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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:
1. Make sure the [[https://www.dokuwiki.org/plugin:mathjax|MathJax Plugin]] is installed and activated 2. 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 `■`.