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.: $$a\,b$ gives a\,b</li><li><u>Ex.:</u> $$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.: $$a\;b$ gives a\;b </li><li><u>Ex.:</u> $$a~\hspace{6}~b$ gives also a~\hspace{6}~b

\:

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

\/ (backslash slash)

  • \/ (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.: $$\sqrt~n$ to produce \sqrt~n$$

\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.: $$\normalsize~3x$ gives \normalsize~3x$$

\qquad

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

\quad

  • 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 (overview)

Absolute Font Sizes
CommandExampleResult
\tiny$$\tiny 3x$</td><td valign="top" width="33%">\tiny 3x$$
\small$$\small 3x$</td><td valign="top" width="33%">\small 3x$$
\normalsize (default)$$\normalsize 3x$$$ or just $$3x$</td><td valign="top" width="33%">\normalsize 3x$$
\large$$\large 3x$</td><td valign="top" width="33%">\large 3x$$
\Large$$\Large 3x$</td><td valign="top" width="33%">\Large 3x$$
\LARGE$$\LARGE 3x$</td><td valign="top" width="33%">\LARGE 3x$$
   

\huge and \Huge are not supported by the mimeTeX filter

  

algebraic expression

using @@ x=y^2@@ to create x=y^{2}

alpha (lower case greek letter)

$$\alpha$ gives \alpha$$

angle bracket

  • Syntax: \left<...\right>
  • Ex.: $$\left<f,g\right>$ gives </li></ul><p align="center">\left<f,g\right>$$

arithmetic operations

  • Type arithmetic operations and "=" as usual.
  • Exp.: $$f(x)=x-2b+(3a/c)$ gives</li></ul><p style="text-align:center;">f(x)=x-2b+(3a/c)$$

    • See also keyword "fraction" for extended capabilities.

array

  • Syntax for an n-dimensional array:
    \begin{array}a1&...&an\end{array}
  • Ex.: $$\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array}$ gives</li></ul><p align="center">(\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array})$$

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.: $$M=\left{a, b, c\right}$ gives </li></ul><p align="center">M=\left{a, b, c\right}$$

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.: $$f(x)=3a+x$ gives</li></ul><p style="text-align:center;">f(x)=3a+x$$

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:

$$\bigoint_{0}^{\infty}$   gives   </p><p align="center">\bigoint_{0}^{\infty} </p><p align="center">and</p><p align="center">$$\oint_{0}^{\infty}$   gives 

\oint_{0}^{\infty}

  • Use font size commands for a nicer picture:

$$\LARGE\bigoint_{\small0}^{\small\infty}$   gives   </p><p></p><p align="center">\LARGE\bigoint_{\small0}^{\small\infty} </p><p align="left"></p><p align="center">and</p><p align="center">$$\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:

$$\bigcoprod_{i=k}^{n}$   gives   </p><p align="center">\bigcoprod_{i=k}^{n} </p><ul><li><div align="left">Use font size commands for a nicer picture:</div></li></ul><p align="left"></p><p align="center">$$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$   gives  

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

D

delimiters (overview)

Delimiters (parentheses, braces, brackets. ...)
CommandExampleResult

\left(... \right)

$$2\left(a+b\right)$</td><td valign="top" width="33%">2~\left(a+b\right)$$
\left[... \right]$$\left[a^2+b^2~\right]$</td><td valign="top" width="33%">\left[a^2+b^2~\right]$$
\left{... \right}$$\left{x^2, x^3, x^4,... \right}$</td><td valign="top" width="33%">\left{x^2, x^3, x^4,... \right}$$
\left\langle... \right\rangle$$\left\langle a,b~\right\rangle$</td><td valign="top" width="33%">\left\langle a,b~\right\rangle$$
\left| ... \right| $$\det\left|\array{a&b\\c&d}\right| $</td><td valign="top" width="33%">\det\left|\array{a&b\\c&d}\right| $$
\left\| ... \right\| $$\left\|f~\right\|$</td><td valign="top" width="33%">\left\|f~\right\|$$

\left{ ... \right.

