> ## Documentation Index
> Fetch the complete documentation index at: https://resources.latex-cloud-studio.com/llms.txt
> Use this file to discover all available pages before exploring further.
# Math Mode
> Mathematical typesetting commands and environments in LaTeX
LaTeX excels at typesetting mathematical content. This reference covers math mode basics, symbols, equations, and advanced mathematical structures.
## Math Mode Basics
LaTeX has two math modes:
Math within text: $a^2 + b^2 = c^2$
Math on separate lines with automatic centering
### Entering Math Mode
```latex Inline Math theme={null}
% Dollar signs (most common)
The equation $E = mc^2$ is famous.
% \(...\) delimiters
The equation \(E = mc^2\) is famous.
% math environment
The equation \begin{math}E = mc^2\end{math} is famous.
```
```latex Display Math theme={null}
% Double dollars
$$E = mc^2$$
% \[...\] delimiters (recommended)
\[E = mc^2\]
% displaymath environment
\begin{displaymath}
E = mc^2
\end{displaymath}
% equation environment (numbered)
\begin{equation}
E = mc^2
\end{equation}
```
**Important:** Text-mode commands don't work in math mode. Use math-specific commands for formatting.
## Basic Math Commands
### Superscripts and Subscripts
```latex theme={null}
x^2 % Superscript
x_i % Subscript
x^{10} % Multi-character superscript
x_{ij} % Multi-character subscript
x^2_i % Both
x^{y^z} % Nested superscripts
\sum_{i=1}^{n} % Limits on operators
```
### Fractions
```latex theme={null}
\frac{a}{b} % Standard fraction
\dfrac{a}{b} % Display style fraction (larger)
\tfrac{a}{b} % Text style fraction (smaller)
\sfrac{1}{2} % Slanted fraction (nicefrac package)
\frac{1}{2+\frac{1}{3}} % Nested fractions
```
### Roots
```latex theme={null}
\sqrt{x} % Square root
\sqrt[3]{x} % Cube root
\sqrt[n]{x} % nth root
\sqrt{\frac{a}{b}} % Root of fraction
```
## Greek Letters
### Lowercase Greek
```latex theme={null}
\alpha \beta \gamma \delta
\epsilon \zeta \eta \theta
\iota \kappa \lambda \mu
\nu \xi \pi \rho
\sigma \tau \upsilon \phi
\chi \psi \omega
% Variants
\varepsilon \vartheta \varpi
\varrho \varsigma \varphi
```
### Uppercase Greek
```latex theme={null}
\Gamma \Delta \Theta \Lambda
\Xi \Pi \Sigma \Upsilon
\Phi \Psi \Omega
```
## Mathematical Operators
### Binary Operators
```latex theme={null}
+ - \times \div
\pm \mp \cdot \ast
\star \circ \bullet \oplus
\ominus \otimes \oslash \odot
```
### Relational Operators
```latex theme={null}
= \neq < >
\leq \geq \ll \gg
\approx \sim \simeq \cong
\equiv \propto \subset \supset
\in \ni \perp \parallel
```
### Arrows
```latex theme={null}
\leftarrow \rightarrow \leftrightarrow
\Leftarrow \Rightarrow \Leftrightarrow
\uparrow \downarrow \updownarrow
\nearrow \searrow \swarrow
\nwarrow \mapsto \longmapsto
```
### Large Operators
```latex theme={null}
\sum_{i=1}^{n} % Summation
\prod_{i=1}^{n} % Product
\int_{a}^{b} % Integral
\oint % Contour integral
\bigcup_{i=1}^{n} % Union
\bigcap_{i=1}^{n} % Intersection
\lim_{x \to \infty} % Limit
```
## Delimiters
### Basic Delimiters
```latex theme={null}
(x) [x] \{x\} |x|
\langle x \rangle \lceil x \rceil
\lfloor x \rfloor \| x \|
```
### Automatic Sizing
```latex theme={null}
% Manual sizing
\big( \Big( \bigg( \Bigg(
% Automatic sizing (recommended)
\left( \frac{a}{b} \right)
\left[ \sum_{i=1}^{n} x_i \right]
\left\{ x : x > 0 \right\}
\left. \frac{df}{dx} \right|_{x=0}
```
## Mathematical Environments
### Single Equations
```latex theme={null}
% Numbered equation
\begin{equation}
E = mc^2
\label{eq:einstein}
\end{equation}
% Unnumbered equation
\begin{equation*}
E = mc^2
\end{equation*}
