Sunday, October 20, 2019, 2:42 AM
Site: Saint Martin's University Moodle
Course: Saint Martin's University Moodle (SMU)
Glossary: Math Notation Help
\

\_ (where _ is blank)

• Ordinary whitespace to be used after a dot not denoting the end of a sentence
• After commands without parameters use \~ (tilde) instead in order to avoid browser specific problems

\,

• \, 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$

\~

• 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.: $$\sqrt~n$to produce$\sqrt~n$$

\hspace{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

\LARGE (all capital letters)

• 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.: $$\LARGE~3x$gives$\LARGE~3x$$

\Large (L capital letter)

• 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.: $$\Large~3x$gives$\Large~3x$$

\large (all lower case letters)

• 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.: $$\large~3x$gives$\large~3x$$

\normalsize

• 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

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

\tiny

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

 Absolute Font Sizes Command Example Result \tiny $$\tiny 3x\tiny 3x$$ \small $$\small 3x\small 3x$$ \normalsize (default) $$\normalsize 3x$$$or just $$3x\normalsize 3x$$ \large $$\large 3x\large 3x$$ \Large $$\Large 3x\Large 3x$$ \LARGE $$\LARGE 3x\LARGE 3x$$ \huge and \Huge are not supported by the mimeTeX filter algebraic expression alpha (lower case greek letter) $$\alpha$gives$\alpha$$ angle bracket • Syntax: \left<...\right> • Ex.: $$\left<f,g\right>gives \left<f,g\right>$$ arithmetic operations • 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. array • Syntax for an n-dimensional array: \begin{array}a1&...&an\end{array} • Ex.: $$$\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array}$gives (\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array})$$ B beta (lower case greek letter) $$\beta$gives$\beta$$ big sum $$\bigsum_{n+2}^x$is$\bigsum_{n+2}^x$$ braces • Syntax: \left{...\right} • Ex.: $$M=\left{a, b, c\right}gives M=\left{a, b, c\right}$$ C cdot (multiplication) $$a\cdot~b$gives$a\cdot~b$$ chi (lower case greek letter) $$\chi$gives$\chi$$ constants • 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.: $$f(x)=3a+xgives f(x)=3a+x$$ contour integral • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • 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

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

coproduct

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

\symbolname_{lowerexpression}^{upperexpression}

• 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:

\left\|af\right\| = \left|a\right|\left\|f\right\|$$E epsilon (lower case greek letter)$$\epsilon$gives$\epsilon$$equals escaping the TeX filter • With two triple 's embracing an expression you can make the filter to escape and the code itself is shown (with two embracing double 's). • Ex.:$$$a^2$$produces$$a^2$$, i.e. prevents the filter to render it as a formula gif. eta (lower case greek letter)$$\eta$gives$\eta$$F formula box$$\fbox{x=\frac{1}{2}}gives \fbox{x=\frac{1}{2}}$$fraction • Syntax: \frac{numerator}{denominator} • Use font sizing commands for specific sizing if you don't want the predefined one to be taken. • Ex. (with predefined sizing):$$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}}$$G gamma (lower case greek letter)$$\gamma$gives$\gamma$$Gamma (upper case greek letter)$$\Gamma$gives$\Gamma$$greater than$$x>ygives x>y$$greater than or equal$$x\ge~y$or x\geq~y$$ gives

$x\ge~y$

greek letters (overview)

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:

 Command Filter Expression Result \alpha $$\alpha\alpha$$ \beta $$\beta\beta$$ \gamma $$\gamma\gamma$$ \delta $$\delta\delta$$ \epsilon $$\epsilon\epsilon$$ \varepsilon $$\varepsilon\varepsilon$$ \zeta $$\zeta\zeta$$ \eta $$\eta\eta$$ \theta $$\theta\theta$$ \vartheta $$\vartheta\vartheta$$ \iota $$\iota\iota$$ \kappa $$\kappa\kappa$$ \lambda $$\lambda\lambda$$ \mu $$\mu\mu$$ \nu $$\nu\nu$$ \xi $$\xi\xi$$ o  (!) $$oo$$ \pi $$\pi\pi$$ \varpi $$\varpi\varpi$$ \rho $$\rho\rho$$ \varrho $$\varrho\varrho$$ \sigma $$\sigma\sigma$$ \varsigma $$\varsima\varsigma$$ \tau $$\tau\tau$$ \upsilon $$\upsilon\upsilon$$ \phi $$\phi\phi$$ \varphi $$\varphi\varphi$$ \chi $$\chi\chi$$ \psi $$\psi\psi$$ \omega $$\omega\omega$$

