Symbol desk card

Accents, big operators, number sets, and stretchy delimiters on one page.

Equation craftbeginnermathcheatsheet

Symbol desk card

This page is a reference card rather than a lesson: the accents, big operators, number sets, and delimiters that cover most day-to-day mathematics, collected in one place. Every command here works in math mode only, and the number sets need \usepackage{amssymb} in the preamble. For the Greek alphabet and the basic relations, see Greek and everyday symbols; for how math mode itself works, start with math mode basics.

Accents

\hat{x} \bar{x} \tilde{x} \vec{x} \dot{x} \ddot{x}
\widehat{xyz} \overline{xyz}

Command	Renders as	Conventional meaning
`\hat{x}`	x with circumflex	Estimators, unit vectors, operators
`\bar{x}`	x with bar	Sample means, complex conjugates
`\tilde{x}`	x with tilde	Approximations, transformed variables
`\vec{x}`	x with arrow	Vectors
`\dot{x}`, `\ddot{x}`	one or two dots	First and second time derivatives
`\widehat{xyz}`, `\overline{xyz}`	stretched accent	Accents over multi-letter expressions

The plain accents fit a single letter; the wide and over variants stretch to span whatever is in the braces.

Big operators

\sum_{i=1}^n \prod_{i=1}^n \int_a^b \oint
\lim_{x \to 0} \max_{x} \inf_{x}

Command	Meaning
`\sum_{i=1}^n`	Sum with lower and upper bounds
`\prod_{i=1}^n`	Product
`\int_a^b`	Definite integral
`\oint`	Contour integral
`\lim_{x \to 0}`	Limit
`\max_{x}`, `\inf_{x}`	Maximum, infimum over a variable

Bounds attach with the ordinary subscript and superscript syntax, braced when longer than one character. In display math, sums, products, and limits place their bounds above and below the symbol; integrals keep theirs at the side, which is the standard convention.

Number sets

\mathbb{N} \mathbb{Z} \mathbb{Q} \mathbb{R} \mathbb{C}

These are the naturals, integers, rationals, reals, and complex numbers in blackboard bold. The \mathbb alphabet and its relatives are covered in Blackboard, script, Fraktur.

Delimiters

\left( \frac{a}{b} \right)
\left\{ x : x > 0 \right\}
\langle v, w \rangle

\left and \right grow their delimiter to the height of the enclosed material, so parentheses around a tall fraction wrap it instead of clipping it at text height. They must come in pairs; to show only one side, close with \right. and the invisible partner satisfies the pairing. Braces are special characters, so set braces are written \{ and \}. Angle brackets for inner products are \langle and \rangle, never the keyboard’s less-than and greater-than signs, which are relation symbols with the wrong shape and spacing.

Any row of this card can be pasted into the live playground to see the rendered form next to the source.

LaTeX used on this page

One-line meanings for every command in the examples above. The full A-to-Z lives in every \command explained.

\bar: Puts a short bar over one symbol: \bar{x}.
\ddot: Puts two dots over a symbol, for second time derivatives: \ddot{x}.
\dot: Puts one dot over a symbol, common for time derivatives: \dot{x}.
\frac: Stacked fraction: \frac{numerator}{denominator}.
\hat: Puts a small hat accent over one symbol: \hat{x}.
\inf: Infimum operator, typeset upright: \inf_{x \in S}.
\int: Integral sign: \int_0^1 f(x)\,dx.
\langle: Left angle bracket delimiter.
\left: Opens an auto-sized delimiter pair: \left( ... \right).
\lim: Limit operator, upright with the subscript below in display math: \lim_{x \to 0}.
\mathbb: Blackboard bold letters for number sets: \mathbb{R} (amssymb).
\max: Maximum operator, typeset upright with limits below in display math.
\oint: Contour (closed loop) integral sign.
\overline: Draws a line over a whole expression: \overline{x + y}.
\prod: Product sign with limits: \prod_{i=1}^{n}.
\rangle: Right angle bracket delimiter.
\right: Closes an auto-sized delimiter pair opened with \left.
\sum: Summation sign with limits: \sum_{i=1}^{n}.

Plus 4 more on the full reference page.

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