Math Notation Help

• \, inserts the smallest predefined space in a formula
• Equivalent: \hspace{2}
• Ex.: $$a\,b$$ gives $a\,b$
• Ex.: $$a~\hspace{2}~b$$ gives also $a~\hspace{2}~b$

• \; (backslash semicolon) inserts the third smallest predefined space in a formula
• Equivalent: \hspace{6}
• Ex.: $$a\;b$$ gives $a\;b$
• Ex.: $$a~\hspace{6}~b$$ gives also $a~\hspace{6}~b$

• \: inserts the second smallest predefined space in a formula
• Equivalent: \hspace{4}
• Ex.: $$a\:b$$ gives $a\:b$
• Ex.: $$a~\hspace{4}~b$$ gives also $a~\hspace{4}~b$

• \/ (backslash slash) avoids ligatures
• Ex.: $$V\/A$$ gives $V\/A$ in contrast to $$VA$$ which gives $VA$

• In order to prevent some browser specific problems with whitespaces, it is advisable to use ~ (tilde) as the whitespace instead of the normal blank key (in places where whitespaces are mandatory, e.g. after commands).
• Ex.: $$\frac~xy$$ to produce $\frac~xy$
• Ex.: $$\sqrt~n$$ to produce $\sqrt~n$

• inserts a space of n pixels
• Ex.: $$f(x)\hspace{6}=\hspace{6}0$$ gives $f(x)\hspace{6}=\hspace{6}0$
• can be combined with the preceding command \unitlength{m}(default: m=1px) , which defines the applied unit
• Ex.: $$\unitlength{20}a\hspace{2}b$$ gives $\unitlength{20}a\hspace{2}b$ , i.e. a space of 20x2=40px

• Everthing following the \LARGE command will be output in the largest predefined font size until the system encounters another font size command.
• Note: This command is case sensitive, since large, Large and LARGE are different sizes! 
• Ex.: $$\LARGE~3x$$ gives $\LARGE~3x$

• Everthing following the \Large command will be output in the second largest font size until the system encounters another font size command.
• Note: This command is case sensitive, since large, Large and LARGE are different sizes! 
• Ex.: $$\Large~3x$$ gives $\Large~3x$

• Everthing following the \large command will be output in the large font size until the system encounters another font size command.
• Note: This command is case sensitive, since large, Large and LARGE are different sizes! 
• Ex.: $$\large~3x$$ gives $\large~3x$

• Everthing following the \normalsize command will be output in the smallest predefined font size until the system encounters another font size command.
• \normalsize is the default font size, i.e. the size automatically chosen if there is no font size command
• Ex.: $$\normalsize~3x$$ gives $\normalsize~3x$

• inserts a double space of current character set size
• Ex.: $$a\qquad~b$$ gives $a\qquad~b$

• inserts a space of current character set size
• Ex.: $$a\quad~b$$ gives $a\quad~b$

• \small
• Ex.: $$\small~3x$$ gives $\small~3x$

• Everthing following the \tiny command will be output in the smallest predefined font size until the system encounters another font size command.
• Ex.: $$\tiny~3x$$ gives $\tiny~3x$

• Syntax: \left<...\right>
• Ex.: $$\left<f,g\right>$$ gives

$\left$

• Type arithmetic operations and "=" as usual.
• Exp.: $$f(x)=x-2b+(3a/c)$$ gives

$f(x)=x-2b+(3a/c)$

• See also keyword "fraction" for extended capabilities.

• Syntax for an n-dimensional array:
  \begin{array}a₁&...&a_n\end{array}
• Ex.: $$$\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array}$$$ gives

$(\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array})$

$$\bigsum_{n+2}^x$$   is   $\bigsum_{n+2}^x$

• Syntax: \left{...\right}
• Ex.: $$M=\left{a, b, c\right}$$ gives

$M=\left{a, b, c\right}$

• Numbers in formulas are interpreted as constants and they are rendered in non-italic roman font face, which is a widely used convention.
• Following this convention, variables are shown in italic.
• Exp.: $$f(x)=3a+x$$ gives

