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Latex Mathematical Format



What is LaTeX?
How math is encoded
Try the editor
Common structures
Symbols by mathematical domain
LaTeX notation across the site
Quick reference
Related tools




What is LaTeX?

LaTeX is a typesetting system for mathematics and technical writing. Math expressions are written as plain text using backslash-prefixed commands - the fraction one over two is \frac{1}{2}, the integral from zero to one is \int_0^1. The source is portable, version-controllable, and is the standard format for scientific publishing.

This section indexes everything on the site that helps you read, write, and look up LaTeX math notation - a live editor, structured references, and the notation blocks embedded throughout the topic pages.

Below: a working editor, an overview of how math is encoded, eight common structures with dedicated reference pages, symbol catalogs by mathematical domain, cross-links to notation blocks on topic pages, and a quick-reference accordion of everyday patterns.

How math is encoded

Four building blocks cover almost every LaTeX expression.

Commands begin with a backslash and name a symbol or operation: \alpha produces the Greek letter alpha, \sqrt a square root, \sum a summation sign. Hundreds of commands exist, but a few dozen cover most everyday writing.

Grouping with braces tells LaTeX what belongs together. x^{2n} raises x to the power 2n, while x^2n raises only to 2 and treats the n as a separate factor. Whenever an argument is more than one character, wrap it in braces.

Subscripts and superscripts attach with ^ for superscripts and _ for subscripts. The same syntax sets summation bounds, integral limits, and tensor indices: ∑i=1nxi\sum_{i=1}^{n} x_i, ∫0∞e−xdx\int_0^\infty e^{-x} dx, TαβμνT^{\mu\nu}_{\alpha\beta}.

Environments wrap content that needs special handling. Matrices use \begin{bmatrix} ... \end{bmatrix}, multi-line equations use \begin{align} ... \end{align}, piecewise definitions use \begin{cases} ... \end{cases}. Inside, ampersand separates columns and double-backslash separates rows.

These four mechanisms compose freely - a fraction whose numerator is a square root whose argument is a sum whose terms are exponentials is just nesting commands and arguments to whatever depth the expression needs.

Try the editor

LATEX
Interactive LaTeX editor
Build formulas visually. Click symbols to insert fractions, roots, integrals, and matrices across multiple equation lines. The combined source updates live and copies to the clipboard with one click.
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Common structures

Each structure below links to a dedicated guide on LaTeXEdit, our companion site for LaTeX - full syntax, variants, and worked examples, with a live editor to try each one.

Symbols by mathematical domain

Symbol catalogs organized by topic. Each one pairs the rendered symbol with its LaTeX command, grouped into categories specific to that domain.
Algebra
Variables, operators, equality, exponents, radicals, and absolute value notation.
Calculus
Derivatives (ddx\frac{d}{dx}, ∂\partial), integrals (∫\int), limits, gradients (∇\nabla), and infinity.
Set theory
Membership (∈\in), unions (∪\cup), intersections (∩\cap), subsets, and empty set (∅\emptyset).
Math logic
Quantifiers (∀\forall, ∃\exists), connectives (∧\land, ∨\lor, ¬\neg), and implication arrows.
Linear algebra
Matrices, transpose (ATA^T), determinants, eigenvalues (λ\lambda), and tensor products (⊗\otimes).
Probability
Probability (P(A)P(A)), expectation (E[X]\mathbb{E}[X]), variance (σ2\sigma^2), and distribution symbols.
Combinatorics
Factorials (n!n!), binomial coefficients ((nk)\binom{n}{k}), permutations, and combinations.
Trigonometry
Trigonometric functions (sin⁡\sin, cos⁡\cos, tan⁡\tan), angles (θ\theta), and degree notation.
Complex numbers
Imaginary unit (ii), modulus (∣z∣|z|), argument (arg⁡z\arg z), conjugate (zˉ\bar{z}), and number sets.

LaTeX notation across the site

Many topic pages include a dedicated notation block showing the formal LaTeX for that concept - definitions, distributions, theorems, and identities written in publication-ready form.

Quick reference

Patterns that cover most everyday math typesetting.
Subscripts and superscripts
Use _ for subscript and ^ for superscript. Wrap multi-character indices in braces: x_{ij} renders as xijx_{ij}, while x_ij renders as xijx_ij - only the i is subscripted. The same syntax sets summation bounds and integral limits.
Fractions and roots
Use \frac{num}{den} for inline fractions and \dfrac{num}{den} for display-size fractions in running text. Square roots are \sqrt{x}; n-th roots use the optional bracket argument: \sqrt[n]{x} for xn\sqrt[n]{x}. Fractions nest freely - 11+1x\dfrac{1}{1+\dfrac{1}{x}}.
Sums, products, and integrals
Sums use \sum, products \prod, integrals \int. Limits attach as subscript and superscript: \sum_{i=1}^{n} for ∑i=1n\sum_{i=1}^{n}. Multiple integrals stack the command: \iint, \iiint, \oint for line integrals.
Greek letters
Lowercase Greek is \letter - \alpha, \beta, \pi for α,β,π\alpha, \beta, \pi. Uppercase Greek capitalizes the first letter: \Gamma, \Sigma, \Omega for Γ,Σ,Ω\Gamma, \Sigma, \Omega. Letters that look identical to Latin (uppercase alpha, beta, etc.) are not aliased; use the Latin letter.
Matrices and arrays
Inside \begin{bmatrix} ... \end{bmatrix} (square brackets), pmatrix (parentheses), or vmatrix (vertical bars for determinants), use ampersand to separate columns and double-backslash to separate rows. Example: \begin{bmatrix} a & b \\ c & d \end{bmatrix} produces [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}.
Delimiters that scale
Bare () stay small. Use \left( and \right) to make parentheses grow with their content: \left( \dfrac{a}{b} \right) for (ab)\left( \dfrac{a}{b} \right). The pairing applies to brackets, braces, absolute value bars, angle brackets, and ceiling/floor symbols.
Operators and functions
Common functions like sine, cosine, log, and limit have dedicated commands that render upright: \sin x, \cos x, \log x, \lim_{x\to 0} produce sin⁡x\sin x, cos⁡x\cos x, log⁡x\log x, lim⁡x→0\lim_{x\to 0}. For custom upright operators, use \operatorname{name}.

Related tools

The math symbols catalogs map every symbol to its LaTeX command, organized by domain. The tables section collects formula and identity references in compact LaTeX-rendered grids. The interactive editor sits at the heart of this section - click symbols, build expressions across multiple lines, and copy the source when ready. When you need the actual Unicode character rather than its LaTeX source - to paste into email, chat, or a plain document - the mathematical keyboard types it directly, with subscript and superscript modes included.

For deeper notation on specific topics, every domain section (probability, set theory, linear algebra, and others) includes pages whose notation blocks are written and rendered in LaTeX directly. Pair this hub with any of them when you need to write something you have only seen rendered, not coded.