Xiang Huang

Testing Math

2023-03-14

This page is for testing all kinds of setups I had for math blogging. I now have everything I need to write math in Markdown/HTML!

Basic Math Mode

I am writing my big theorem here with the following wonderful equation

\(\int_a^b f(x) = F(b)-F(a)\)

\begin{equation*} e^{\pi i} + 1 = 0 \end{equation*}

\begin{equation} E = mc^2 \label{eq:zhineng} \tag{1} \end{equation}

\begin{equation} \int_a^b f(x) = F(b) - F(a) \end{equation}

It is powerful enough that I can do referencing 1. I can then write very complicated math (\ref{eq:zhineng}).

Testing mathbb: $\mathbb{1}$

$$ \begin{bmatrix} a & b \\ c & d \\ e & f \\ \end{bmatrix} $$

\begin{bmatrix} a & b \\ c & d \\ e & f \\ \end{bmatrix}
\[ \begin{bmatrix} a & b \\ c & d \\ e & f \\ \end{bmatrix} \]

\begin{bmatrix} a & b \\ c & d \\ e & f \\ \end{bmatrix}

$ \begin{bmatrix} a & b \\ c & d \\ e & f \\ \end{bmatrix} $
\[a \ne 0\]

Mathjax Macro

The following formulas use some macroes. I aslo test cross references and equation tag/numbering. \[ \f\relax{x} = \int_{-\infty}^\infty \f\hat\xi,e^{2 \pi i \xi x} \tag{fancy}\label{eq:fancy} ,d\xi \]

\(x < y\) \(\frac{x}{y}\) \begin{align} a &=b \\ &=c \notag
\end{align}

\begin{align} A & = B \\ & = C \end{align}

\begin{braced} \frac{x}{y} \end{braced}

\begin{ABC}{Z} xyz \end{ABC}

Crossreference: Here I add a pointer to fancy \eqref{eq:fancy}.

CSS Theorem Style and Automatic Theorem Counter

I don’t really know any CSS or HTML very well. But luckily I manage to make things work! I use different counters for theorems and for definitions.

hahahahhahahahsdf alsjdfljasfdljla asdfjlajsdf
All prime number are odd except 2.
There are no natural numbers. Xiang is editing this place. is a natural number greater than 2. There are no natural numbers $\mathbf{N} = (1, 2, 3, \ldots)$ $x$, $y$, and $z$ such that $x^n + y^n = z^n$, in which $n$ is a natural number greater than 2.
Here we define lasdkljflkj asdfljlj.
Here we proof this very useful lemma.
Here we proof another very useful lemma.
Here we proof this very useful observation with x new def.
Here we proof this very $$\int_a^b f(x)= F(b) - F(a)$$ observation with x new def.
There are no natural numbers $\mathbf{N} = (1, 2, 3, \ldots)$ $x$, $y$, and $z$ such that $x^n + y^n = z^n$, in which $n$ is a natural number greater than 2. A dollar sign \$.
Here we define lasdkljflkj asdfljlj.
kjhkasdhf lklasjdflj ljljasd fljl alsdjfl $$\int_a^b f(x)= F(b) - F(a).$$
ljasldfj llkjasdf

alsfjdla jsdflljasdfl jals

lajsdlfj ljalsdfj
lajslfj ljasdlfj l aljsdflj jljasdlf

\begin{align} A &= B \\ &= C \end{align}

\begin{gather} A = B \\ C = D \end{gather}

$safjljsf$

$$ \int_a^b f(x) = F(b)- F(a) $$

adsllljlajsf lajsdflj
ljal sjfdlajsd flj ljalsfjd
My big, important theorem: $$ \int f(x) = F(x) + c. $$
My big, important theorem: $$ \int f(x) = F(x) + c. $$
My big, important theorem: $$ \int f(x) = F(x) + c. $$ and $$ \int_a^b f(x)= F(b) - F(a). $$
My Main Theorem today without automatic numbering.

By doing all the things above. I think I now have a very good webpage template to write math.

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public class Graph {

    private Set<Node> nodes = new HashSet<>();
    
    public void addNode(Node nodeA) {
        nodes.add(nodeA);
    }

    // getters and setters 
}

Checklists

[ ] a task list item [ ] list syntax required [ ] incomplete [x] completed [ ] asfdsaf [ ] asdfsa

Tables

Sublime Text’s Table Editor extension makes editing table very smooth for me.

people money
dlkjsdjf ljasjdfljaslfd
asdfjlajs sldkfjalsjf

Better table:

| askfdhkajhfd | colum head | sadfhkajshdf | asdfasdfasfdas |

Column 1 Column 2 Column 3
fasfdasdf asdfjsaflk safdasfd sfasfdasfd
asdffsadasdf asdfasdf sadfasdf asdfasd
asdfasdf sadfasd asdfasdf sadfsadf
asdfajsldkfj asldfjlkj alksjdflkaj asdfljaslkdfj
asdfasdfklj asjdflkja asdfklajsdfl aksldfjkaljsdf
asdfjalksjdf asdlfkjalksjdf asdfjlasjdf sadfljasfkdlasdfasdf
dsfasfd safdasdf asdfas sadfasdfffasfda

| askfdhkajhfd | colum head | sadfhkajshdf | asdfasdfasfdas |

Column 1 Column 2 Column 3
fasfdasdf asdfjsaflk safdasfd sfasfdasfd
asdffsadasdf asdfasdf sadfasdf asdfasd
asdfasdf sadfasd asdfasdf sadfsadf
asdfajsldkfj asldfjlkj alksjdflkaj asdfljaslkdfj
asdfasdfklj asjdflkja asdfklajsdfl aksldfjkaljsdf
asdfjalksjdf asdlfkjalksjdf asdfjlasjdf sadfljasfkdlasdfasdf
sadfkl Column 2asdfjalkjs adfkalsjdf asdjfkha
Cell 1-1sdkjfhaksjdh Cell 1-2asdkjfhkahsdf asdfkjhaksjdfh kahsdfkha
Cell 2-1asdkjfhkaj Cell 2-2aksjdfhkajshdf aksdfhskjdh asdfasfasdf
asfjlkj asljdflj alsjdflj lkjaslfjd
asdfas asdf asdf asdfsfd

add the newest version. Not Updated on the website?

Test Video

Here I plugin a video.

  1. Some footnote here. ↩︎