$f(x)=3a+x$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{<em>lowerexpression</em>}^{<em>upperexpression</em>}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for the contour integral symbol:

$$\bigoint_{0}^{\infty}$$   gives  

$\bigoint_{0}^{\infty}$

and

$$\oint_{0}^{\infty}$$   gives 

$\oint_{0}^{\infty}$

• Use font size commands for a nicer picture:

$$\LARGE\bigoint_{\small0}^{\small\infty}$$   gives  

$\LARGE\bigoint_{\small0}^{\small\infty}$

and

$$\large\oint_{\small0}^{\small\infty}$$   gives 

$\large\oint_{\small0}^{\small\infty}$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{<em>lowerexpression</em>}^{<em>upperexpression</em>}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Note: mimeTeX seems currently only to support the \bigcoprod command.
• Syntax for coproduct symbol:

$$\bigcoprod_{i=k}^{n}$$   gives  

$\bigcoprod_{i=k}^{n}$

• Use font size commands for a nicer picture:

$$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$$   gives  

$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$

Note: The delimiters are automatically sizes.

• Syntax: \left\|...\right\|
• Exp.: $$\left\|af\right\| = \left|a\right|\left\|f\right\|$$ gives

$\left\|af\right\| = \left|a\right|\left\|f\right\|$

• With two triple $'s embracing an expression you can make the filter to escape and the code itself is shown (with two embracing double $'s).
• Ex.: $$$a^2$$$ produces $$a^2$$, i.e. prevents the filter to render it as a formula gif.

$$\fbox{x=\frac{1}{2}}$$  gives

$\fbox{x=\frac{1}{2}}$

• Syntax: \frac{numerator}{denominator}
• Use font sizing commands for specific sizing if you don't want the predefined one to be taken.
• Ex. (with predefined sizing): $$f(x,y)=\frac{2a}{x+y}$$ gives

$f(x,y)=\frac{2a}{x+y}$

• Ex. (with specific sizing): $$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$$ gives

$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$

• You may nest fractions as much as you want.
• Ex. (nested fractions): $$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$$ gives

$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$

$$x>y$$  gives

$x>y$

$$x\ge~y$$ or $$x\geq~y$$ gives

$x\ge~y$

Simply write \greekletter for lower case and \Greekletter for upper case.

Here's a list of all known greek letters (Note: not all upper case greek letters are known):

Lower Case Greek Letters:

Upper Case Greek Letters:

$$\infty$$  gives $\infty$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{<em>lowerexpression</em>}^{<em>upperexpression</em>}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for integral symbol:

$$\bigint_{0}^{\infty}$$   gives  

$\bigint_{0}^{\infty}$

and

$$\int_{0}^{\infty}$$   gives 

$\int_{0}^{\infty}$

• Use font size commands for a nicer picture:

$$\LARGE\bigint_{\small0}^{\small\infty}$$   gives  

$\LARGE\bigint_{\small0}^{\small\infty}$

and

$$\large\int_{\small0}^{\small\infty}$$   gives 

$\large\int_{\small0}^{\small\infty}$

• Syntax: \left{...\right.  <em><font color="#ff0000">(note the dot at the end!)</font></em></li><li><font color="#000000"><u>Ex.:</u> $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$ gives

$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$

(\rm~something switches to roman style)

$$<$$   gives

$$x\le~y$$ or $$x\leq~y$$ gives

$x\le~y$

List of predefined spaces:

Note: Simple blank spaces and tildes (~) are ignored by the TeX filter and don't produce any space. You must use one of the defined math spaces to get a visible (extra) space.

• A valid expression inside the $'s is rendered as mathematics in an inserted gif image.
• Ex.: $$x=y^2$$ creates 

$x=y^2$

• An (m,n)-matrix is considered as an array of m*n elements, where the elements of a column are separated by "&" and the rows by "\\".

• Syntax for an (m,n)-matrix:
  \begin{array}{<em>colformat}a₁₁&...&a_1n\\a₂₁&...&a_2n\\... \\a_m1&...&a_mn \end{array}

  where
  colformat defines the format of each of the n columns: l for left, r for right and c for center (hence {ccccc} defines for a (m,5)-matrix in which all columns are centered)

• Ex.: $$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$$ gives

$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$

Note in the example above that "lcr" has the effect that column 1 is left aligned, column 2 centered and colums 3 right aligned.

$$x\neq~y$$ gives

$x\neq~y$

note: \neg produces the logical negation, i.e. $$\neg~A$$ gives

$\neg~A$

$$o$$ gives $o$

(note this exceptional syntax!)

