Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revision | |||
| wiki:math [2025/03/15 23:25] – root | wiki:math [Unknown date] (current) – removed - external edit (Unknown date) 127.0.0.1 | ||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ====== 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 [[https:// | ||
| - | * Use LaTeX syntax for mathematical notation | ||
| - | |||
| - | ===== Inline Mathematics ===== | ||
| - | |||
| - | For inline mathematical expressions, | ||
| - | |||
| - | `$expression$` | ||
| - | |||
| - | 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: | ||
| - | |||
| - | **Proof:** | ||
| - | [Proof steps...] | ||
| - | |||
| - | Therefore, [conclusion]. ■ | ||
| - | ``` | ||
| - | |||
| - | The ■ symbol (black square) is typically used to denote the end of a proof, which you can create with `■`. | ||
| - | |||
| - | ===== Additional Resources ===== | ||
| - | |||
| - | * [[https:// | ||
| - | * [[https:// | ||
| - | * [[https:// | ||