This is an old revision of the document!
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 `■`.