### MathJax on Blogger Cheatsheet

**1. Placement**

**will generate the formula inline \(\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\) of a paragraph, where**

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

**will render the formula as a seperate image $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$ and not inline to the paragraph.**

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

**2. Greek letters**

For Greek letters, use

\(\alpha\)`$\alpha$`

\(\beta\)`$\beta$`

\(\delta\) or`$\delta$`

\(\Delta\)`$\Delta$`

\(\gamma\) or`$\gamma$`

\(\Gamma\)`$\Gamma$`

\(\ldots\)`$\ldots$`

\(\omega\) or`$\omega$`

\(\Omega\)`$\Omega$`

**3. Superscripts and subscripts**

For superscripts and subscripts, use

**and**

`^`

**.**

`_`

\(x_i^2\)`$x_i^2$`

\(\log_2x\)`$\log_2x$`

**4. Grouping**

Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}.

If you do

**, you will get a surprise: \(10^10\). But**

`$10^10$`

**gives what you probably wanted: \(10^{1-}\).**

`10^{10}`

Use curly braces to delimit a formula to which a superscript or subscript applies:

**is an error;**

`$x^5^6$`

**is \({x^y}^z\), and**

`${x^y}^z$`

**is \(x^{y^z}\).**

`$x^{y^z}$`

Observe the difference between

**\(x_i^2\) and**

`$x_i^2$`

**\(x_{i^2}\).**

`$x_{i^2}$`

**5. Parentheses**

Ordinary symbols

**make parentheses and brackets \((2+3)[4+4](2+3)[4+4]\).**

`$()[]$`

Use

**and**

`$\{$`

**for curly braces \(\{\ldots\}\) and use**

`$\}$`

**and**

`$\($`

**for round braces \((\ldots)\).**

`$\)$`

These do not scale with the formula in between, so if you write

**the parentheses will be too small: \(\frac{\sqrt x}{y^3}\).**

`$(\frac{\sqrt x}{y^3})$`

Using

**and**

`$\left$`

**$\right$**

will make the sizes adjust automatically to the formula they enclose: **is \(\left(\frac{\sqrt x}{y^3}\right)\).**

