Help:Math
- Help:Math
This page provides a comprehensive guide to using mathematical formulas and expressions within MediaWiki, specifically geared towards beginner users. MediaWiki utilizes LaTeX for rendering mathematical content, providing a powerful and flexible system for displaying complex equations. This guide will cover the basics of inline and displayed math, common symbols, fractions, exponents, subscripts, matrices, and more. Understanding these concepts will allow you to effectively communicate mathematical ideas within your wiki pages. This guide assumes no prior knowledge of LaTeX, but a basic understanding of mathematical notation is helpful.
What is LaTeX?
LaTeX (pronounced "LAY-tek" or "LAH-tek") is a typesetting system widely used for creating technical and scientific documentation, particularly documents containing mathematical formulas. MediaWiki doesn't directly understand mathematical symbols; instead, it relies on LaTeX to interpret and render them correctly. When you write LaTeX code within MediaWiki, the system converts it into visually appealing mathematical notation.
Basic Syntax
There are two primary ways to enter math mode in MediaWiki: inline and displayed.
- Inline Math: Used for including mathematical expressions *within* a line of text. Inline math is enclosed within single dollar signs (`$`). For example: `$E=mc^2$` renders as $E=mc^2$.
- Displayed Math: Used for displaying mathematical expressions on their own line, centered and often with larger formatting. Displayed math is enclosed within double dollar signs (`$$`). For example:
```wiki $$ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2} $$ ```
renders as:
$$ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2} $$
Displayed math is ideal for longer equations or those requiring more complex formatting. It provides better readability and visual separation. Using `\[ ... \]` is an older, still supported syntax for displayed math, but `$$ ... $$` is generally preferred for consistency.
Common Mathematical Symbols
Here's a table of some frequently used mathematical symbols and their corresponding LaTeX codes:
| Symbol | LaTeX Code | Description | |---|---|---| | π | `\pi` | Pi (3.14159...) | | e | `\e` | Euler's number (2.71828...) | | ∞ | `\infty` | Infinity | | ± | `\pm` | Plus or minus | | × | `\times` | Multiplication | | ÷ | `\div` | Division | | √ | `\sqrt{}` | Square root. Argument goes inside the curly braces. Example: `\sqrt{2}` renders as $\sqrt{2}$ | | ⁿ√ | `\sqrt[n]{}` | nth root. 'n' goes inside the square brackets. Example: `\sqrt[3]{8}` renders as $\sqrt[3]{8}$| | Σ | `\sum` | Summation | | ∫ | `\int` | Integral | | ≠ | `\neq` | Not equal to | | ≤ | `\leq` | Less than or equal to | | ≥ | `\geq` | Greater than or equal to | | < | `<` | Less than | | > | `>` | Greater than | | ∝ | `\propto` | Proportional to | | ∂ | `\partial` | Partial derivative | | ∇ | `\nabla` | Nabla operator | | ∠ | `\angle` | Angle | | ∅ | `\emptyset` | Empty set | | ∈ | `\in` | Element of | | ∉ | `\notin` | Not an element of | | ∪ | `\cup` | Union | | ∩ | `\cap` | Intersection | | ⊆ | `\subseteq` | Subset of | | ⊇ | `\supseteq` | Superset of | | ∧ | `\land` | Logical AND | | ∨ | `\lor` | Logical OR | | ¬ | `\neg` | Logical NOT | | ⇒ | `\Rightarrow` | Implies | | ⇔ | `\Leftrightarrow` | If and only if |
Fractions
Fractions are created using the `\frac{numerator}{denominator}` command. For example:
```wiki $\frac{1}{2}$ ```
renders as:
$\frac{1}{2}$
You can also create mixed fractions:
```wiki $1\frac{1}{2}$ ```
renders as:
$1\frac{1}{2}$
For complex fractions (fractions within fractions), use nested `\frac` commands or the `\cfrac` command for continued fractions.
Exponents and Subscripts
- Exponents: Use the `^` symbol to denote exponents. For example:
```wiki $x^2 + y^2 = z^2$ ```
renders as:
$x^2 + y^2 = z^2$
If the exponent is more than one character, enclose it in curly braces:
```wiki $x^{n+1}$ ```
renders as:
$x^{n+1}$
- Subscripts: Use the `_` symbol to denote subscripts. For example:
```wiki $x_1 + x_2 + x_3$ ```
renders as:
$x_1 + x_2 + x_3$
Similar to exponents, enclose multi-character subscripts in curly braces:
```wiki $a_{i,j}$ ```
renders as:
$a_{i,j}$
You can combine exponents and subscripts:
```wiki $x_i^2$ ```
renders as:
$x_i^2$
Greek Letters
LaTeX provides commands for all Greek letters. Here are a few examples:
| Letter | LaTeX Code | |---|---| | α | `\alpha` | | β | `\beta` | | γ | `\gamma` | | δ | `\delta` | | ε | `\epsilon` | | θ | `\theta` | | λ | `\lambda` | | μ | `\mu` | | ν | `\nu` | | π | `\pi` | | ρ | `\rho` | | σ | `\sigma` | | τ | `\tau` | | φ | `\phi` | | χ | `\chi` | | ψ | `\psi` | | ω | `\omega` |
Capital Greek letters are similarly represented (e.g., `\Alpha`, `\Beta`, `\Gamma`).