Upper Case Greek Letters:

 Command Filter Expression Result \Gamma $$\Gamma\Gamma$$ \Delta $$\Delta\Delta$$ \Theta $$\Theta\Theta$$ \Lambda $$\Lambda\Lambda$$ \Xi $$\Xi\Xi$$ \Pi $$\Pi\Pi$$ \Sigma $$\Sigma\Sigma$$ \Upsilon $$\Upsilon\Upsilon$$ \Phi $$\Phi\Phi$$ \Psi $$\Psi\Psi$$ \Omega $$\Omega\Omega$$

I

infinity

$$\infty$gives$\infty$$

integral

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

\symbolname_{lowerexpression}^{upperexpression}

• 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 $\large\int_{\small0}^{\small\infty}$ iota (lower case greek letter) $$\iota$gives$\iota$$ K kappa $$\kappa$gives$\kappa$$ L lambda (lower case greek letter) $$\lambda$gives$\lambda$$ Lambda (upper case greek letter) $$\Lambda$gives$\Lambda$$ Learning Formula $\frac{success}{problem}=~\unitlength{.6}~\picture(100){~~(50,50){\circle(99)}~ ~(20,55;50,0;2){+1\hat\bullet}~~(50,40){\bullet}~~(50,35){\circle(50,25;34)}~ ~(50,35){\circle(50,45;34)}}$ left only brace • Syntax: \left{...\right. (note the dot at the end!) • Ex.: $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.gives f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$ (\rm~something switches to roman style) less than $$<gives <$$ less than or equal $$x\le~y$or x\leq~y$ gives $x\le~y$ M math spaces List of predefined spaces:  Math Spaces Command Example Result \, (smallest predefined)$$a\,ba\,b$$\: (second smallest predefined)$$a\:ba\:b$$\; (third smallest predefined)$$a\;ba\;b\/ (avoiding ligatures)V\/A$ instead of $$VAV\/A$instead of$VA$$ \quad  (space of current character set size) $$a\quad~ba\quad~b$$ \qquad  (double space of current character set size) $$a\qquad~ba\qquad~b\_ (where _ is blank!)a\ b(whereas$$a\bis not a valid filter expression since the blank space is missing; it is recommended to use the tilde ~ instead of the simple whitespace)a\ b\hspace{n} ,where n positive integer (= n Pixels)a~\hspace{30}~b$$a~\hspace{15}~b$a~\hspace{2}~b$$$$a~\hspace{1}~ba~\hspace{30}~b$$a~\hspace{15}~b$$a~\hspace{2}~b$$a~\hspace{1}~b\unitlength{m}\hspace{n}, changes the default unit length (m=1px) to be applieda~\hspace{2}~b\unitlength{10}~\hspace{2}~c$(second space is 10x2=20px) $a~\hspace{2}~b\unitlength{10}~\hspace{2}~c$

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.: $$x=y^2creates x=y^2$$ matrix • 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}{colformat}a11&...&a1n\\a21&...&a2n\\... \\am1&...&amn \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. minus $$-$is$-$$ minus plus $$\mp~a$gives$\mp~a$$ mu (lower case greek letter) $$\mu$gives$\mu$$ multiplication $$x*y=z$is$x*y=z$$ multiplication (with cdot) $$a\cdot~b$gives$a\cdot~b$$ N not equal $$x\neq~ygives x\neq~y$$ note: \neg produces the logical negation, i.e. $$\neg~Agives \neg~A$$ nu (lower case greek letter) $$\nu$gives$\nu$$ O omega (lower case greek letter) $$\omega$gives$\omega$$ Omega (upper case greek letter) $$\Omega$gives$\Omega$$ omikron (lower case greek letter) $$o$ gives$o$$ (note this exceptional syntax!) P parentheses • Syntax: \left(...\right) or $...$ • Ex.: $$2a\left(b+c\right)gives 2a\left(b+c\right)$$ phi (lower case greek letter) $$\phi$gives$\phi$$ Phi (upper case greek letter) $$\Phi$gives$\Phi$$ pi $$x=\pi r^2$is$x=\pi r^2$$ pi (lower case greek letter) $$\pi$gives$\pi$$ Pi (upper case greek letter) $$\Pi$gives$\Pi$$ plus $$+$is$+$$ plus minus $$a\pm~b$gives$a\pm~b$$ product • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • 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

