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For inline formulas, enclose the formula in $…$. For displayed formulas, use $$…$$.

• These render differently. For example, type the following to show inline mode:
  $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
  $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
• or type the following for display mode:
  $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
  $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$

For Greek letters, use \alpha, \beta, …, \omega: $\alpha$, $\beta$, …, $\omega$.

• For uppercase letters, use \Gamma, \Delta, …, \Omega: $\Gamma$, $\Delta$, …, $\Omega$.
• For other Greek capital letters, use Latin $A,, B, E$ and so on: $A, B, E$.
• Some Greek letters have variant forms: \epsilon \varepsilon $\epsilon$, $\varepsilon$, \phi \varphi $\phi$, $\varphi$, and others.

For superscripts and subscripts, use ^ and _. For example, x_i^2: $x_i^2$, \log_2 x: $\log_2 x$. For the prime symbol, use an apostrophe x' x'' x''': $x'\ x''\ x'''$.

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^y^z is an error; {x^y}^z is ${x^y}^z$, and x^{y^z} is $x^{y^z}$. Observe the differences between x_i^2 $x_i^2$, x_{i^2} $x_{i^2}$ and {x_i}^2 ${x_i}^2$.

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 .: use \left.x^2\right\rvert_3^5 = 5^2-3^2 to get $$\left.x^2\right\rvert_3^5 = 5^2-3^2$$

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 $\iiint$, \idotsint $\idotsint$.

Fractions There are three ways to make fractions. \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 ${a+1\over b+1}$.
• For continued fractions, use \cfrac instead of \frac.

Fonts

For inline formulas, enclose the formula in $…$. For displayed formulas, use $$…$$.

• These render differently. For example, type the following to show inline mode:
  $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
  $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
• or type the following for display mode:
  $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
  $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$

For Greek letters, use \alpha, \beta, …, \omega: $\alpha$, $\beta$, …, $\omega$.

• For uppercase letters, use \Gamma, \Delta, …, \Omega: $\Gamma$, $\Delta$, …, $\Omega$.
• Other Greek capital letters are the same as the Latin ones: A,B,E,Z and so on: $A, B, E, Z$….
• Some Greek letters have variant forms: \epsilon \varepsilon $\epsilon$, $\varepsilon$, \phi \varphi $\phi$, $\varphi$, and others.

For superscripts and subscripts, use ^ and _. For example, x_i^2: $x_i^2$, \log_2 x: $\log_2 x$. For the prime symbol, use an apostrophe x' x'' x''': $x'\ x''\ x'''$.

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^y^z is an error; {x^y}^z is ${x^y}^z$, and x^{y^z} is $x^{y^z}$. Observe the differences between x_i^2 $x_i^2$, x_{i^2} $x_{i^2}$ and {x_i}^2 ${x_i}^2$.

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 .: use \left.x^2\right\rvert_3^5 = 5^2-3^2 to get $$\left.x^2\right\rvert_3^5 = 5^2-3^2$$

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 $\iiint$, \idotsint $\idotsint$.

Fractions There are three ways to make fractions. \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 ${a+1\over b+1}$.
• For continued fractions, use \cfrac instead of \frac.

Fonts

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 remove spaces use \! also repeatedly $\boldsymbol{\cos}\!\text{ine}$

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

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.

Special characters used for MathJax interpreting can be escaped using the \ character: \\$ $\$$, \{ $\{$, \} $\}$, \_ $\_$, \# $\#$, \& $\&$. If you want \ itself, you should use \backslash (symbol) or \setminus (binary operation) for $\backslash$, because \\ is for a new line.

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{…}, for example to access spaces.

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.

Special characters used for MathJax interpreting can be escaped using the \ character: \\$ $\$$, \{ $\{$, \} $\}$, \_ $\_$, \# $\#$, \& $\&$. If you want \ itself, you should use \backslash (symbol) or \setminus (binary operation) for $\backslash$, because \\ is for a new line.