Tuesday, 3 October 2017

MathJax on Blogger Cheatsheet

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

2. Greek letters
For Greek letters, use
  1. $\alpha$ \(\alpha\)
  2. $\beta$ \(\beta\)
  3. $\delta$ \(\delta\) or $\Delta$ \(\Delta\)
  4. $\gamma$ \(\gamma\) or $\Gamma$ \(\Gamma\)
  5. $\ldots$ \(\ldots\)
  6. $\omega$ \(\omega\) or $\Omega$ \(\Omega\)

3. Superscripts and subscripts

For superscripts and subscripts, use ^ and _.
  1. $x_i^2$ \(x_i^2\)
  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 $10^10$, you will get a surprise: \(10^10\). But 10^{10} gives what you probably wanted: \(10^{1-}\).

Use curly braces to delimit a formula to which a superscript or subscript applies: $x^5^6$ is an error; ${x^y}^z$ is \({x^y}^z\), and $x^{y^z}$ is \(x^{y^z}\).

Observe the difference between $x_i^2$ \(x_i^2\) and $x_{i^2}$ \(x_{i^2}\).

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

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

6. Sums and integrals

$\sum$ and $\int the subscript is the lower limit and the superscript is the upper limit, so for example $\sum_1^n$ renders as \(\sum_1^n\).

Remember that {…} if the limits are more than a single symbol. For example, $\sum_{i=0}^\infty i^2$ renders as \(\sum_{i=0}^\infty i^2\).

Similarly, $\prod$ \(\prod\), $\int$ \(\int\), $\bigcup$ \(\bigcup\), $\bigcap$ \(\bigcup\) and/or \iint \(\iint\).

7. Fractions

There are two approaches
  1. $\frac ab$ applies to the next two groups renders as \(\frac ab\); and
  2. more complicated numerators and denominators use $/{…/}$
, eg. $\frac{a+1}{b+1}$ 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. ${a+1\over b+1}$ renders as \({a+1\over b+1}\).

8. Radical signs

Use $\sqrt$, which adjusts to the size of its argument, eg. $\sqrt{x^3}$ renders as \(\sqrt{x^3}\) and $\sqrt[3]{\frac xy}$ renders as \(\sqrt[3]{\frac xy}\).

For complicated expressions, consider using ${...}^{1/2}$ instead.

9. Special functions

Such as $\lim$, $\sin$, $\max$, $\ln$, etc. are normally set in roman font instead of italic font. $\sin x$ renders as \(\sin x\), and not $/sin x$ renders as \(sin x\).

Use subscripts to attach a notation to $\lim$, eg. $\lim_{x\to 0}$ renders as \(\lim_{x\to 0}\).

10. Some special symbols and notations

  1. $\lt$ \(\lt\) and $\not\lt$ \(\not\lt\)
  2. $\gt$ \(\gt\) and $\not\gt$ \(\not\gt\)
  3. $\le$ \(\le\) and $\not\le$ \(\not\le\)
  4. $\ge$ \(\ge\) and $\not\ge$ \(\not\ge\)
  5. $\times$ \(\times\) and $\div$ \(\div\)
  6. $\pm$ \(\pm\) and $\mp$ \(\mp\)
  7. $\ell \(\ell\)
  8. $\cdot$ \(\cdot\) and $\cup$ \(\cup\) and $\cap$ \(\cap\)
  9. $\setminus$ \(\setminus\)
  10. $\subset$ \(\subset\) and $\subseteq$ \(\subseteq\) and $\subsetneq$ \(\subsetneq\) and $\supset$ \(\supset\)
  11. $\in$ \(\in\) and $\notin$ \(\notin\)
  12. $\emptyset$ \(\emptyset\) and $\varnothing$ \(\varnothing\)
  13. ${n+1 \choose 2k}$ or $${n+1 \choose 2k}$ or $\binom{n+1}{2k}$ \(n+1 \choose 2k\)
  14. $\to$ \(\to\) or $\rightarrow$ \(\rightarrow\) or $\leftarrow$ \(\leftarrow\) or $\Rightarrow$ \(\Rightarrow\) or $\Leftarrow$ \(\Leftarrow\) or $\mapsto$ \(\mapsto\)
  15. $\land$ \(\land\) or $\lor$ \(\lor\) or $\lnot$ \(\lnot\) or $\forall$ \(\forall\) or $\exists$ \(\exists\) or $\top$ \(\top\) or $\bot$ \(\bot\) or $\vdash$ \(\vdash\) or $\vDash$ \(\vDash\)
  16. $\star$ \(\star\) or $\ast$ \(\ast\) or $\oplus$ \(\oplus\) or $\circ$ \(\circ\) or $\bullet$ \(\bullet\)
  17. $\approx$ \(\approx\) or $\sim$ \(\sim\) or $\simeq$ \(\simeq\) or $\cong$ \(\cong\) or $\equiv$ \(equiv\) or $\prec$ \(\prec\) or $\lhd$ \(\lhd\)
  18. $\infty$ \(\infty\) and $\aleph_0$ \(\aleph_0\) or $\nabla$ \(\nabla\) and $\partial$ \(\partial\) or $\Im$ \(\Im\) or $\Re$ \(\Re\)
  19. $\pmod$ for modular equivalence eg. $a\equiv b\pmod n$$ would render as \(a\equiv b\pmod n\)
  20. $\ldots is the dots in $a1,a2,\ldots,an$ renders as \(a1,a2,\ldots,an\) and $\cdots$ is the dots in $a1+a2+⋯+ana1+a2+⋯+an$ renders as \(a1+a2+\cdots+ana1+a2+\cdots+an\)
  21. $\epsilon$ renders as \(\epsilon\) and $\varepsilon$ renders as \(\varepsilon\)
  22. $\phi$ renders as \(\phi\) and $\varphi$ renders as \(\varphi\)

11. Spaces

$a_b$ and $a____b$ are both \(ab\).
  1. $\,$ renders as \(a\,b\)
  2. $\;$ renders as \(a\;b\)
  3. $\quad$ renders as \(a \quad b\)
  4. $\qquad$ renders as \(a \qquad b\)
12. Examples
  1. $sum_(i=1)^n i^3=((n(n+1))/2)^2$
    renders as
    \(sum_(i=1)^n i^3=((n(n+1))/2)^2\)
  2. $\begin{align}
    & = \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)

    renders as
    \(\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align} \)
  3. $P(Z\le z) = \Phi(z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-w^2/2}\,dw$ renders as \(P(Z\le z) = \Phi(z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-w^2/2}\,dw\)
  4. $\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}$ renders as \(\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}\)
13. Other references
  1. MathJAX - https://www.mathjax.org
  2. Calculatorium.com - http://www.calculatorium.com/mathjax-quick-start-tutorial/

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