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

psi (lower case greek letter)

$$\psi$gives$\psi$$

Psi (upper case greek letter)

$$\Psi$gives$\Psi$$
R

relativity

$E=mc^2$

rho (lower case greek letter)

$$\rho$gives$\rho$$

right only brace

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

(\rm~something switches to roman style)

root

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

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

S

s.u.m

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

sigma (lower case greek letter)

$$\sigma$gives$\sigma$$

Sigma (upper case greek letter)

$$\Sigma$gives$\Sigma$$

smiley

$$~\unitlength{.6}~\picture(100){~~(50,50){\circle(99)}~ ~(20,55;50,0;2){+1\hat\bullet}~~(50,40){\bullet}~~(50,35){\circle(50,25;34)}~ ~(50,35){\circle(50,45;34)}}$is$~\unitlength{.6}~\picture(100){~~(50,50){\circle(99)}~ ~(20,55;50,0;2){+1\hat\bullet}~~(50,40){\bullet}~~(50,35){\circle(50,25;34)}~ ~(50,35){\circle(50,45;34)}}$$

square bracket

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

square root

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

\sqrt{x+y}$$subscript • The command character "_" triggers subscription of the following expression(s). • For more than one subscripted character put them in braces {...}. • Use font sizing commands for appropriate sizing. • Ex.:$$x_1gives

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}}$$sum (summation) • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix. • Syntax for summation symbol:$$\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: $$\LARGE\bigsum_{\small{i=1}}^{\small{n}}gives \LARGE\bigsum_{\small{i=1}}^{\small{n}} and \large\sum_{\small{i=1}}^{\small{n}} gives $\large\sum_{\small{i=1}}^{\small{n}}$ superscript • The command character "^" triggers superscription of the following expression(s). • For more than one superscripted character put them in braces {...}. • Use font sizing commands for appropriate sizing. • Ex.:$$x^2gives 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}}$$T tau (lower case greek letter)$$\tau$gives$\tau$$TeX $TeX$ notation allows for the expression of ASCII characters to generate formatted graphics output theta (lower case greek letter)$$\theta$gives$\theta$$Theta (upper case greek letter)$$\Theta$gives$\Theta$$times$$a\times~b$gives$a\times~b$$triangle$$\triangle~abc$gives$\triangle~abc$$triggering the TeX filter • Two double 's embracing a valid math expression trigger the filter to generate and insert the formula gif. • Ex.:$$a^2$produces$a^2$$U upsilon (lower case greek letter)$$\upsilon$gives$\upsilon$$Upsilon (upper case greek letter)$$\Upsilon$gives$\Upsilon$$V varepsilon (special lower case greek letter)$$\varepsilon$gives$\varepsilon$$variables • Variables in formulas are rendered in italic roman font face, which is a widely used convention. • Following this convention, constants are shown as non-italic. • Exp.:$$f(x)=3a+xgives f(x)=3a+x$$varphi (special lower case greek letter)$$\varphi$gives$\varphi$$varpi (special lower case greek letter)$$\varpi$gives$\varpi$$varrho (special lower case greek letter)$$\varrho$gives$\varrho$$varsigma (special lower greek letter)$$\varsigma$gives$\varsigma$$vartheta (special lower case greek letter)$$\vartheta$gives$\vartheta$$vertical line (absolute value, determinant, ...etc. symbol) • Syntax: \left|...\right| • Ex.:$$\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)

X

xi (lower case greek letter)

$$\xi$gives$\xi$$

Xi (upper case greek letter)

$$\Xi$gives$\Xi$$
Z

zeta (lower case greek letter)

$$\zeta$gives$\zeta$$