(note the dot!)

$$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$</p><p>(\rm switches to roman style)</p></td><td valign="top" width="33%"><p>f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$

\left.{ ... \right\}

(note the dot!)

$$\left.{{\rm~term1\atop\rm~term2}\right}=y$</td><td valign="top" width="33%">\left.{{\rm~term1\atop \rm~term2}\right}=y$$

Note: The delimiters are automatically sizes.

delta

$$\delta$ is \delta $$

Delta (upper case greek letter)

$$\Delta$ gives \Delta$$

delta (lower case greek letter)

$$\delta$ gives \delta $$

div (division)

$$x\div~y$ gives x\div~y$$

division

@@1/2@@   is \frac{1}{2}

double vertical line (norm symbol)

  • Syntax: \left\|...\right\|
  • Exp.: $$\left\|af\right\| = \left|a\right|\left\|f\right\|$ gives </li></ul><p align="center">\left\|af\right\| = \left|a\right|\left\|f\right\|$$

E

epsilon (lower case greek letter)

$$\epsilon$ gives \epsilon$$

equals

@@x=2@@   is x=2

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

$$\fbox{x=\frac{1}{2}}$  gives </p><p align="center">\fbox{x=\frac{1}{2}}$$

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): $$f(x,y)=\frac{2a}{x+y}$ gives </li></ul><p style="text-align:center;">f(x,y)=\frac{2a}{x+y}$$

    • Ex. (with specific sizing): $$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$ gives </li></ul><p style="text-align:center;">f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$$

      • You may nest fractions as much as you want.
      • Ex. (nested fractions): $$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$ gives </li></ul><p style="text-align:center;">\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$$

G

gamma (lower case greek letter)

$$\gamma$ gives \gamma$$

Gamma (upper case greek letter)

$$\Gamma$ gives \Gamma$$

greater than

$$x>y$  gives </p><p align="center">x>y$$

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:

CommandFilter ExpressionResult
\alpha$$\alpha$</td><td valign="top" width="33%">\alpha$$
\beta$$\beta$</td><td valign="top" width="33%">\beta$$
\gamma$$\gamma$</td><td valign="top" width="33%">\gamma$$
\delta$$\delta$</td><td valign="top" width="33%">\delta$$
\epsilon$$\epsilon$</td><td valign="top" width="33%">\epsilon$$
\varepsilon$$\varepsilon$</td><td valign="top" width="33%">\varepsilon$$
\zeta$$\zeta$</td><td valign="top" width="33%">\zeta$$
\eta$$\eta$</td><td valign="top" width="33%">\eta$$
\theta$$\theta$</td><td valign="top" width="33%">\theta$$
\vartheta$$\vartheta$</td><td valign="top" width="33%">\vartheta$$
\iota$$\iota$</td><td valign="top" width="33%">\iota$$
\kappa$$\kappa$</td><td valign="top" width="33%">\kappa$$
\lambda$$\lambda$</td><td valign="top" width="33%">\lambda$$
\mu$$\mu$</td><td valign="top" width="33%">\mu$$
\nu$$\nu$</td><td valign="top" width="33%">\nu$$
\xi$$\xi$</td><td valign="top" width="33%">\xi$$
(!)$$o$</td><td valign="top" width="33%">o$$
\pi$$\pi$</td><td valign="top" width="33%">\pi$$
\varpi$$\varpi$</td><td valign="top" width="33%">\varpi$$
\rho$$\rho$</td><td valign="top" width="33%">\rho$$
\varrho$$\varrho$</td><td valign="top" width="33%">\varrho$$
\sigma$$\sigma$</td><td valign="top" width="33%">\sigma$$
\varsigma$$\varsima$</td><td valign="top" width="33%">\varsigma$$
\tau$$\tau$</td><td valign="top" width="33%">\tau$$
\upsilon$$\upsilon$</td><td valign="top" width="33%">\upsilon$$
\phi$$\phi$</td><td valign="top" width="33%">\phi$$
\varphi$$\varphi$</td><td valign="top" width="33%">\varphi$$
\chi$$\chi$</td><td valign="top" width="33%">\chi$$
\psi$$\psi$</td><td valign="top" width="33%">\psi$$
\omega$$\omega$</td><td valign="top" width="33%">\omega$$