• Syntax: \left(...\right) or $...$
• Ex.: $$2a\left(b+c\right)$$ gives

$2a\left(b+c\right)$

$$x=\pi r^2$$ is $x=\pi r^2$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{<em>lowerexpression</em>}^{<em>upperexpression</em>}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for product symbol:

$$\bigprod_{i=k}^{n}$$   gives  

$\bigprod_{i=k}^{n}$

and

$$\prod_{i=k}^{n}$$   gives 

$\prod_{i=k}^{n}$

• Use font size commands for a nicer picture:

$$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}$$   gives  

$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}$ 

and

$$\large\prod_{\small{i=k}}^{\small{n}}$$   gives 

$\large\prod_{\small{i=k}}^{\small{n}}$

• Syntax: \left.{...\right}  (note the dot!)
• Ex.: $$\left.{{\rm~term1\atop\rm~term2}\right}=y$$ gives

$\left.{{\rm~term1\atop\rm~term2}\right}=y$

(\rm~something switches to roman style)

• Syntax: \sqrt[n]{arg} or simply  \sqrt{arg} for \sqrt[2]{arg}
• Ex.: $$\sqrt[3]{8}$$ gives

$\sqrt[3]{8}$

• Ex.: $$\sqrt{-1}$$ gives

$\sqrt{-1}$

• Nesting of roots (and combining with fractions, ...etc.) are possible.
• Ex.: $$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$$ gives

$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$

• Ex.: $$\sqrt[3]{-q+\sqrt{q^2+p^3}}$$ gives

$\sqrt[3]{-q+\sqrt{q^2+p^3}}$

• Synatx: \left[...\right]
• Ex.: $$\left[a,b\right]$$ gives $\left[a,b\right]$

• $$\sqrt{a}$$ or $$\sqrt~a$$ gives $\sqrt~a$
• Use braces for terms with more than one character: $$\sqrt{x+y}$$ gives

$\sqrt{x+y}$

• The command character "_" triggers subscription of the following expression(s).
• For more than one subscripted character put them in braces {...}.
• Use font sizing commands for appropriate sizing.
• Ex.:$$x_1$$ gives

$x_1$

• Ex.:$$a_{m+2n}$$ gives

$a_{m+2n}$

• Ex. (with specific sizing):  $$x_{\small1}=a_{\small{m+2n}}$$ gives

$x_{\small1}=a_{\small{m+2n}}$

• Combine subscripting with superscripting (command character "^").
  Syntax: Expr_{subExpr}^{supExpr}.
• Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$$ gives

$A_{\small{i,j,k}}^{\small{-n+2}}$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{<em>lowerexpression</em>}^{<em>upperexpression</em>}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for summation symbol:

$$\bigsum_{i=k}^{n}$$   gives  

$\bigsum_{i=k}^{n}$

and

$$\sum_{i=k}^{n}$$   gives 

$\sum_{i=k}^{n}$

• Use font size commands for a nicer picture:

$$\LARGE\bigsum_{\small{i=1}}^{\small{n}}$$   gives  

$\LARGE\bigsum_{\small{i=1}}^{\small{n}}$

and

$$\large\sum_{\small{i=1}}^{\small{n}}$$   gives 

$\large\sum_{\small{i=1}}^{\small{n}}$

• The command character "^" triggers superscription of the following expression(s).
• For more than one superscripted character put them in braces {...}.
• Use font sizing commands for appropriate sizing.
• Ex.: $$x^2$$ gives

$x^2$

• Ex.: $$a^{m+2n}$$ gives

$a^{m+2n}$

• Ex. (with specific sizing): $$x^{\small2}=a^{\small{m+2n}}$$ gives

$x^{\small2}=a^{\small{m+2n}}$

• Combine superscripting with subscripting (command character "_").
  Syntax: Expr_{subExpr}^{supExpr}.
• Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$$ gives

$A_{\small{i,j,k}}^{\small{-n+2}}$

• Two double $'s embracing a valid math expression trigger the filter to generate and insert the formula gif.
• Ex.:  $$a^2$$ produces $a^2$
  

• Variables in formulas are rendered in italic roman font face, which is a widely used convention.
• Following this convention, constants are shown as non-italic.
• Exp.: $$f(x)=3a+x$$ gives

$f(x)=3a+x$

• Syntax: \left|...\right|
• Ex.: $$\left|b-a\right|$$ gives $\left|b-a\right|$
• Ex.: $${\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$$ gives  

${\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$ 

 
("\rm~something" renders "something" in roman style)