Mathematical Expression Formatting Guide

Mathematical Expression Formatting Guide

This guide explains how to format mathematical expressions in this DokuWiki using the MathJax plugin.

Basic Setup

To ensure mathematical expressions render correctly:

* Make sure the MathJax Plugin is installed and activated
* Use LaTeX syntax for mathematical notation

Inline Mathematics

For inline mathematical expressions, use single dollar signs:

`$expression$`

Examples:

`$a^2 + b^2 = c^2$` renders as $a^2 + b^2 = c^2$
`$\alpha + \beta = \gamma$` renders as $\alpha + \beta = \gamma$
`$f(x) = \int_{a}^{b} g(x) dx$` renders as $f(x) = \int_{a}^{b} g(x) dx$

Display Mathematics

For centered mathematical expressions on their own line, use double dollar signs:

`$$expression$$`

Example: ``` $$ \frac{d}{dx}\left( \int_{a}^{x} f(t) dt \right) = f(x) $$ ```

Renders as: $$ \frac{d}{dx}\left( \int_{a}^{x} f(t) dt \right) = f(x) $$

Common Mathematical Notation

Sets and Logic

Symbol	LaTeX Code	Description
——	———-	———–
$\in$	`\in`	Element of
$\subset$	`\subset`	Subset
$\cup$	`\cup`	Union
$\cap$	`\cap`	Intersection
$\emptyset$	`\emptyset`	Empty set
$\mathbb{R}$	`\mathbb{R}`	Real numbers
$\mathbb{Z}$	`\mathbb{Z}`	Integers
$\mathbb{N}$	`\mathbb{N}`	Natural numbers
$\forall$	`\forall`	For all
$\exists$	`\exists`	There exists
$\neg$	`\neg`	Negation
$\wedge$	`\wedge`	Logical and
$\vee$	`\vee`	Logical or
$\implies$	`\implies`	Implies
$\iff$	`\iff`	If and only if

Calculus and Analysis

Symbol	LaTeX Code	Description
——	———-	———–
$\lim_{x \to a}$	`\lim_{x \to a}`	Limit
$\sum_{i=1}^{n}$	`\sum_{i=1}	{n}`	Summation
$\prod_{i=1}^{n}$	`\prod_{i=1}	{n}`	Product
$\int_{a}^{b}$	`\int_{a}	{b}`	Definite integral
$\frac{d}{dx}$	`\frac{d}{dx}`	Derivative
$\partial$	`\partial`	Partial derivative
$\nabla$	`\nabla`	Gradient
$\infty$	`\infty`	Infinity

Algebra and Linear Algebra

Symbol	LaTeX Code	Description
——	———-	———–
$\times$	`\times`	Cross product
$\cdot$	`\cdot`	Dot product
$\otimes$	`\otimes`	Tensor product
$A^{-1}$	`A	{-1}`	Matrix inverse
$A^T$	`A	T`	Matrix transpose
$\det(A)$	`\det(A)`	Determinant
$\text{tr}(A)$	`\text{tr}(A)`	Trace

Multi-line Equations

For aligned multi-line equations, use the `align` environment:

``` $$ \begin{align} a &= b + c \\ &= d + e \\ &= f \end{align} $$ ``` Renders as: $$ \begin{align} a &= b + c \\ &= d + e \\ &= f \end{align} $$ ===== Cases ===== For definitions with multiple cases, use the `cases` environment: ``` $$ f(x) = \begin{cases} x^2, & \text{if } x \geq 0
-x^2, & \text{if } x < 0 \end{cases} $$ ``` Renders as: $$ f(x) = \begin{cases} x^2, & \text{if } x \geq 0
-x^2, & \text{if } x < 0 \end{cases} $$

Theorems, Lemmas, and Proofs

Use the following formatting for theorems and proofs:

``` Theorem: [Statement of theorem]

Proof: [Proof steps…]

Therefore, [conclusion]. ■ ```

The ■ symbol (black square) is typically used to denote the end of a proof, which you can create with `■`.

Table of Contents