Here is the displayed-math

$$\begin{equation} \int_0^{2\pi} \sin x\rd x, \end{equation}$$
and the inline math $x>0$. Of course you can put math between the nonmath label to escape the process of MathJaX, for example $x>0$, is produced by the following code:

Now, I will turn to test some new environment, like theorems:

which is produced by

similarly, I also defined an environment of example, as:

The aboving example can be produced by the following code:

The next thing I want to do is make these objects/ environments auto-numbering and cross-ref possible. If you are also interesting in it, maybe you can help me out here.