## Abstract

$$J(\theta) = \frac 1 2 \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2$$

My blog integrates mathjax module, which makes Markdown more advanced. This post is intended to deal with my essay demands during SE studying, and of course I hope that this post can help those who are struggling in the field of System Engineering.

I only posted my frequently-used LaTeX notations of math on my own need, and I will update this post constantly.
For more advanced techs, please refer to the official document link at the end of the article.

## Content

• 行内公式

• 行间公式

### 上划线·下划线·其他线

$$\underbrace{a + \overbrace{b + \dots + b}^{m\mbox{个}} + c}_{20\mbox{个}}$$

### 堆叠符号

$$\vec{x} \stackrel{\mathrm{def}}{=}(x_1,\dots,x_n)$$

$$\sum_{k+0,k_1,\ldots>0 \atop k_0+k_1+\cdots=n} A_{0k_0}A_{1K_1}\cdots$$

$${n+1 \choose k} = {n \choose k} + {n \choose k-1}$$

### 定界符尺寸

$$\left. \frac{\partial f(x, y)}{\partial x}\right|_{x=0}$$

### 矩阵

{ }中指定了对应的列格式，c为内容居中对齐，l为靠左，r为靠右；&为对齐符号，输出：

$$\left(\begin{array}{ccc} 11 & 12 & 13 \\ 21 & 22 & 23 \end{array}\right)$$

## Forms

Greek alphabet Input Symbols Input
$\alpha$ $\alpha$ $\vec{a}$ $\vec{a}$
$\beta$ $\beta$ $\dot{x}\ddot{x}$ $\dot{x}\ddot{x}$
$\gamma$ $\gamma$ $\dots \vdots \ddots$ $\dots\vdots\ddots$
$\delta$ $\delta$ $\bar{x}$ $\bar{x}$
$\epsilon$ $\epsilon$ $x’x’’x’’’$ $x'x''x'''$
$\varepsilon$ $\varepsilon$ $^{\circ}$C $^{\circ}$C
$\zeta$ $\zeta$ $\hbar$ $\hbar$
$\eta$ $\eta$ $\mu m$ $\mu m$
$\theta$ $\theta$ $\pm$ $\pm$
$\kappa$ $\kappa$ $\nabla$ $\nabla$
$\lambda$ $\lambda$ $\mp$ $\mp$
$\mu$ $\mu$ $\times\div$ $\times\div$
$\nu$ $\nu$ $A^{\dagger}$ $A^{\dagger}$
$\xi$ $\xi$ $\oplus\otimes$ $\oplus\otimes$
$\pi$ $\pi$ $\Leftrightarrow\Updownarrow$ $\Leftrightarrow\Updownarrow$
$\rho$ $\rho$ $\cdot\bullet$ $\cdot\bullet$
$\sigma$ $\sigma$ $\le\ge\ll\gg$ $\le\ge\ll\gg$
$\tau$ $\tau$ $\ne\approx\sim\simeq\propto$ $\ne\approx\sim\simeq\propto$
$\upsilon$ $\upsilon$ $\in\ni\equiv$ $\in\ni\equiv$
$\phi$ $\phi$ $\infty$ $\infty$
$\varphi$ $\varphi$ $\forall\exists$ $\forall\exists$
$\chi$ $\chi$ $\rightarrow\Rightarrow$ $\rightarrow\Rightarrow$
$\psi$ $\psi$ $\Box$ $\Box$
$\omega$ $\omega$ $B_{\bot}B_{\parallel}$ $B_{\bot}B_{\parallel}$

## Resolve the Conflict (Optional)

• 去掉\的额外转义。
• em标签对应的符号中，去掉_,因为markdown中有*可以表示斜体，_就可以去掉了。

### 实例

\begin{align} D(x) &= \int_{x_0}^x P(x^{\prime})\,\mathrm{dx^{\prime}} \\ &= C\int_{x_0}^x x^{\prime n}\,\mathrm{dx^{\prime}} \\ &= \frac{C}{n+1}(x^{n+1}-x_0^{n+1}) \\ &\equiv y \end{align}

### 结论

--- The following is a wasteland without any knowledge.---