# MathJax basic tutorial and quick reference

1. To see how any formula was written in any question or answer, including this one, right-click on the expression it and choose "Show Math As > TeX Commands". (When you do this, the '$$' will not display. Make sure you add these. See the next point.)$$

2. For inline formulas, enclose the formula in $.... For displayed formulas, use $$...$$. These render differently. For example, type $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}
to show $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$(which is inline mode) or type \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} to show \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} (which is display mode).$$ 3. For Greek letters, use \alpha, \beta, …, \omega:$\alpha, \beta, … \omega$$. For uppercase, use \Gamma, \Delta, …, \Omega:$$\Gamma, \Delta, …, \Omega$$.$$

4. For superscripts and subscripts, use ^ and _. For example, x_i^2: $x_i^2$$, \log_2 x:$$\log_2 x$$.$$ 5. Groups. 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^{10}$$. Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is$${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}$$.$$

6. Parentheses Ordinary symbols ()[] make parentheses and brackets $(2+3)[4+4]$$. Use \{ and \} for curly braces$$\{\}$.

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

\left and\right apply to all the following sorts of parentheses: ( and ) $$(x)$$, [ and ] $$[x]$$, \{ and \} $$\{ x \}$$, | $$|x|$$, \vert $$\vert x \vert$$, \Vert $$\Vert x \Vert$$, \langle and \rangle $$\langle x \rangle$$, \lceil and \rceil $$\lceil x \rceil$$, and \lfloor and \rfloor $$\lfloor x \rfloor$$. \middle can be used to add additional dividers. There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is $$\left.\frac12\right\rbrace$$.

If manual size adjustments are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives $$\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)$$.

7. 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 $$\sum_1^n$$. Don't forget {} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is $$\sum_{i=0}^\infty i^2$$. Similarly, \prod $$\prod$$, \int $$\int$$, \bigcup $$\bigcup$$, \bigcap $$\bigcap$$, \iint $$\iint$$, \iiint $$\iiint$$.

8. Fractions There are three ways to make these. \frac ab applies to the next two groups, and produces $$\frac ab$$; for more complicated numerators and denominators use {}: \frac{a+1}{b+1} is $$\frac{a+1}{b+1}$$. If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1} is $${a+1\over b+1}$$. Using \cfrac{a}{b} command is useful for continued fractions $$\cfrac{a}{b}$$, more details for which are given in this sub-article.

9. Fonts

• Use \mathbb or \Bbb for "blackboard bold": $$\mathbb{CHNQRZ}$$.
• Use \mathbf for boldface: $$\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\mathbf{abcdefghijklmnopqrstuvwxyz}$$.
• Use \mathit for italics: $$\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\mathit{abcdefghijklmnopqrstuvwxyz}$$.
• Use \pmb for boldfaced italics: $$\pmb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\pmb{abcdefghijklmnopqrstuvwxyz}$$.
• Use \mathtt for "typewriter" font: $$\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\mathtt{abcdefghijklmnopqrstuvwxyz}$$.
• Use \mathrm for roman font: $$\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\mathrm{abcdefghijklmnopqrstuvwxyz}$$.
• Use \mathsf for sans-serif font: $$\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\mathsf{abcdefghijklmnopqrstuvwxyz}$$.
• Use \mathcal for "calligraphic" letters: $$\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$
• Use \mathscr for script letters: $$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$
• Use \mathfrak for "Fraktur" (old German style) letters: $$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}$$.
10. Radical signs Use sqrt, which adjusts to the size of its argument: \sqrt{x^3} $$\sqrt{x^3}$$; \sqrt[3]{\frac xy} $$\sqrt[3]{\frac xy}$$. For complicated expressions, consider using {...}^{1/2} instead.

11. Some special functions such as "lim", "sin", "max", "ln", and so on are normally set in roman font instead of italic font. Use \lim, \sin, etc. to make these: \sin x $$\sin x$$, not sin x $$sin x$$. Use subscripts to attach a notation to \lim: \lim_{x\to 0} $$\lim_{x\to 0}$$

12. There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:

• \lt \gt \le \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq $$\lt\, \gt\, \le\, \leq\, \leqq\, \leqslant\, \ge\, \geq\, \geqq\, \geqslant\, \neq$$. You can use \not to put a slash through almost anything: \not\lt $$\not\lt$$ but it often looks bad.
• \times \div \pm \mp $$\times\, \div\, \pm\, \mp$$. \cdot is a centered dot: $$x\cdot y$$
• \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing $$\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing$$
• {n+1 \choose 2k} or \binom{n+1}{2k} $${n+1 \choose 2k}$$
• \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto $$\to\, \rightarrow\, \leftarrow\, \Rightarrow\, \Leftarrow\, \mapsto$$
• \land \lor \lnot \forall \exists \top \bot \vdash \vDash $$\land\, \lor\, \lnot\, \forall\, \exists\, \top\, \bot\, \vdash\, \vDash$$
• \star \ast \oplus \circ \bullet $$\star\, \ast\, \oplus\, \circ\, \bullet$$
• \approx \sim \simeq \cong \equiv \prec \lhd \therefore $$\approx\, \sim \, \simeq\, \cong\, \equiv\, \prec\, \lhd\, \therefore$$
• \infty \aleph_0 $$\infty\, \aleph_0$$ \nabla \partial $$\nabla\, \partial$$ \Im \Re $$\Im\, \Re$$
• For modular equivalence, use \pmod like this: a\equiv b\pmod n $$a\equiv b\pmod n$$.
• \ldots is the dots in $$a_1, a_2, \ldots ,a_n$$ \cdots is the dots in $$a_1+a_2+\cdots+a_n$$
• Some Greek letters have variant forms: \epsilon \varepsilon $$\epsilon\, \varepsilon$$, \phi \varphi $$\phi\, \varphi$$, and others. Script lowercase l is \ell $$\ell$$.

Detexify lets you draw a symbol on a web page and then lists the $$\TeX$$ symbols that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supported $$\LaTeX$$ commands, and one can also check Dr. Carol JVF Burns's page of $$\TeX$$ Commands Available in MathJax.

13. Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in: a␣b and a␣␣␣␣b are both $$a b$$. To add more space, use \, for a thin space $$a\,b$$; \; for a wider space $$a\;b$$. \quad and \qquad are large spaces: $$a\quad b$$, $$a\qquad b$$.

To set plain text, use \text{…}: $$\{x\in s\mid x\text{ is extra large}\}$$. You can nest $$…$$ inside of \text{…}.

14. Accents and diacritical marks Use \hat for a single symbol $$\hat x$$, \widehat for a larger formula $$\widehat{xy}$$. If you make it too wide, it will look silly. Similarly, there are \bar $$\bar x$$ and \overline $$\overline{xyz}$$, and \vec $$\vec x$$ and \overrightarrow $$\overrightarrow{xy}$$ and \overleftrightarrow $$\overleftrightarrow{xy}$$. For dots, as in $$\frac d{dx}x\dot x = \dot x^2 + x\ddot x$$, use \dot and \ddot.


• It must have taken more than a thousand words to write that picture though :D – user477343 Jul 20 at 9:25

## protected by MJDMay 28 '15 at 17:18

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