MathJax basic tutorial and quick reference

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$$
f(n) =
\begin{cases}
n/2,  & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$

$$
f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \
3n+1, & \text{if $n$ is odd}
\end{cases}
$$

行内公式

$x_mu$ $x_mu$

$\sigma$ $\sigma$

$x_mu$ $x_mu$

$y=ax+b$ $y=ax+b$

行间公式

$$\cos 2\theta = \cos^2 \theta - \sin^2 \theta = 2 \cos^2 \theta$$
$$\cos 2\theta = \cos^2 \theta - \sin^2 \theta = 2 \cos^2 \theta$$

$$M(\beta^{\ast}(D),D) \subseteq C$$
$$M(\beta^{\ast}(D),D) \subseteq C$$

$$ \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} $$

$$ x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

自动编号

$$
\begin{equation}
\sum_{i=0}^n F_i \cdot \phi (H, p_i) - \sum_{i=1}^n a_i \cdot ( \tilde{x_i}, \tilde{y_i}) + b_i \cdot ( \tilde{x_i}^2 , \tilde{y_i}^2 )
\end{equation}
$$

$$
\begin{equation}
\beta^*(D) = \mathop{argmin} \limits_{\beta} \lambda {||\beta||}^2 + \sum_{i=1}^n max(0, 1 - y_i f_{\beta}(x_i))
\end{equation}
$$