From http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference
For inline formulas, enclose the formula in
$...$. For displayed formulas, use$$...$$.-
ForGreek letters, use
\alpha,\beta, …,\omega:α,β,…ω. For uppercase, use\Gamma,\Delta, …,\Omega:Γ,Δ,…,Ω.
Formulas -
Forsuperscripts and subscripts, use
^and_.
For example,x_i^2:
x_i^2 -
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 do10^10, you will get a surprise:
But
10^1010^{10}gives what you probably wanted:
Use curly braces to delimit a formula to which a superscript or subscript applies:
10^{10}x^5^6is an error;{x^y}^zis
and
{x^y}^zx^{y^z}is
Observe the difference between
x^{y^z}x_i^2
and
x_i^2x_{i^2}
x_{i^2} -
ParenthesesOrdinary symbols
()[]make parentheses and brackets(2+3)[4+4]. Use\{and\}for curly braces{}.
These donotscale with the formula in between, so if you write(\frac{\sqrt x}{y^3})the parentheses will be too small:
Using
(\frac{\sqrt x}{y^3})\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)\leftand\rightapply to all the following sorts of parentheses:(and)(x),[and][x],\{and\}{x},||x|,\langleand\rangle⟨x⟩,\lceiland\rceil⌈x⌉, and\lfloorand\rfloor⌊x⌋. There are also invisible parentheses, denoted by.:\left.\frac12\right\rbraceis
\left.\frac12\right\rbrace -
Sums and integrals
\sumand\int; the subscript is the lower limit and the superscript is the upper limit, so for example\sum_1^n
Don't forget
\sum_1^n{…}if the limits are more than a single symbol. For example,\sum_{i=0}^\infty i^2is
Similarly,
\sum_{i=0}^\infty i^2\prod∏,\int∫,\bigcup⋃,\bigcap⋂,\iint∬. -
FractionsThere are two ways to make these.
\frac abapplies to the next two groups, and produces
for more complicated numerators and enominators use
\frac ab{…}:\frac{a+1}{b+1}is
If the numerator and denominator are complicated, you may prefer
\frac{a+1}{b+1}\over, which splits up the group that it is in:{a+1\over b+1}is
{a+1\over b+1} Fonts
- Use
\mathbbor\Bbbfor "blackboard bold":
blackboard bold - Use
\mathbffor boldface:
boldface - Use
\mathttfor "typewriter" font:
typewriter - Use
\mathrmfor roman font:
roman - Use
\mathsffor sans-serif font:
sans-serif font - Use
\mathcalfor "calligraphic" letters:
calligraphic - Use
\mathscrfor script letters:
script - Use
\mathfrakfor "Fraktur" (old German style) letters:
Fraktur
-
Radical signsUse
sqrt, which adjusts to the size of its argument:\sqrt{x^3}:
\sqrt{x^3}\sqrt[3]{\frac xy}:
For complicated expressions, consider using
\sqrt[3]{\frac xy}{...}^{1/2}instead. -
Somespecial functionssuch 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
not
\sin xsin x
Use subscripts to attach a notation to
sin x\lim:\lim_{x\to 0}
\lim_{x\to 0} There are a very large number ofspecial symbols and notations, too many to list here; seethis shorter listing, orthis exhaustive listing. Some of the most common include:
-
\lt\gt\le\ge\neq<>≤≥≠. You can use\notto put a slash through almost anything:\not\lt≮but it often looks bad. -
\times\div\pm\mp×÷±∓.\cdotis a centered dot:x⋅y -
\cup\cap\setminus\subset\subseteq\subsetneq\supset\in\notin\emptyset\varnothing∪∩∖⊂⊆⊊⊃∈∉∅∅ -
{n+1\choose 2k}or\binom{n+1}{2k}
\binom{n+1}{2k} -
\to\rightarrow\leftarrow\Rightarrow\Leftarrow\mapsto→→←⇒⇐ -
\land\lor\lnot\forall\exists\top\bot\vdash\vDash∧∨¬∀∃⊤⊥⊢⊨ -
\star\ast\oplus\circ\bullet⋆∗⊕∘∙ -
\approx\sim\simeq\cong\equiv\prec≈∼≃≅≡≺ -
\infty\aleph_0∞ℵ0\nabla\partial∇∂\Im\Reℑℜ - For modular equivalence, use
\pmodlike this:a\equiv b\pmod na≡b (mod n). -
\ldotsis the dots in
an
\ldots\cdotsis the dots in
\cdots - Some Greek letters have variant forms:\epsilon \varepsilonϵε,\phi \varphiϕφ, and others. Script lowercase l is\ellℓ.
Detexifylets you draw a symbol on a web page and then lists theTEXsymbols 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 alist of currently supportedLATEXcommands, and one can also check Dr. Carol JVF Burns's page of[TEXCommands Available in MathJax(http://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm).
-
SpacesMathJax 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␣banda␣␣␣␣bare both
To add more space, use
ab\,for a thin space
a b\;for a wider space
a b\quadand\qquadare large spaces:
To set plain text, use
a b,a b\text{…}:{x∈s∣xis extra large}. You can nest$…$inside of\text{…}. -
Accents and diacritical marksUse
\hatfor a single symbol
\hat\widehatfor a larger formula
If you make it too wide, it will look silly. Similarly, there are
\widehat\bar
and
\bar\overline
and
\overline\vec
and
\vec\overrightarrow
and
\overrightarrow\overleftrightarrow
For dots, as in
\overleftrightarrow
use
\dotand\ddot\dotand\ddot. Special characters used for MathJax interpreting can be escaped using the
\character:\$$,\{{,\__, etc. If you want\itself, you should use\backslash∖, because\\\is for a new line.
Examples
- Use
$$\begin{matrix}…\end{matrix}$$In between the\beginand\end, put the matrix elements. End each matrix row with\\\, and separate matrix elements with&. For example,
$$
\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
$$
produces:
MathJax will adjust the sizes of the rows and columns so that everything fits.
-
To add brackets, either use
\left…\rightas in section 6 of the tutorial, or replacematrixwithpmatrix
Paste_Image.pngbmatrix
Paste_Image.pngBmatrix
Paste_Image.pngvmatrix
Paste_Image.pngVmatrix
Paste_Image.png -
Use
\cdots⋯\ddots⋱\vdots⋮when you want to omit some of the entries:
Paste_Image.png -
For "augmented" matrices, put parentheses or brackets around a suitably-formatted table; seearraysbelow for details. Here is an example:
Paste_Image.png
$$ \left[
\begin{array}{cc|c}
1&2&3\\
4&5&6
\end{array}
\right] $$
Thecc|cis the crucial part here; it says that there are three centered columns with a vertical bar between the second and third.
-
For small inline matrices use\bigl(\begin{smallmatrix} ... end{smallmatrix}\bigr), e.g.
Paste_Image.pngis produced by:
$\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$
-
Often people want a series of equations where the equals signs are aligned. To get this, use\begin{align}…\end{align}. Each line should end with\, and should contain an ampersand at the point to align at, typically immediately before the equals sign.
For example,
Paste_Image.png
is produced by
\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}
by writing this:
f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
The brace can be moved to the right:
by writing this:
\left.
\begin{array}{l}
\text{if $n$ is even:}&n/2\\
\text{if $n$ is odd:}&3n+1
\end{array}
\right\}
=f(n)
To get a larger vertical space between cases we can use\\\[2ex]
instead of\\\. For example, you get this:
by writing this:
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if $n$ is even} \\[2ex]
3n+1, & \text{if $n$ is odd}
\end{cases}