Math Mode

Mathematical typesetting commands and environments in LaTeX

Math Mode

LaTeX excels at typesetting mathematical content. This reference covers math mode basics, symbols, equations, and advanced mathematical structures.

Math Mode Basics

LaTeX has two math modes:

Inline Math

Math within text: $a^2 + b^2 = c^2$

Display Math

Math on separate lines with automatic centering

Entering Math Mode

Inline Math

% Dollar signs (most common)
The equation $E = mc^2$ is famous.

% \(...\) delimiters
The equation \(E = mc^2\) is famous.

% math environment
The equation \begin{math}E = mc^2\end{math} is famous.

Important: Text-mode commands don’t work in math mode. Use math-specific commands for formatting.

Basic Math Commands

Superscripts and Subscripts

x^2              % Superscript
x_i              % Subscript  
x^{10}           % Multi-character superscript
x_{ij}           % Multi-character subscript
x^2_i            % Both
x^{y^z}          % Nested superscripts
\sum_{i=1}^{n}   % Limits on operators

Fractions

\frac{a}{b}           % Standard fraction
\dfrac{a}{b}          % Display style fraction (larger)
\tfrac{a}{b}          % Text style fraction (smaller)
\sfrac{1}{2}          % Slanted fraction (nicefrac package)
\frac{1}{2+\frac{1}{3}} % Nested fractions

Roots

\sqrt{x}              % Square root
\sqrt[3]{x}           % Cube root
\sqrt[n]{x}           % nth root
\sqrt{\frac{a}{b}}    % Root of fraction

Greek Letters

Lowercase Greek

\alpha    \beta     \gamma    \delta    
\epsilon  \zeta     \eta      \theta    
\iota     \kappa    \lambda   \mu       
\nu       \xi       \pi       \rho      
\sigma    \tau      \upsilon  \phi      
\chi      \psi      \omega              

% Variants
\varepsilon  \vartheta  \varpi  
\varrho      \varsigma  \varphi

Uppercase Greek

\Gamma    \Delta    \Theta    \Lambda   
\Xi       \Pi       \Sigma    \Upsilon  
\Phi      \Psi      \Omega              

Mathematical Operators

Binary Operators

+         -         \times    \div      
\pm       \mp       \cdot     \ast      
\star     \circ     \bullet   \oplus    
\ominus   \otimes   \oslash   \odot     

Relational Operators

=         \neq      <         >         
\leq      \geq      \ll       \gg       
\approx   \sim      \simeq    \cong     
\equiv    \propto   \subset   \supset   
\in       \ni       \perp     \parallel 

Arrows

\leftarrow     \rightarrow    \leftrightarrow
\Leftarrow     \Rightarrow    \Leftrightarrow
\uparrow       \downarrow     \updownarrow   
\nearrow       \searrow       \swarrow       
\nwarrow       \mapsto        \longmapsto    

Large Operators

\sum_{i=1}^{n}      % Summation
\prod_{i=1}^{n}     % Product
\int_{a}^{b}        % Integral
\oint               % Contour integral
\bigcup_{i=1}^{n}   % Union
\bigcap_{i=1}^{n}   % Intersection
\lim_{x \to \infty} % Limit

Delimiters

Basic Delimiters

(x)        [x]        \{x\}      |x|       
\langle x \rangle    \lceil x \rceil        
\lfloor x \rfloor    \| x \|                

Automatic Sizing

% Manual sizing
\big( \Big( \bigg( \Bigg(

% Automatic sizing (recommended)
\left( \frac{a}{b} \right)
\left[ \sum_{i=1}^{n} x_i \right]
\left\{ x : x > 0 \right\}
\left. \frac{df}{dx} \right|_{x=0}

Mathematical Environments

Single Equations

% Numbered equation
\begin{equation}
E = mc^2
\label{eq:einstein}
\end{equation}

% Unnumbered equation
\begin{equation*}
E = mc^2
\end{equation*}

Multiple Equations

Aligned Equations

\begin{align}
x + y &= 5 \\
2x - y &= 1
\end{align}

% With custom alignment
\begin{align}
f(x) &= x^2 + 2x + 1 \\
     &= (x + 1)^2
\end{align}

Matrices

% Basic matrix
\begin{matrix}
a & b \\
c & d
\end{matrix}

% Matrix with delimiters
\begin{pmatrix}        % Parentheses
a & b \\
c & d
\end{pmatrix}

\begin{bmatrix}        % Brackets
a & b \\
c & d
\end{bmatrix}

\begin{vmatrix}        % Vertical lines (determinant)
a & b \\
c & d
\end{vmatrix}

\begin{Vmatrix}        % Double vertical lines
a & b \\
c & d
\end{Vmatrix}

Advanced Features

Text in Math Mode

% Basic text
\text{if } x > 0

% Text with math inside
\text{for all } x \in \mathbb{R}

% Common text operators
\sin x   \cos x   \tan x   \log x
\exp x   \max x   \min x   \det A

Math Fonts

\mathbb{R}     % Blackboard bold (reals)
\mathbb{N}     % Natural numbers
\mathbb{Z}     % Integers
\mathbb{C}     % Complex numbers

\mathcal{L}    % Calligraphic
\mathscr{F}    % Script (mathrsfs package)
\mathfrak{g}   % Fraktur (amssymb package)
\mathbf{v}     % Bold (vectors)
\boldsymbol{\alpha} % Bold Greek

Spacing in Math

% Automatic spacing (usually best)
a + b

% Manual spacing
a \, b         % Thin space
a \: b         % Medium space  
a \; b         % Thick space
a \quad b      % Quad space
a \qquad b     % Double quad

% Negative space
a \! b         % Negative thin space

Theorems and Proofs

\usepackage{amsthm}

% Define theorem environments
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proof}{Proof}

% Use in document
\begin{theorem}
For all $x \in \mathbb{R}$, we have $x^2 \geq 0$.
\end{theorem}

\begin{proof}
This follows from the definition of real numbers.
\end{proof}

Common Constructions

Derivatives

% Basic derivative
\frac{df}{dx}

% Partial derivative  
\frac{\partial f}{\partial x}

% Higher derivatives
\frac{d^2f}{dx^2}

% At a point
\left.\frac{df}{dx}\right|_{x=0}

Integrals

% Definite integral
\int_0^1 x^2 \, dx

% Indefinite integral
\int f(x) \, dx

% Multiple integrals
\iint_D f(x,y) \, dx \, dy
\iiint_V f(x,y,z) \, dV

Sums and Products

% Sum
\sum_{n=1}^{\infty} \frac{1}{n^2}

% Product
\prod_{i=1}^{n} x_i

% Inline versions
$\sum\limits_{i=1}^{n}$ % Forces display style
$\sum\nolimits_{i=1}^{n}$ % Forces inline style

Best Practices

Math typesetting tips:

1. Use proper math mode - Never use text italic for math
2. Choose appropriate environments - align for equations that should align
3. Label important equations - Use \label{eq:descriptive-name}
4. Use \text{} for words - Don’t write words directly in math mode
5. Let LaTeX handle spacing - Avoid manual spacing unless necessary

Quick Reference

Symbol	Command	Symbol	Command
±	\pm	≤	\leq
×	\times	≥	\geq
÷	\div	≠	\neq
∞	\infty	≈	\approx
∑	\sum	∈	\in
∫	\int	⊂	\subset
√	\sqrt{}	∪	\cup
α	\alpha	∩	\cap

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Next: Explore Lists and Enumerations or learn about Tables for data presentation.