LaTeX Maths Guide

Inline Maths: Use single dollar signs to keep equations flowing with your text. For example, Einstein's famous equation is $E = mc^2$.

Block Maths: Use double dollar signs to center an equation on its own line:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Lowercase:
$\alpha, \beta, \gamma, \delta, \epsilon, \theta, \lambda, \mu, \pi, \sigma, \omega$

Uppercase:
$\Gamma, \Delta, \Theta, \Lambda, \Pi, \Sigma, \Omega$

Variants:
$\varepsilon, \varphi, \varrho, \vartheta$

Fractions and Roots:
$f(x) = \frac{\sqrt{x^2 + 1}}{\sqrt[3]{x - 2}}$

Summations and Products:
$\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$
$\prod_{k=1}^{\infty} \frac{4k^2}{4k^2 - 1} = \frac{\pi}{2}$

Calculus:
$\lim_{x \to 0} \frac{\sin x}{x} = 1$
$\int_{a}^{b} x^2 \, dx = \left[ \frac{x^3}{3} \right]_a^b$
$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$

Inequalities:
$x \le y, \quad a \ge b, \quad p \neq q, \quad \approx 3.14$

Set Theory:
$x \in A, \quad y \notin B$
$A \subset B, \quad C \subseteq D$
$A \cup B, \quad X \cap Y, \quad \emptyset$

Logic:
$\forall x \in \mathbb{R}, \exists y \in \mathbb{C}$
$\neg (P \land Q) \iff (\neg P \lor \neg Q)$

Basic Arrows:
$\leftarrow, \rightarrow, \leftrightarrow, \uparrow, \downarrow, \updownarrow$

Implications:
$\Leftarrow, \Rightarrow, \Leftrightarrow, \implies, \iff$

Special Vectors & Maps:
$f: X \mapsto Y$
$\vec{v} = \langle x, y, z \rangle$

Matrices (pmatrix, bmatrix, vmatrix):

$$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, \quad |A| = \begin{vmatrix} a & b \\ c & d \end{vmatrix}$$

Piecewise Functions (cases):

$$f(n) = \begin{cases} n/2 & \text{if } n \text{ even} \\ 3n+1 & \text{if } n \text{ odd} \end{cases}$$

Accents:
$\hat{x}, \bar{x}, \vec{x}, \dot{x}, \ddot{x}, \tilde{x}$

Text Styles:
$\mathbb{R}, \mathbb{N}, \mathbb{Z}$ (Blackboard bold)
$\mathcal{L}, \mathcal{F}$ (Calligraphic)
$\mathfrak{M}$ (Fraktur)

Annotations:
$\underbrace{a + b + \cdots + z}_{n \text{ terms}}$
$\overbrace{1 + 2 + 3}^{6}$