B.2 Math Expression/ Syntax

Aligning equations

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

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

Cross-reference equation

\begin{equation} 
a = b
(\#eq:test)
\end{equation}

\[\begin{equation} a = b \tag{B.1} \end{equation}\]

to refer in a sentence (B.1) (\@ref(eq:test))

Math Syntax	Notation
$\pm$	$\pm$
$\ge$	$\ge$
$\le$	$\le$
$\neq$	$\neq$
$\equiv$	$\equiv$
$^\circ$	$^\circ$
$\times$	$\times$
$\cdot$	$\cdot$
$\leq$	$\leq$
$\geq$	$\geq$
`\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$`	$\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$
$x \in A$	$x \in A$
$\|A\|$	$\|A\|$
$x \in A$	$x \in A$
$x \subset B$	$x \subset B$
$x \subseteq B$	$x \subseteq B$
$A \cup B$	$A \cup B$
$A \cap B$	$A \cap B$
$X \sim Binom(n, \pi)$	$X \sim Binom(n, \pi)$
$\mathrm{P}(X \le x) = \text{pbinom}(x, n, \pi)$	$\mathrm{P}(X \le x) = \text{pbinom}(x, n, \pi)$
$P(A \mid B)$	$P(A \mid B)$
$\mathrm{P}(A \mid B)$	$\mathrm{P}(A \mid B)$
$\{1, 2, 3\}$	$\{1, 2, 3\}$
$\sin(x)$	$\sin(x)$
$\log(x)$	$\log(x)$
$\int_{a}^{b}$	$\int_{a}^{b}$
$\left(\int_{a}^{b} f(x) \; dx\right)$	$\left(\int_{a}^{b} f(x) \; dx\right)$
$\left[\int_{\-infty}^{\infty} f(x) \; dx\right]$	$\left[\int_{-\infty}^{\infty} f(x) \; dx\right]$
$\left. F(x) \right\|_{a}^{b}$	$\left. F(x) \right\|_{a}^{b}$
$\sum_{x = a}^{b} f(x)$	$\sum_{x = a}^{b} f(x)$
$\prod_{x = a}^{b} f(x)$	$\prod_{x = a}^{b} f(x)$
$\lim_{x \to \infty} f(x)$	$\lim_{x \to \infty} f(x)$
$\displaystyle \lim_{x \to \infty} f(x)$	$\displaystyle \lim_{x \to \infty} f(x)$
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{for $x\in[a,b]$}\\
0&\text{otherwise}\\
\end{cases}

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

Math Syntax	Notation
$\pm$	\(\pm\)
$\ge$	\(\ge\)
$\le$	\(\le\)
$\neq$	\(\neq\)
$\equiv$	\(\equiv\)
$^\circ$	\(^\circ\)
$\times$	\(\times\)
$\cdot$	\(\cdot\)
$\leq$	\(\leq\)
$\geq$	\(\geq\)
`\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$`	\(\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle\)
$x \in A$	\(x \in A\)
$\|A\|$	\(\|A\|\)
$x \in A$	\(x \in A\)
$x \subset B$	\(x \subset B\)
$x \subseteq B$	\(x \subseteq B\)
$A \cup B$	\(A \cup B\)
$A \cap B$	\(A \cap B\)
$X \sim Binom(n, \pi)$	\(X \sim Binom(n, \pi)\)
$\mathrm{P}(X \le x) = \text{pbinom}(x, n, \pi)$	\(\mathrm{P}(X \le x) = \text{pbinom}(x, n, \pi)\)
$P(A \mid B)$	\(P(A \mid B)\)
$\mathrm{P}(A \mid B)$	\(\mathrm{P}(A \mid B)\)
$\{1, 2, 3\}$	\(\{1, 2, 3\}\)
$\sin(x)$	\(\sin(x)\)
$\log(x)$	\(\log(x)\)
$\int_{a}^{b}$	\(\int_{a}^{b}\)
$\left(\int_{a}^{b} f(x) \; dx\right)$	\(\left(\int_{a}^{b} f(x) \; dx\right)\)
$\left[\int_{\-infty}^{\infty} f(x) \; dx\right]$	\(\left[\int_{-\infty}^{\infty} f(x) \; dx\right]\)
$\left. F(x) \right\|_{a}^{b}$	\(\left. F(x) \right\|_{a}^{b}\)
$\sum_{x = a}^{b} f(x)$	\(\sum_{x = a}^{b} f(x)\)
$\prod_{x = a}^{b} f(x)$	\(\prod_{x = a}^{b} f(x)\)
$\lim_{x \to \infty} f(x)$	\(\lim_{x \to \infty} f(x)\)
$\displaystyle \lim_{x \to \infty} f(x)$	\(\displaystyle \lim_{x \to \infty} f(x)\)
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 $	\(\zeta Z \sigma\)
$\eta H$	\(\eta H\)
$\theta \vartheta \Theta$	\(\theta \vartheta \Theta\)
$\iota I$	\(\iota I\)
$\kappa K$	\(\kappa K\)
$\lambda \Lambda$	\(\lambda \Lambda\)
$\mu M$	\(\mu M\)
$\nu N$	\(\nu N\)
$\xi\Xi$	\(\xi\Xi\)
$o O$	\(o O\)
$\pi \Pi$	\(\pi \Pi\)
$\rho\varrho P$	\(\rho\varrho P\)
$\sigma \Sigma$	\(\sigma \Sigma\)
$\tau T$	\(\tau T\)
$\upsilon \Upsilon$	\(\upsilon \Upsilon\)
$\phi \varphi \Phi$	\(\phi \varphi \Phi\)
$\chi X$	\(\chi X\)
$\psi \Psi$	\(\psi \Psi\)
$\omega \Omega$	\(\omega \Omega\)
$\cdot$	\(\cdot\)
$\cdots$	\(\cdots\)
$\ddots$	\(\ddots\)
$\ldots$	\(\ldots\)