Inline and Display Formulas
Inline formulas are enclosed in single dollar signs: $E = mc^2$.
Display formulas use double dollar signs: $$\int_a^b f(x)dx$$.
For Typora users, enable inline math support via:
File → Preferences → Markdown → Markdown Extensions → Check "Inline Math"
Common Mathematical Symbols
Superscripts and Subscripts
| Notation |
Example |
Syntax |
| Vector |
$\vec{v}$ |
\vec{v} |
| Mean |
$\bar{x}$ |
\bar{x} |
| Estimate |
$\hat{\theta}$ |
\hat{\theta} |
| First derivative |
$\dot{x}$ |
\dot{x} |
| Second derivative |
$\ddot{x}$ |
\ddot{x} |
| Superscript |
$x^n$ |
x^n |
| Subscript |
$x_i$ |
x_i |
Fractions and Roots
| Expression |
Syntax |
| $\frac{a}{b}$ |
\frac{a}{b} |
| $\sqrt{x}$ |
\sqrt{x} |
| $\sqrt[n]{x}$ |
\sqrt[n]{x} |
Mathematical Operators
Summation and Integration
- Summation: $\sum_{i=1}^{n} a_i$ (
\sum_{i=1}^{n} a_i)
- Limit: $\lim_{x \to \infty} f(x)$ (
\lim_{x \to \infty} f(x))
- Integral: $\int_{0}^{\infty} e^{-x} dx$ (
\int_{0}^{\infty} e^{-x} dx)
- Double integral: $\iint_D f(x,y) dA$ (
\iint_D f(x,y) dA)
Set Operations
- Union: $A \cup B$ (
A \cup B)
- Intersection: $A \cap B$ (
A \cap B)
- Subset: $A \subset B$ (
A \subset B)
- Element: $x \in A$ (
x \in A)
- Empty set: $\emptyset$ (
\emptyset)
Brackets and Matrices
- Binomial: $\binom{n}{k}$ (
\binom{n}{k})
- Matrix:
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
Relational Operators
| Operator |
Symbol |
Syntax |
| Not equal |
$\neq$ |
\neq |
| Less then or equal |
$\leq$ |
\leq |
| Greater then or equal |
$\geq$ |
\geq |
| Approximately equal |
$\approx$ |
\approx |
| Plus/minus |
$\pm$ |
\pm |
| Multiplication |
$\times$ |
\times |
| Division |
$\div$ |
\div |
Complex Mathematical Expressions
Matrix Equation
$$
\begin{bmatrix}
1 & x_1 & x_1^2 \\
1 & x_2 & x_2^2 \\
1 & x_3 & x_3^2
\end{bmatrix}
\begin{bmatrix}
a_0 \\ a_1 \\ a_2
\end{bmatrix}
=
\begin{bmatrix}
y_1 \\ y_2 \\ y_3
\end{bmatrix}
$$
System of Equations
$$
\begin{cases}
a_0 + a_1x_1 + a_2x_1^2 = y_1 \\
a_0 + a_1x_2 + a_2x_2^2 = y_2 \\
a_0 + a_1x_3 + a_2x_3^2 = y_3
\end{cases}
$$
Greek Alphabet
| Lowercase |
Syntax |
Uppercase |
Syntax |
| $\alpha$ |
\alpha |
$A$ |
A |
| $\beta$ |
\beta |
$B$ |
B |
| $\gamma$ |
\gamma |
$\Gamma$ |
\Gamma |
| $\delta$ |
\delta |
$\Delta$ |
\Delta |
| $\epsilon$ |
\epsilon |
$E$ |
E |
Text Formatting and Spacing
Font Styles
- Bold: $\mathbf{Sample}$ (
\mathbf{Sample})
- Italic: $\mathit{Sample}$ (
\mathit{Sample})
- Sans-serif: $\mathsf{Sample}$ (
\mathsf{Sample})
Spacing
- Thin space: $a,b$ (
a\,b)
- Medium space: $a;b$ (
a\;b)
- Quad space: $a\quad b$ (
a\quad b)
- Double quad: $a\qquad b$ (
a\qquad b)
Annotated Formulas
$$
f(x) = \begin{cases}
\frac{x}{2}, & \text{if $x$ is even} \\
3x+1, & \text{if $x$ is odd}
\end{cases}
$$