LaTeX & MathJax basic tutorial and quick reference for commands

A basic tutorial

  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,
    $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
    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 $\lfloor x \rfloor$. 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

  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 $\iint$.

  8. Fractions There are two 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 ${a+1\over b+1}$.

  9. Fonts

    • Use \mathbb or \Bbb for “blackboard bold”: $\mathbb{CHNQRZ}$.
    • Use \mathbf for boldface: $\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ $\mathbf{abcdefghijklmnopqrstuvwxyz}$.
    • 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 \ge \neq $\lt\, \gt\, \le\, \ge\, \neq$. 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 $\approx\, \sim \, \simeq\, \cong\, \equiv\, \prec, \lhd$.
    • \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 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.

  15. Special characters used for MathJax interpreting can be escaped using the \ character: \$ $\$$, \{ $\{$, \_ $\_$, etc. If you want \ itself, you should use \backslash $\backslash$, because \\ is for a new line.

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