Math mode in LaTeX allows rendering mathematical equations and symbols. Inline math uses $...$ or \(...\) delimiters; display (block) math uses $$...$$ or \[...\]. Inside math mode, special commands render operators, Greek letters, fractions, subscripts, and more. Math mode is where LaTeX shines—fine control over spacing, alignment, and mathematical notation.
Inline: The equation $E = mc^2$ shows energy-mass equivalence. renders as: The equation $E = mc^2$ shows energy-mass equivalence.
Display: $$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$ renders centered on its own line:
$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$
Greek letters are typed with backslash and name: $\alpha, \beta, \gamma, \delta, \epsilon$ renders as $\alpha, \beta, \gamma, \delta, \epsilon$. Uppercase is \Gamma, \Delta, \Lambda, \Sigma, \Phi, \Psi, \Omega (only some have uppercase forms). \epsilon is regular epsilon; \varepsilon is the alternate form.
Subscripts and superscripts use _ and ^: $x_1$ is subscript, $x^2$ is superscript, $x_{i,j}$ groups subscript, $2^{2^3} = 2^8$ nests powers. Everything after _ or ^ is grouped; use braces to group multiple characters.
Fractions use \frac{numerator}{denominator}: $\frac{1}{2}$ is $\frac{1}{2}$. For inline fractions that don't resize, use \tfrac: $\tfrac{1}{2}$ is $\tfrac{1}{2}$.
Operators and functions have special names:
\sin, \cos, \tan -- trigonometric
\log, \ln -- logarithms
\int, \sum, \prod -- integral, sum, product
\lim, \min, \max -- limits and extrema
\sqrt{x} -- square root
\sqrt[n]{x} -- nth root
Examples: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ is $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. $\lim_{x \to \infty} f(x)$ is $\lim_{x \to \infty} f(x)$.
Matrices and arrays use the array environment. Rows are separated by \\, columns by &:
$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
renders as:
$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
Other matrix delimiters: pmatrix (parentheses), vmatrix (vertical bars), Vmatrix (double bars), matrix (no delimiters).
Accents on symbols: $\hat{x}$ is $\hat{x}$, $\bar{x}$ is $\bar{x}$, $\vec{v}$ is $\vec{v}$, $\tilde{x}$ is $\tilde{x}$, $\dot{x}$ is $\dot{x}$ (time derivative).
Relational operators: =, \neq, <, >, \leq, \geq, \ll, \gg, \approx, \equiv, \propto. Write \neq not !=. \ll is $\ll$ (much less than). \approx is $\approx$ (approximately).
Blackboard bold for number sets: use the \mathbb command. $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}$ renders as $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}$ (or use the wiki's macros \NN, \ZZ, \QQ, \RR, \CC which may be available in your setup).
For complex equations spanning multiple lines, use align* environment (not numbered) or align (numbered):
\begin{align*} E &= mc^2 \\ p &= mv \end{align*}
renders as:
$$\begin{align*} E &= mc^2 \\ p &= mv \end{align*}$$ The `&` aligns equations at the `=` sign.