $$\mathrm{P}(A \mid B)$$ $\{1, 2, 3\}$ $$\{1, 2, 3\}$$ $\sin(x)$ $$\sin(x)$$ $\log(x)$ $$\log(x)$$ $\int_{a}^{b}$ $$\int_{a}^{b}$$ $\left(\int_{a}^{b} f(x) \; dx\right)$ $$\left(\int_{a}^{b} f(x) \; dx\right)$$ $\left[\int_{\-infty}^{\infty} f(x) \; dx\right]$ $$\left[\int_{-\infty}^{\infty} f(x) \; dx\right]$$ $\left. F(x) \right|_{a}^{b}$ $$\left. F(x) \right|_{a}^{b}$$ $\sum_{x = a}^{b} f(x)$ $$\sum_{x = a}^{b} f(x)$$ $\prod_{x = a}^{b} f(x)$ $$\prod_{x = a}^{b} f(x)$$ $\lim_{x \to \infty} f(x)$ $$\lim_{x \to \infty} f(x)$$ $\displaystyle \lim_{x \to \infty} f(x)$ $$\displaystyle \lim_{x \to \infty} f(x)$$ Greek Letters $\alpha A$ $$\alpha A$$ $\beta B$ $$\beta B$$ $\gamma \Gamma$ $$\gamma \Gamma$$ $\delta \Delta$ $$\delta \Delta$$ $\epsilon \varepsilon E$ $$\epsilon \varepsilon E$$ $\zeta Z \sigma \,\!$ $$\zeta Z \sigma \,\!$$ $\eta H$ $$\eta H$$ $\theta \vartheta \Theta$ $$\theta \vartheta \Theta$$ $\iota I$ $$\iota I$$ $\kappa K$ $$\kappa K$$ $\lambda \Lambda$ $$\lambda \Lambda$$ $\mu M$ $$\mu M$$ $\nu N$ $$\nu N$$ $\xi\Xi$ $$\xi\Xi$$ $o O$ $$o O$$ $\pi \Pi$ $$\pi \Pi$$ $\rho\varrho P$ $$\rho\varrho P$$ $\sigma \Sigma$ $$\sigma \Sigma$$ $\tau T$ $$\tau T$$ $\upsilon \Upsilon$ $$\upsilon \Upsilon$$ $\phi \varphi \Phi$ $$\phi \varphi \Phi$$ $\chi X$ $$\chi X$$ $\psi \Psi$ $$\psi \Psi$$ $\omega \Omega$ $$\omega \Omega$$ $\cdot$ $$\cdot$$ $\cdots$ $$\cdots$$ $\ddots$ $$\ddots$$ $\ldots $$\ldots$$ Limit P(\lim_{n\to \infty}\bar{X}_n =\mu) =1 $P(\lim_{n\to \infty}\bar{X}_n =\mu) =1$ Matrices $$\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}$$ $\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}$ $$\mathbf{X} = \left[\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right]$$ $\mathbf{X} = \left[\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right]$ Aligning Equations Aligning Equations with Comments \begin{aligned} 3+x &=4 && \text{(Solve for} x \text{.)}\\ x &=4-3 && \text{(Subtract 3 from both sides.)}\\ x &=1 && \text{(Yielding the solution.)} \end{aligned} \begin{aligned} 3+x &=4 && \text{(Solve for} x \text{.)}\\ x &=4-3 && \text{(Subtract 3 from both sides.)}\\ x &=1 && \text{(Yielding the solution.)} \end{aligned} ### B.2.1 Statistics Notation $$f(y|N,p) = \frac{N!}{y!(N-y)!}\cdot p^y \cdot (1-p)^{N-y} = {{N}\choose{y}} \cdot p^y \cdot (1-p)^{N-y}$$ $f(y|N,p) = \frac{N!}{y!(N-y)!}\cdot p^y \cdot (1-p)^{N-y} = {{N}\choose{y}} \cdot p^y \cdot (1-p)^{N-y}$ \begin{cases} \frac{1}{b-a}&\text{forx\in[a,b]\$}\\
0&\text{otherwise}\\
\end{cases}

$\begin{cases} \frac{1}{b-a} & \text{for } x\in[a,b]\\ 0 & \text{otherwise}\\ \end{cases}$