Matrices
Matrices are created using the `\begin{matrix} ... \end{matrix}` environment. Elements are arranged in rows, separated by `&` within each row, and rows are separated by `\\`.
```wiki $$ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} $$ ```
renders as:
$$ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} $$
You can use different matrix environments for different bracket styles:
- `\begin{pmatrix} ... \end{pmatrix}`: Parentheses
- `\begin{bmatrix} ... \end{bmatrix}`: Square brackets
- `\begin{Bmatrix} ... \end{Bmatrix}`: Curly braces
- `\begin{vmatrix} ... \end{vmatrix}`: Single vertical bars (determinant)
- `\begin{Vmatrix} ... \end{Vmatrix}`: Double vertical bars (norm)
Equations and Alignments
For more complex equations, especially those spanning multiple lines, consider using the `\begin{align} ... \end{align}` environment. This allows for alignment of equations at specific points (e.g., at the equals sign).
```wiki $$ \begin{align} y &= mx + b \\ y &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{align} $$ ```
renders as:
$$ \begin{align} y &= mx + b \\ y &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{align} $$
The `&` symbol is used to specify the alignment point. The `\\` separates the lines. The `align*` environment suppresses equation numbering.
Functions
LaTeX provides commands for common mathematical functions:
- `\sin(x)`: Sine
- `\cos(x)`: Cosine
- `\tan(x)`: Tangent
- `\log(x)`: Natural logarithm
- `\ln(x)`: Natural logarithm (alternative)
- `\exp(x)`: Exponential function
- `\lim_{x \to \infty} f(x)`: Limit
- `\max(x, y)`: Maximum
- `\min(x, y)`: Minimum
Advanced Techniques
- Integrals with Limits: `\int_a^b f(x) dx` renders as $\int_a^b f(x) dx$
- Sums with Limits: `\sum_{i=1}^{n} i` renders as $\sum_{i=1}^{n} i$
- Brackets and Parentheses: Use `\left(` and `\right)` to automatically size brackets and parentheses. `\left[` and `\right]` for square brackets, and `\left\{` and `\right\}` for curly braces.
- Spacing: Use `\,`, `\:`, `\;`, `\quad`, and `\qquad` for adjusting spaces.
- Colors: Use the `\color{colorname}` command. For example, `\color{red}x` renders as $\color{red}x$. (Color support may vary depending on the wiki's configuration).
Helpful Resources
- Help:Templates - For utilizing pre-defined mathematical templates.
- Help:Linking - For linking to other relevant wiki pages.
- Wikipedia's LaTeX page
- The LaTeX Project website
- Overleaf - Online LaTeX Editor
- Detexify - Helps you find LaTeX commands from images
Trading & Financial Applications
Mathematical formulas are crucial in various trading and financial contexts. Here are some examples and related concepts:
- **Moving Averages:** Calculating simple moving averages (SMA) or exponential moving averages (EMA) involves summation and averaging. See Technical analysis.
- **Standard Deviation:** Used to measure volatility. The formula involves calculating the square root of the variance.
- **Bollinger Bands:** Calculated using standard deviation from a moving average. See Bollinger Bands strategy.
- **Fibonacci Retracements:** Based on the Fibonacci sequence. See Fibonacci retracement.
- **Relative Strength Index (RSI):** Involves calculating average gains and losses. See RSI indicator.
- **Sharpe Ratio:** Used to evaluate risk-adjusted returns.
- **Black-Scholes Model:** Used for options pricing.
- **Monte Carlo Simulation:** A computational technique using random numbers and probability distributions for forecasting.
- **Time Series Analysis:** Uses statistical methods to analyze data points indexed in time order. See Trend analysis.
- **Correlation:** Measures the statistical relationship between two variables.
- **Regression Analysis:** Used to identify the relationship between a dependent variable and one or more independent variables.
- **Momentum Indicators:** Calculated based on price changes over a specific period. See Momentum trading.
- **Volume Weighted Average Price (VWAP):** Calculated by summing the typical price multiplied by the volume for each period.
- **Average True Range (ATR):** Measures market volatility. See ATR indicator.
- **Ichimoku Cloud:** A comprehensive indicator using multiple calculations. See Ichimoku cloud strategy.
- **Parabolic SAR:** Identifies potential reversal points.
- **MACD (Moving Average Convergence Divergence):** A trend-following momentum indicator. See MACD strategy.
- **Stochastic Oscillator:** Compares a security's closing price to its price range over a given period.
- **Elliott Wave Theory:** Uses Fibonacci numbers and wave patterns to predict market movements.
- **Support and Resistance Levels:** Identified using price action and mathematical concepts. See Support and resistance.
- **Risk Management:** Calculating position sizes and stop-loss orders requires mathematical calculations.
- **Profit Factor:** A ratio of gross profits to gross losses.
- **Drawdown:** Measures the peak-to-trough decline during a specific period.
- **Compounding Interest:** Calculated using exponential functions.
- **Value at Risk (VaR):** A statistical measure of risk.
- **Capital Asset Pricing Model (CAPM):** A model used to determine the theoretically appropriate rate of return of an asset.
Remember to practice and experiment with these commands to become comfortable with writing mathematical expressions in MediaWiki. Consult the resources listed above for more advanced techniques and assistance.
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