Upper Case Greek Letters:

CommandFilter ExpressionResult
\Gamma$$\Gamma$</td><td valign="top" width="33%">\Gamma$$
\Delta$$\Delta$</td><td valign="top" width="33%">\Delta$$
\Theta$$\Theta$</td><td valign="top" width="33%">\Theta$$
\Lambda$$\Lambda$</td><td valign="top" width="33%">\Lambda$$
\Xi$$\Xi$</td><td valign="top" width="33%">\Xi$$
\Pi$$\Pi$</td><td valign="top" width="33%">\Pi$$
\Sigma$$\Sigma$</td><td valign="top" width="33%">\Sigma$$
\Upsilon$$\Upsilon$</td><td valign="top" width="33%">\Upsilon$$
\Phi$$\Phi$</td><td valign="top" width="33%">\Phi$$
\Psi$$\Psi$</td><td valign="top" width="33%">\Psi$$
\Omega$$\Omega$</td><td valign="top" width="33%">\Omega$$

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:

$$\bigint_{0}^{\infty}$   gives   </p><p align="center">\bigint_{0}^{\infty} </p><p align="center">and</p><p align="center">$$\int_{0}^{\infty}$   gives 

\int_{0}^{\infty}

  • Use font size commands for a nicer picture:

$$\LARGE\bigint_{\small0}^{\small\infty}$   gives   </p><p></p><p align="center">\LARGE\bigint_{\small0}^{\small\infty} </p><p align="left"></p><p align="center">and</p><p align="center">$$\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.: $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$ gives </font></li></ul><p align="center"><font color="#000000">f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$

    (\rm~something switches to roman style)

less than

$$<$   gives</p><p align="center"><$$

less than or equal

$$x\le~y$ or $$x\leq~y$ gives

x\le~y

M

math spaces

List of predefined spaces:

Math Spaces
CommandExampleResult
\, (smallest predefined)$$a\,b$</td><td valign="top" width="33%">a\,b$$
\:  (second smallest predefined)$$a\:b$</td><td valign="top" width="33%">a\:b$$
\;  (third smallest predefined)$$a\;b$</td><td valign="top" width="33%">a\;b </td></tr><tr><td valign="top" width="33%">\/  (avoiding ligatures)</td><td valign="top" width="33%">$$V\/A$ instead of $$VA$</td><td valign="top" width="33%">V\/A instead of VA$$
\quad  (space of current character set size)$$a\quad~b$</td><td valign="top" width="33%">a\quad~b$$
\qquad  (double space of current character set size)$$a\qquad~b$</td><td valign="top" width="33%">a\qquad~b</td></tr><tr><td valign="top" width="33%">\_ <em>(where _ is blank!)</em></td><td valign="top" width="33%"><p>$$a\ b$

(whereas $$a\b$ is <em>not</em> a valid filter expression since the blank space is missing; it is recommended to use the tilde ~ instead of the simple whitespace)</font></p></td><td valign="top" width="33%"><p>a\ b</p><p></p></td></tr><tr><td valign="top" width="33%">\hspace{n} ,where n positive integer (= n Pixels)</td><td valign="top" width="33%"><p>$$a~\hspace{30}~b$

$$a~\hspace{15}~b$</p><p>$$a~\hspace{2}~b$

$$a~\hspace{1}~b$</p></td><td valign="top" width="33%"><p>a~\hspace{30}~b</p><p>a~\hspace{15}~b</p><p>a~\hspace{2}~b</p><p>a~\hspace{1}~b</p></td></tr><tr><td valign="top" width="33%">\unitlength{m}\hspace{n}, changes the default unit length (m=1px) to be applied</td><td valign="top" width="33%"><p>$$a~\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.

mathematics expression

  • A valid expression inside the $'s is rendered as mathematics in an inserted gif image.
  • Ex.: $$x=y^2$ creates  </li></ul><p align="center">x=y^2$$

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.: $$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$ gives</li></ul><p align="center">\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$$

    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

$$x\neq~y$ gives </p><p align="center">x\neq~y$$

note: \neg produces the logical negation, i.e. $$\neg~A$ gives </p><p align="center">\neg~A$$

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)

$$o$</font> gives o$$

(note this exceptional syntax!)

