1 Intorduction

This note list commands for creating mathematics formulas in RMarkdown.

2 Greek Letters

Symbol	Script
\(\alpha\)	`\alpha`
\(A\)	`A`
\(\beta\)	`\beta`
\(B\)	`B`
\(\gamma\)	`\gammma`
\(\Gamma\)	`\Gamma`
\(\pi\)	`\pi`
\(\Pi\)	`\Pi`
\(\phi\)	`\phi`
\(\Phi\)	`\Phi`
\(\varphi\)	`\varphi`
\(\theta\)	`\theta`

3 Operators

Symbol	Script
\(\cos\)	`\cos`
\(\sin\)	`\sin`
\(\lim\)	`\lim`
\(\exp\)	`\exp`
\(\to\)	`\to`
\(\infty\)	`\infty`
\(\equiv\)	`\equiv`
\(\bmod\)	`\bmod`
\(\times\)	`\times`

4 Power and Indicies

Symbol	Script
\(k_{n+1}\)	`k_{n+1}`
\(n^2\)	`n^2`
\(k_n^2\)	`k_n^2`

5 Fractions and Binomials

Symbol	Script
\(\frac{n!}{k!(n-k)!}\)	`\frac{n!}{k!(n-k)!}`
\(\binom{n}{k}\)	`\binom{n}{k}`
\(\frac{\frac{x}{1}}{x - y}\)	`\frac{\frac{x}{1}}{x - y}`
\(^3/_7\)	`^3/_7`

6 Radical Roots

Symbol	Script
\(\sqrt{k}\)	`\sqrt{k}`
\(\sqrt[n]{k}\)	`\sqrt[n]{k}`

7 Sums, Integrals, and Related Symbols

Symbol	Script
\(\sum_{i=1}^{10} t_i\)	`\sum_{i=1}^{10} t_i`
\(\int_0^\infty \mathrm{e}^{-x},\mathrm{d}x\)	`\int_0^\infty \mathrm{e}^{-x},\mathrm{d}x`
\(\sum\)	`\sum`
\(\prod\)	`\prod`
\(\coprod\)	`\coprod`
\(\bigoplus\)	`\bigoplus`
\(\bigotimes\)	`\bigotimes`
\(\bigodot\)	`\bigodot`
\(\bigcup\)	`\bigcup`
\(\bigcap\)	`\bigcap`
\(\biguplus\)	`\biguplus`
\(\bigsqcup\)	`\bigsqcup`
\(\bigvee\)	`\bigvee`
\(\bigwedge\)	`\bigwedge`
\(\int\)	`\int`
\(\oint\)	`\oint`
\(\iint\)	`\iint`
\(\iiint\)	`\iiint`
\(\idotsint\)	`\idotsint`
\(\sum_{\substack{0<i<m, \ 0<j<n}} P(i, j)\)	`\sum_{\substack{0<i<m, \ 0<j<n}} P(i, j)`
\(\int\limits_a^b\)	`\int\limits_a^b`

8 More Special Symbols

Symbol	Script
\(a^{\prime}\)	`a^{\prime}`
\(a^{\prime\prime}\)	`a^{\prime\prime}`
\(\hat{a}\)	`\hat{a}`
\(\bar{a}\)	`\bar{a}`
\(\grave{a}\)	`\grave{a}`
\(\acute{a}\)	`\acute{a}`
\(\dot{a}\)	`\dot{a}`
\(\ddot{a}\)	`\ddot{a}`
\(\not{a}\)	`\not{a}`
\(\mathring{a}\)	`\mathring{a}`
\(\overrightarrow{AB}\)	`\overrightarrow{AB}`
\(\overleftarrow{AB}\)	`\overleftarrow{AB}`
\(a^{\prime\prime\prime}\)	`a^{\prime\prime\prime}`
\(\overline{aaa}\)	`\overline{aaa}`
\(\check{a}\)	`\check{a}`
\(\vec{a}\)	`\vec{a}`
\(\underline{a}\)	`\underline{a}`
\(\color{red}x\)	`\color{red}x`
\(\pm\)	`\pm`
\(\mp\)	`\mp`
\(\int y \mathrm{d}x\)	`\int y \mathrm{d}x`
\(,\)	`,`
\(:\)	`:`
\(;\)	`;`
\(!\)	`!`
\(\int y, \mathrm{d}x\)	`\int y, \mathrm{d}x`
\(\dots\)	`\dots`
\(\ldots\)	`\ldots`
\(\cdots\)	`\cdots`
\(\vdots\)	`\vdots`
\(\ddots\)	`\ddots`

