Latex with wikidot

# Basics

When you are editing a post in a forum or creating a wiki page in wikidot, mathematical symbols by clicking on the $x/2$
and on the $\sqrt{x}$ symbol on the bottom of the menu above the textbox.

By clicking on the $\sqrt{x}$, you will be writing a new equation in a separate line, for example

(1)
\begin{align} _nC_k={n \choose k}=\frac{n!}{k!(n-k)!} \end{align}

Notice that the equation will then be numbered.
Such equations are written between [$] and [$]. For this one in particular, the text between the two math quotes is:
_nC_k={n \choose k}=\frac{n!}{k!(n-k)!}
Go below for more information on mathematical expressions.

By clicking on the x/2, you will be writing a new equation in the same line, for example $nPk = \frac{n!}{(n-k)!}$.
Such equations are written between [[$and$]].

The mathematical symbols in between are written in Latex.

# Brief summary of mathematical symbols/expressions

Below is a very brief summary of symbols written in Latex

• To write fractions type *\frac{}{}*, for example:
• \frac{2}{3} is $\frac{2}{3}$
• \frac{2+x}{x-y} is $\frac{2+x}{x-y}$
• To write powers type ^:
• 3^2 is $3^2$
• {x^y}^z is ${x^y}^z$
• To write a square root, one types \sqrt{ }, for example
• \sqrt{64x^2}=8x is $\sqrt{64x^2}=8x$
• To write the sigma sign for sum, one types \sum, and if one wants to specify the limits of this sum, those are introduced with *_* (lower limit) and ^ (upper limit), for example:
• \sum\limits_{i=1}^{10} i =1+2+3+…+9+10 = 5050 is $\sum\limits_{i=1}^{10} i=1+2+3+...+9+10 = 5050$
• \sum_{n=0}^{\infty}r^n=\frac{1}{1-r}, \ \ r<1, where the \ \ with spaces in between just generate some space:
(2)
\begin{align} \sum_{n=0}^{\infty}r^n=\frac{1}{1-r}, \ \ r<1 \end{align}

To write a formula for the population standard deviation, one types: \sigma = \sqrt{\frac{\sum{(x-\mu)^2{N}} }}

(3)
\begin{align} \sigma = \sqrt{\frac{\sum{(x-\mu)^2}}{N}} \nonumber \end{align}

# Table of symbols

## Latex special characters

These tables shows the latex syntax for some common mathematical expressions.1

Group Syntax Expression
math functions \cos x + \ln y +\operatorname{sgn} z $\cos x + \ln y +\operatorname{sgn} z$
modular arithmetic s_k \equiv 0 \pmod{m} $s_k \equiv 0 \pmod{m}$
Derivatives \nabla \partial dx \dot x \ddot y $\nabla \partial dx \dot x \ddot y$
Sets \forall x\not\in\varnothing\subseteq A\cap B\cup \exists \{x,y\} \times C $\forall x\not\in\varnothing\subseteq A\cap B\cup \exists \{x,y\} \times C$
Logic p \land \bar{q} \to p\lor \lnot q $p \land \bar{q} \to p\lor \lnot q$
Roots \sqrt{2}\approx 1.4 , \sqrt[n]{x} $\sqrt{2}\approx 1.4 , \sqrt[n]{x}$
Relational operators \sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne $\sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne$
Geometry \Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; \ \; 45^\circ $\Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; \ \; 45^\circ$
Arrows \leftarrow \rightarrow \leftrightarrow \longleftarrow \longrightarrow \mapsto \longmapsto \nearrow \searrow \swarrow \nwarrow \uparrow \downarrow \updownarrow $\leftarrow \rightarrow \leftrightarrow \longleftarrow \longrightarrow \mapsto \longmapsto \nearrow \searrow \swarrow \nwarrow \uparrow \downarrow \updownarrow$
Special \oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \times \bullet \infty $\oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \times \bullet \infty$