```
### Multiple Equations
```latex Aligned Equations theme={null}
\begin{align}
x + y &= 5 \\
2x - y &= 1
\end{align}
% With custom alignment
\begin{align}
f(x) &= x^2 + 2x + 1 \\
&= (x + 1)^2
\end{align}
```
```latex Gathered Equations theme={null}
\begin{gather}
x + y = 5 \\
2x - y = 1
\end{gather}
% Multiple columns
\begin{gather}
a = b \qquad c = d \\
e = f \qquad g = h
\end{gather}
```
```latex Cases theme={null}
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x^2 & \text{if } x < 0
\end{cases}
```
### Matrices
```latex theme={null}
% Basic matrix
\begin{matrix}
a & b \\
c & d
\end{matrix}
% Matrix with delimiters
\begin{pmatrix} % Parentheses
a & b \\
c & d
\end{pmatrix}
\begin{bmatrix} % Brackets
a & b \\
c & d
\end{bmatrix}
\begin{vmatrix} % Vertical lines (determinant)
a & b \\
c & d
\end{vmatrix}
\begin{Vmatrix} % Double vertical lines
a & b \\
c & d
\end{Vmatrix}
```
## Advanced Features
### Text in Math Mode
```latex theme={null}
% Basic text
\text{if } x > 0
% Text with math inside
\text{for all } x \in \mathbb{R}
% Common text operators
\sin x \cos x \tan x \log x
\exp x \max x \min x \det A
```
### Math Fonts
```latex theme={null}
\mathbb{R} % Blackboard bold (reals)
\mathbb{N} % Natural numbers
\mathbb{Z} % Integers
\mathbb{C} % Complex numbers
\mathcal{L} % Calligraphic
\mathscr{F} % Script (mathrsfs package)
\mathfrak{g} % Fraktur (amssymb package)
\mathbf{v} % Bold (vectors)
\boldsymbol{\alpha} % Bold Greek
```
### Spacing in Math
```latex theme={null}
% Automatic spacing (usually best)
a + b
% Manual spacing
a \, b % Thin space
a \: b % Medium space
a \; b % Thick space
a \quad b % Quad space
a \qquad b % Double quad
% Negative space
a \! b % Negative thin space
```
### Theorems and Proofs
```latex theme={null}
\usepackage{amsthm}
% Define theorem environments
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proof}{Proof}
% Use in document
\begin{theorem}
For all $x \in \mathbb{R}$, we have $x^2 \geq 0$.
\end{theorem}
\begin{proof}
This follows from the definition of real numbers.
\end{proof}
```
## Common Constructions
### Derivatives
```latex theme={null}
% Basic derivative
\frac{df}{dx}
% Partial derivative
\frac{\partial f}{\partial x}
% Higher derivatives
\frac{d^2f}{dx^2}
% At a point
\left.\frac{df}{dx}\right|_{x=0}
```
### Integrals
```latex theme={null}
% Definite integral
\int_0^1 x^2 \, dx
% Indefinite integral
\int f(x) \, dx
% Multiple integrals
\iint_D f(x,y) \, dx \, dy
\iiint_V f(x,y,z) \, dV
```
### Sums and Products
```latex theme={null}
% Sum
\sum_{n=1}^{\infty} \frac{1}{n^2}
% Product
\prod_{i=1}^{n} x_i
% Inline versions
$\sum\limits_{i=1}^{n}$ % Forces display style
$\sum\nolimits_{i=1}^{n}$ % Forces inline style
```
## Best Practices
**Math typesetting tips:**
1. **Use proper math mode** - Never use text italic for math
2. **Choose appropriate environments** - `align` for equations that should align
3. **Label important equations** - Use `\label{eq:descriptive-name}`
4. **Use `\text{}` for words** - Don't write words directly in math mode
5. **Let LaTeX handle spacing** - Avoid manual spacing unless necessary
## Quick Reference
| Symbol | Command | Symbol | Command |
| ------ | --------- | ------ | --------- |
| ± | `\pm` | ≤ | `\leq` |
| × | `\times` | ≥ | `\geq` |
| ÷ | `\div` | ≠ | `\neq` |
| ∞ | `\infty` | ≈ | `\approx` |
| ∑ | `\sum` | ∈ | `\in` |
| ∫ | `\int` | ⊂ | `\subset` |
| √ | `\sqrt{}` | ∪ | `\cup` |
| α | `\alpha` | ∩ | `\cap` |
***
Next: Explore [Lists](/learn/latex/basics/lists) or learn about [Tables](/learn/latex/tables/creating-tables) for data presentation.