P

parentheses

  • Syntax: \left(...\right) or ...
  • Ex.: $$2a\left(b+c\right)$ gives </li></ul><p align="center">2a\left(b+c\right)$$

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:

$$\bigprod_{i=k}^{n}$   gives   </p><p align="center">\bigprod_{i=k}^{n} </p><p align="center">and</p><p align="center">$$\prod_{i=k}^{n}$   gives 

\prod_{i=k}^{n}

  • Use font size commands for a nicer picture:

$$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}$   gives   </p><p></p><p align="center">\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}  </p><p align="left"></p><p align="center">and</p><p align="center">$$\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.: $$\left.{{\rm~term1\atop\rm~term2}\right}=y$ gives </li></ul><p align="center">\left.{{\rm~term1\atop\rm~term2}\right}=y$$

    (\rm~something switches to roman style)

root

  • Syntax: \sqrt[n]{arg} or simply  \sqrt{arg} for \sqrt[2]{arg}
  • Ex.: $$\sqrt[3]{8}$ gives</li></ul><p align="center">\sqrt[3]{8}$$

    • Ex.: $$\sqrt{-1}$ gives</li></ul><p align="center">\sqrt{-1}$$

      • Nesting of roots (and combining with fractions, ...etc.) are possible.
      • Ex.: $$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$ gives</li></ul><p align="center">\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$$

        • Ex.: $$\sqrt[3]{-q+\sqrt{q^2+p^3}}$ gives</li></ul><p align="center">\sqrt[3]{-q+\sqrt{q^2+p^3}}$$

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: $$\sqrt{x+y}$ gives</li></ul><p align="center">\sqrt{x+y}$$

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.:$$x_1$ gives </li></ul><p style="text-align:center;">x_1$$

    • Ex.:$$a_{m+2n}$ gives </li></ul><p style="text-align:center;">a_{m+2n}$$

      • Ex. (with specific sizing):  $$x_{\small1}=a_{\small{m+2n}}$ gives</li></ul><p style="text-align:center;">x_{\small1}=a_{\small{m+2n}}$$

        • Combine subscripting with superscripting (command character "^").
          Syntax: Expr_{subExpr}^{supExpr}.
        • Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$ gives</li></ul><p style="text-align:center;">A_{\small{i,j,k}}^{\small{-n+2}}$$

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:

$$\bigsum_{i=k}^{n}$   gives   </p><p align="center">\bigsum_{i=k}^{n} </p><p align="center">and</p><p align="center">$$\sum_{i=k}^{n}$   gives 

\sum_{i=k}^{n}

  • Use font size commands for a nicer picture:

$$\LARGE\bigsum_{\small{i=1}}^{\small{n}}$   gives   </p><p></p><p align="center">\LARGE\bigsum_{\small{i=1}}^{\small{n}} </p><p align="left"></p><p align="center">and</p><p align="center">$$\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.: $$x^2$ gives </li></ul><p style="text-align:center;">x^2$$

    • Ex.: $$a^{m+2n}$ gives </li></ul><p style="text-align:center;">a^{m+2n}$$

      • Ex. (with specific sizing): $$x^{\small2}=a^{\small{m+2n}}$ gives</li></ul><p style="text-align:center;">x^{\small2}=a^{\small{m+2n}}$$

        • Combine superscripting with subscripting (command character "_").
          Syntax: Expr_{subExpr}^{supExpr}.
        • Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$ gives</li></ul><p style="text-align:center;">A_{\small{i,j,k}}^{\small{-n+2}}$$

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.: $$f(x)=3a+x$ gives</li></ul><p style="text-align:center;">f(x)=3a+x$$

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.: $$\left|b-a\right|$ gives \left|b-a\right| </li><li><u>Ex.:</u> $${\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)

$$\zeta$ gives \zeta$$