## Subscript, superscript

Group Syntax Expression
Superscript a^2 $a^2$
Subscript a_2 $a_2$
Grouped a^{2+2} , a_{i,j} $a^{2+2} , a_{i,j}$
Combining super and subscript x_2^3 $x_2^3$
Derivatives x' $x'$
Underlines, overline, vectors \hat a \ \bar b \ \vec c \ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \ \overline{g h i} \ \underline{j k l} $\hat a \ \bar b \ \vec c \ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \ \overline{g h i} \ \underline{j k l}$
Overbraces \begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix} $\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}$
Underbraces \begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix} $\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}$
Sums, summation \sum_{k=1}^{N} k^2 $\sum_{k=1}^{N} k^2$
Products \prod_{i=1}^{N} x_{i} $\prod_{i=1}^{N} x_{i}$
Limits \lim_{n \to \infty}x_n $\lim_{n \to \infty}x_n$
Integrals \int_{-N}^{N} e^x\, dx $\int_{-N}^{N} e^x\, dx$
Line Integrals \oint_{C} x^3\, dx + 4y^2\, dy $\oint_{C} x^3\, dx + 4y^2\, dy$

## Fractions, matrices, curly brakets

Group Syntax Expression
Fractions \frac{2}{4} or {2 \over 4} $\frac{2}{4} or {2 \over 4}$
Binomial Coefficients {n \choose k} ${n \choose k}$
Matrices \begin{pmatrix} x & y \\ z & v \end{pmatrix} $\begin{pmatrix} x & y \\ z & v \end{pmatrix}$
Matrices \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} $\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}$
Matrices \begin{Bmatrix} x & y \\ z & v \end{Bmatrix} $\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$
Matrices \begin{vmatrix} x & y \\ z & v \end{vmatrix} $\begin{vmatrix} x & y \\ z & v \end{vmatrix}$
Matrices \begin{Vmatrix} x & y \\ z & v \end{Vmatrix} $\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$
Matrices \begin{matrix} x & y \\ z & v \end{matrix} $\begin{matrix} x & y \\ z & v \end{matrix}$
Distinction small/large cap f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right $f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right$
Equations in more than one line \begin{matrix}f(n+1)&=& (n+1)^2 \\ \ &=& n^2 + 2n + 1\end{matrix} $\begin{matrix}f(n+1)&=& (n+1)^2 \\ \ &=& n^2 + 2n + 1\end{matrix}$

## Fonts

Group Syntax Expression
Small greek alphabet \alpha \beta \chi \delta \epsilon \varepsilon \phi \varphi \gamma \eta \iota \kappa \lambda \mu \nu o \pi \varpi \theta \vartheta \rho \varrho \sigma \varsigma \tau \upsilon \omega \xi \psi \zeta $\alpha \beta \chi \delta \epsilon \varepsilon \phi \varphi \gamma \eta \iota \kappa \lambda \mu \nu o \pi \varpi \theta \vartheta \rho \varrho \sigma \varsigma \tau \upsilon \omega \xi \psi \zeta$
Big greek alphabet A B X \Delta E \Phi \Gamma H I K \Lambda M N O \Pi \Theta P \Sigma T \Upsilon \Omega \Xi \Psi Z $A B X \Delta E \Phi \Gamma H I K \Lambda M N O \Pi \Theta P \Sigma T \Upsilon \Omega \Xi \Psi Z$
Strong bold font x\in\mathbb{N}\subset\mathbb{Z}\subset\mathbb{R}\sub\mathbb{C} $x\in\mathbb{N}\subset\mathbb{Z}\subset\mathbb{R}\sub\mathbb{C}$
Negrito (vetores) \mathbf{x} \cdot \mathbf{y} = 0 $\mathbf{x} \cdot \mathbf{y} = 0$
Negrito (grego) \boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma} $\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}$
Fraktur font \mathfrak{a} \mathfrak{B} $\mathfrak{a} \mathfrak{B}$
Script \mathcal{ABC} $\mathcal{ABC}$
Hebrew \aleph \beth \gimel \daleth $\aleph \beth \gimel \daleth$
non-leaning font \mbox{abc} $\mbox{abc}$