B.2 Math Expression/ Syntax

Full list

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}

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