`$\left(\frac{\sqrt x}{y^3}\right)$`

**6. Sums and integrals**

**and**

`$\sum$`

**the subscript is the lower limit and the superscript is the upper limit, so for example**

`$\int`

**renders as \(\sum_1^n\).**

`$\sum_1^n$`

Remember that

**if the limits are more than a single symbol. For example,**

`{…}`

**renders as \(\sum_{i=0}^\infty i^2\).**

`$\sum_{i=0}^\infty i^2$`

Similarly,

**\(\prod\),**

`$\prod$`

**\(\int\),**

`$\int$`

**\(\bigcup\),**

`$\bigcup$`

**\(\bigcup\) and/or**

`$\bigcap$`

**\(\iint\).**

`\iint`

**7. Fractions**

There are two approaches

applies to the next two groups renders as \(\frac ab\); and`$\frac ab$`

- more complicated numerators and denominators use
`$/{…/}$`

**renders as \(\frac{a+1}{b+1}\). If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in, eg.**

`$\frac{a+1}{b+1}$`

**renders as \({a+1\over b+1}\).**

`${a+1\over b+1}$`

**8. Radical signs**

Use

**, which adjusts to the size of its argument, eg.**

`$\sqrt$`

**renders as \(\sqrt{x^3}\) and**

`$\sqrt{x^3}$`

**renders as \(\sqrt[3]{\frac xy}\).**

`$\sqrt[3]{\frac xy}$`

For complicated expressions, consider using

**instead.**

`${...}^{1/2}$`

**9. Special functions**

Such as

**,**

`$\lim$`

**,**

`$\sin$`

**,**

`$\max$`

**, etc. are normally set in roman font instead of italic font.**

`$\ln$`

**renders as \(\sin x\), and not**

`$\sin x$`

**renders as \(sin x\).**

`$/sin x$`

Use subscripts to attach a notation to

**, eg.**

`$\lim$`

**renders as \(\lim_{x\to 0}\).**

`$\lim_{x\to 0}$`

**10. Some special symbols and notations**

\(\lt\) and`$\lt$`

\(\not\lt\)`$\not\lt$`

\(\gt\) and`$\gt$`

\(\not\gt\)`$\not\gt$`

\(\le\) and`$\le$`

\(\not\le\)`$\not\le$`

\(\ge\) and`$\ge$`

\(\not\ge\)`$\not\ge$`

\(\times\) and`$\times$`

\(\div\)`$\div$`

\(\pm\) and`$\pm$`

\(\mp\)`$\mp$`

\(\ell\)`$\ell`

\(\cdot\) and`$\cdot$`

\(\cup\) and`$\cup$`

\(\cap\)`$\cap$`

\(\setminus\)`$\setminus$`

\(\subset\) and`$\subset$`

\(\subseteq\) and`$\subseteq$`

\(\subsetneq\) and`$\subsetneq$`

\(\supset\)`$\supset$`

\(\in\) and`$\in$`

\(\notin\)`$\notin$`

\(\emptyset\) and`$\emptyset$`

\(\varnothing\)`$\varnothing$`

or`${n+1 \choose 2k}$`

or`$${n+1 \choose 2k}$`

\(n+1 \choose 2k\)`$\binom{n+1}{2k}$`

\(\to\) or`$\to$`

\(\rightarrow\) or`$\rightarrow$`

\(\leftarrow\) or`$\leftarrow$`

\(\Rightarrow\) or`$\Rightarrow$`

\(\Leftarrow\) or`$\Leftarrow$`

\(\mapsto\)`$\mapsto$`

\(\land\) or`$\land$`

\(\lor\) or`$\lor$`

\(\lnot\) or`$\lnot$`

\(\forall\) or`$\forall$`

\(\exists\) or`$\exists$`

\(\top\) or`$\top$`

\(\bot\) or`$\bot$`

\(\vdash\) or`$\vdash$`

\(\vDash\)`$\vDash$`

\(\star\) or`$\star$`

\(\ast\) or`$\ast$`

\(\oplus\) or`$\oplus$`

\(\circ\) or`$\circ$`

\(\bullet\)`$\bullet$`

\(\approx\) or`$\approx$`

\(\sim\) or`$\sim$`

\(\simeq\) or`$\simeq$`

\(\cong\) or`$\cong$`

\(equiv\) or`$\equiv$`

\(\prec\) or`$\prec$`

\(\lhd\)`$\lhd$`

\(\infty\) and`$\infty$`

\(\aleph_0\) or`$\aleph_0$`

\(\nabla\) and`$\nabla$`

\(\partial\) or`$\partial$`

\(\Im\) or`$\Im$`

\(\Re\)`$\Re$`

for modular equivalence eg.`$\pmod$`

would render as \(a\equiv b\pmod n\)`$a\equiv b\pmod n$$`

is the dots in`$\ldots`

renders as \(a1,a2,\ldots,an\) and`$a1,a2,\ldots,an$`

is the dots in`$\cdots$`

renders as \(a1+a2+\cdots+ana1+a2+\cdots+an\)`$a1+a2+⋯+ana1+a2+⋯+an$`

renders as \(\epsilon\) and`$\epsilon$`

renders as \(\varepsilon\)`$\varepsilon$`

renders as \(\phi\) and`$\phi$`

renders as \(\varphi\)`$\varphi$`

**11. Spaces**

**and**

`$a_b$`

**are both \(ab\).**

`$a____b$`

renders as \(a\,b\)**$\,$**

renders as \(a\;b\)**$\;$**

renders as \(a \quad b\)**$\quad$**

renders as \(a \qquad b\)**$\qquad$**

**12. Examples**

**$sum_(i=1)^n i^3=((n(n+1))/2)^2$**

renders as

\(sum_(i=1)^n i^3=((n(n+1))/2)^2\)**$\begin{align}**

\sqrt{37}

& = \sqrt{\frac{73^2-1}{12^2}} \\

& = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\

& = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\

& = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\

& \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)

\end{align}$

renders as

\(\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align} \)

renders as \(P(Z\le z) = \Phi(z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-w^2/2}\,dw\)**$P(Z\le z) = \Phi(z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-w^2/2}\,dw$**

renders as \(\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}\)**$\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}$**

**13. Other references**

- MathJAX - https://www.mathjax.org
- Calculatorium.com - http://www.calculatorium.com/mathjax-quick-start-tutorial/