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. $\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align} renders as \begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align} 3. P(Z\le z) = \Phi(z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-w^2/2}\,dw$ 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/
MathJax on Blogger Cheatsheet Reviewed by Johan Els on October 03, 2017 Rating: 5