Math is why LaTeX exists. This lesson covers the four forms you need — inline, display, numbered, aligned — and the symbol patterns that make up almost every expression in a paper.

Step 1 — Inline vs display

Math inside a sentence goes between dollar signs; math that deserves its own line goes in a display block:

The energy is $E = mc^2$ for a body at rest.

\[
  \int_0^\infty e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}
\]

^ raises, _ lowers, and braces group: x^{2n} is x2nx^{2n} while x^2n is x2nx^2n. That single rule explains most beginner surprises.

Step 2 — Numbered equations you can reference

Use the equation environment (from amsmath, loaded in the preamble) with a \label, and point at it with \eqref:

\begin{equation}
  \label{eq:gauss}
  \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}
\end{equation}

Equation~\eqref{eq:gauss} is Gauss's law.

Numbers update themselves when equations are added or reordered — never number by hand.

Step 3 — Multi-line derivations

align lines up steps at the & and numbers each line; \\ breaks lines. Use \nonumber on lines that don’t deserve a number:

\begin{align}
  (a+b)^2 &= (a+b)(a+b) \nonumber \\
          &= a^2 + 2ab + b^2
\end{align}

Step 4 — The symbols you’ll actually use

\frac{dy}{dx}          % fractions
\sqrt{2}               % roots
\sum_{i=1}^{N} x_i     % sums (and \prod, \int alike)
\alpha, \beta, \gamma  % greek letters
\mathbf{v}             % bold vectors
\langle x \rangle      % angle brackets
x \approx y, x \neq y  % relations

Guessing usually works: the command is the symbol’s name. When it doesn’t, sketch-to-symbol tools and the compiled preview settle it quickly.

Step 5 — See it live

In Writano you don’t compile to check an equation: LaTeX mode previews math as you type, and in the Visual editor an equation renders in place — click it to edit its source in a popover. Use whichever surface you like; it is the same document.

Tip: Thin spaces matter in display math — \, before dx in an integral (e^{-x^2}\,dx) is the difference between typeset math and typewriter math.