Writing Mathematical Equations in RMarkdown

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