Problems in Mathematics

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MathJax in WordPress and LaTeX for Math Blogs

The mathematical equations and symbols in this website is created using MathJax service.
MathJax enables us to use LaTeX code in WordPress for mathematical equations/symbols.

How to Use MathJax on WordPress

To use MathJax on WordPress, write the following code in header.php.
(I put the code just before </head > .)
That’s it!!

 

<script type="text/x-mathjax-config">
  MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ["\\(","\\)"]] } });
</script>
<script type="text/javascript"
  src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
</script>
<meta http-equiv="X-UA-Compatible" CONTENT="IE=EmulateIE7" />

 

For example,
if you type $\sin x$ in an editor, it gives $\sin x$.

\begin{align*}
 \cos^2 x +\sin^ 2 x=1
\end{align*}

creates
\begin{align*}
\cos^2 x +\sin^ 2 x=1
\end{align*}

My setting with macros

Here is my current setting. The following codes include macros as well.

 

<script type="text/x-mathjax-config">// <![CDATA[
MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ["\\(","\\)"]] },
TeX: {
Macros: {
R: "{\\mathbb R}",
N: "{\\mathbb N}",
C: "{\\mathbb C}",
Z: "{\\mathbb Z}",
Q: "{\\mathbb Q}",
SL: "{\\operatorname {SL}}",
SO: "{\\operatorname {SO}}",
GL: "{\\operatorname {GL}}",
id: "{\\mathbb {id}}",
tr: "{\\operatorname {tr}}",
trans: "{\\mathrm T}",
Span: "{\\operatorname {Span}}",
Hom: "{\\operatorname {Hom}}",
Rep: "{\\operatorname {Rep}}",
Aut: "{\\operatorname {Aut}}",
End: "{\\operatorname {End}}",
Repart: "{\\operatorname {Re}}",
Impart: "{\\operatorname {Im}}",
im: "{\\operatorname {im}}",
rk: "{\\operatorname {rank}}",
nullity: "{\\operatorname {null}}",
Stab: "{\\operatorname {Stab}}",
Zmod: ["{\\mathbb Z / #1 \\mathbb Z}",1],
bold: ["{\\bf #1}",1],
Abs: ['\\left\\lvert #2 \\right\\rvert_{\\text{#1}}', 2, ""]
}
}
});
</script>
<script type="text/javascript"
 src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
</script>
<meta http-equiv="X-UA-Compatible" CONTENT="IE=EmulateIE7" />

Useful LaTeX code for MathJax.

Here is the list of LaTeX codes that I used in this website and I found them useful.

System of equations

Here is the LaTeX code for the system of equations.

\[
\left\{ 
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\ 
a_2x+b_2y+c_2z=d_2 \\ 
a_3x+b_3y+c_3z=d_3
\end{array}
\right. 
\]

The result is
\[
\left\{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{array}
\right.
\]

If you don’t need the big bracket, then omit \left\{ and \right. from the above code.
The LaTex code

\[\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\ 
a_2x+b_2y+c_2z=d_2 \\ 
a_3x+b_3y+c_3z=d_3
\end{array} 
\]

generates
\[\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{array}.
\]

Augmented matrix

By writing

\[
 \left[\begin{array}{rrr|rrr}
  1 & 0 & 0 & 1 &1 & 1 \\
   0 & 1 & 0 & 0 & 1 & 1 \\
   0 & 0 & 1 & 0 & 0 & 1 \\ 
   \end{array} \right]
\]

You get
\[ \left[\begin{array}{rrr|rrr}
1 & 0 & 0 & 1 &1 & 1 \\
0 & 1 & 0 & 0 & 1 & 1 \\
0 & 0 & 1 & 0 & 0 & 1 \\
\end{array} \right]\]

Block matrix

To write a block matrix using MathJax, write the following LaTeX code

\[
M=
\left[\begin{array}{c|c}
  A & B\\
  \hline
  C & D
\end{array}
\right] 
\]

The result is
\[
M=
\left[\begin{array}{c|c}
A & B\\
\hline
C & D
\end{array}
\right] \]

Matrix with fractions

When you write a matrix whose entries are fractions, you might feel the line are cramped.
So to widen the gap between lines, use \\[6pt] instead of \\ as in the following code.

\[
A=\begin{bmatrix}
  \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\[6pt]
   \frac{2}{3} &\frac{-1}{3} &\frac{-1}{3} \\[6pt]
   \frac{1}{3} & \frac{1}{3} & \frac{-2}{3}
\end{bmatrix}
\]

The result is
\[
A=\begin{bmatrix}
\frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\
\frac{2}{3} &\frac{-1}{3} &\frac{-1}{3} \\
\frac{1}{3} & \frac{1}{3} & \frac{-2}{3}
\end{bmatrix}
\]

Elementary row operations (Gauss-Jordan elimination)

To get
\[ \left[\begin{array}{rrrr|r}
1 & 1 & 1 & 1 &1 \\
0 & 1 & 2 & 3 & 5 \\
0 & -2 & 0 & -2 & 2 \\
0 & 1 & -2 & 3 & 1 \\
\end{array}\right] \xrightarrow{\substack{R_1-R_2 \\ R_3-R_2\\R_4-R_2}}
\left[\begin{array}{rrrr|r}
1 & 0& -1 & -2 &-4 \\
0 & 1 & 2 & 3 & 5 \\
0 & 0 & 4 & 4 & 12 \\
0 & 0 & -4 & 0 & -4 \\
\end{array}\right] \xrightarrow[\frac{-1}{4}R_4]{\frac{1}{4}R_3}
\left[\begin{array}{rrrr|r}
1 & 0& -1 & -2 &-4 \\
0 & 1 & 2 & 3 & 5 \\
0 & 0 & 1 & 1 & 3 \\
0 & 0 & 1 & 0& 1 \\
\end{array}\right] \] write the LaTeX code