9 Brackets

Symbol	Script
\((a)\)	`(a)`
\([a]\)	`[a]`
\(\{a\}\)	`\{a\}`
\(\langle f \rangle\)	`\langle f \rangle`
\(\lfloor f \rfloor\)	`\lfloor f \rfloor`
\(\lceil f \rceil\)	`\lceil f \rceil`
\(\ulcorner f \urcorner\)	`\ulcorner f \urcorner`

10 Matrices and System of Equations

10.1 Matrix

$$
X_{m,n} = 
\begin{pmatrix}
  x_{1,1} & x_{1,2} & \cdots & x_{1,n} \\
  x_{2,1} & x_{2,2} & \cdots & x_{2,n} \\
  \vdots  & \vdots  & \ddots & \vdots  \\
  x_{m,1} & x_{m,2} & \cdots & x_{m,n} 
\end{pmatrix}
$$

produces

\[ X_{m,n} = \begin{pmatrix} x_{1,1} & x_{1,2} & \cdots & x_{1,n} \\ x_{2,1} & x_{2,2} & \cdots & x_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ x_{m,1} & x_{m,2} & \cdots & x_{m,n} \end{pmatrix} \]

$$
M = 
\begin{bmatrix}
\frac{5}{6} & \frac{1}{6} & 0 \\[0.3em]
\frac{5}{6} & 0 & \frac{1}{6} \\[0.3em]
0 & \frac{5}{6} & \frac{1}{6}
\end{bmatrix}
$$

produces

\[ M = \begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \\[0.3em] \frac{5}{6} & 0 & \frac{1}{6} \\[0.3em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix} \]

10.2 Aligned Equations

$$
\begin{aligned}
Bias(\hat{\theta})  &= E(\hat{\theta}) - \theta \\
Bias(\hat{\theta})  &= E(2 \bar{X} -1) - \theta \\
Bias(\hat{\theta})  &= \frac{2}{n}\sum_{i=1}^n E(X_i) -1 -\theta \\
Bias(\hat{\theta})  &= 2E(X) - 1 - \theta \\
Bias(\hat{\theta})  &= 2 \cdot \frac{\theta+1}{2} - 1 - \theta \\
Bias(\hat{\theta})  &= 0 \\
\end{aligned}
$$

Produces the following system of equations

\[ \begin{aligned} Bias(\hat{\theta}) &= E(\hat{\theta}) - \theta \\ Bias(\hat{\theta}) &= E(2 \bar{X} -1) - \theta \\ Bias(\hat{\theta}) &= \frac{2}{n}\sum_{i=1}^n E(X_i) -1 -\theta \\ Bias(\hat{\theta}) &= 2E(X) - 1 - \theta \\ Bias(\hat{\theta}) &= 2 \cdot \frac{\theta+1}{2} - 1 - \theta \\ Bias(\hat{\theta}) &= 0 \\ \end{aligned} \]

10.3 Piece-wise Function

$$ f(x) = \begin{cases} \frac{1}{b-a} \\ 0 \end{cases} $$

produces the following piece-wise function

\[ f(x) = \begin{cases} \frac{1}{b-a} \\ 0 \end{cases} \]

11 Pseudo-code of Algorithms

while not convergence:

compute \(\nabla(J)\)

\(\theta_0 := \theta_0 - \alpha\nabla(J)_0\)

\(\theta_1 := \theta_1 - \alpha\nabla(J)_1\)

end while

Writing Mathematical Equations in RMarkdown

Cheng Peng