\left[\begin{array}{rrrr|r}
  1 & 1 & 1 & 1 &1 \\
  0 & 1 & 2 & 3 & 5 \\
   0 & -2 & 0 & -2 & 2 \\
  0 & 1 & -2 & 3 & 1 \\
  \end{array}\right]
  \xrightarrow{\substack{R_1-R_2 \\ R_3-R_2\\R_4-R_2}}
  \left[\begin{array}{rrrr|r}
  1 &  0& -1 & -2 &-4 \\
  0 & 1 & 2 & 3 & 5 \\
   0 & 0 & 4 & 4 & 12 \\
  0 & 0 & -4 & 0 & -4 \\
  \end{array}\right]
  \xrightarrow[\frac{-1}{4}R_4]{\frac{1}{4}R_3}
\left[\begin{array}{rrrr|r}
  1 &  0& -1 & -2 &-4 \\
  0 & 1 & 2 & 3 & 5 \\
   0 & 0 & 1 & 1 & 3 \\
  0 & 0 & 1 &  0& 1 \\
  \end{array}\right]

Use array for tabular

The LaTeX code for the following table
\begin{array}{ |c|c|c| }
\hline
a & a^2 \pmod{5} & 2a^2 \pmod{5} \\
\hline
0 & 0 & 0 \\
1& 1 & 2 \\
2& 4 & 3 \\
3 & 4 & 3\\
4 & 1 & 2\\
\hline
\end{array}
is

\begin{array}{ |c|c|c| } 
\hline
a & a^2 \pmod{5} & 2a^2 \pmod{5} \\
\hline
0 & 0 & 0 \\ 
1 & 1 & 2 \\ 
2 & 4 & 3 \\ 
3 & 4 & 3\\
4 & 1 & 2\\
\hline
\end{array}

Giving reasons for each line in align

To give a reason how to obtain each equality, like
\begin{align*}
f(ab)&=(ab)^2 && (\text{by definition of $f$})\\
&=(ab)(ab)\\
&=a^2 b^2 && (\text{since $G$ is abelian})\\
&=f(a)f(b) && (\text{by definition of $f$}).
\end{align*}

write the LaTex code 

\begin{align*}
f(ab)&=(ab)^2 && (\text{by definition of $f$})\\
&=(ab)(ab)\\
&=a^2 b^2 && (\text{since $G$ is abelian})\\
&=f(a)f(b) && (\text{by definition of $f$}).
\end{align*}

Cases

If the values of a function depends on cases (like parity), you might want to write:
\begin{align*}
\det(A)&=1+(-1)^{n+1} \\
&= \begin{cases}
2 & \text{ if } n \text{ is odd}\\
0 & \text{ if } n \text{ is even}.
\end{cases}
\end{align*}
The following LaTex code produces the above equation with cases:

\begin{align*}
		\det(A)&=1+(-1)^{n+1} \\
		&= \begin{cases}
			2 & \text{ if } n \text{ is odd}\\
			0 & \text{ if } n \text{ is even}.
		\end{cases}

Arrows

When you want to say $A$ implies $B$, and want to write $A\implies B$, then use
\implies for the allow $\implies$.

The opposite direction arrow $\impliedby$ is given by \impliedby.

When you want to say $A$ if and only if $B$, and want to write $A\iff B$, then use
\iff for the allow $\iff$.

Symbols Latex codes
$\implies$ \implies
$\impliedby$ \impliedby
$\iff$ \iff
$\mapsto$ \mapsto
$\to$ \to
$\gets$ \gets
$\rightarrow$ \rightarrow
$\leftarrow$ \leftarrow
$\Rightarrow$ \Rightarrow
$\Leftarrow$ \Leftarrow
$\hookrightarrow$ \hookrightarrow
$\hookleftarrow$ \hookleftarrow

Second derivative

If you want to write the second derivative $f^{\prime\prime}$, then write the LaTeX code f^{\prime\prime}.

Note that for the first derivative $f’$, the latex code f' works but f'' produces $f”$.

The length (magnitude) of vectors

To write a length of a vector such as
\[\|\mathbf{v}\| \text{ or } \left\|\frac{a}{b}\right \|,\] use the LateX codes

\|\mathbf{v}\|

or

\left\|\frac{a}{b}\right \|

Explanations under equations

If you want to add some explanations under an equation like
\[n=\underbrace{1+1+\cdots+1}_{\text{$n$ times}},\] then use the Latex code

 \[n=\underbrace{1+1+\cdots+1}_{\text{$n$ times}}.\]

Integral

An integral of a function
\[\int_{a}^{b} \! f(x)\,\mathrm{d}x\] is generated by the LaTex code

\int_{a}^{b} \! f(x)\,\mathrm{d}x.

Note that \! narrows the space between the integral sign and the function, and \, increases the space between the function and $\mathrm{d}x$.

Crossing things out

To strike through an expression obliquely like \(\require{cancel}\)$\cancel{A}$ to cancel the expression $A$, we first need to put the code 

\(\require{cancel}\)

before the formula where you want to put $\cancel{A}$.
You just need only one \(\require{cancel}\) per page.

Then write the LaTex code \cancel{A}.

  

Reference

The following website contains more useful LaTex codes for MathJax.

MathJax basic tutorial and quick reference

For LaTex symbols, check the website LaTeX:Symbols (Art of Problem Solving).