A quick-reference guide, on how to write mathematical notation in Markdown documents. This is achieved by use of a formatting markup language called, LaTeX.

The scope of mathematical notation included in this cheat sheet is drawn from the Math Notation Cheat Sheet poster, created by Dominic Walliman , included below with permission. The associated YouTube video, which is excellent, is The Map of Mathematics .

## Adding Math Notation To Markdown Documents

LaTeX is sometimes stylised as $\LaTeX$.

Typesetting is based on $\TeX$, created by Donald Knuth .

Open Source editor, VSCode, supports mathematical typesetting with $\LaTeX$ in Markdown documents. Equations are rendered in the Live Preview Pane, enabled with Ctrl + K V. No other libraries, extensions or apps need to be installed. Rendering in Live Preview is performed by KaTeX , a fast, easy-to-use JavaScript library for $\TeX$ math rendering on the web.

## Including LaTeX in Markdown

There are two ways to include $\LaTeX$ mathematical typesetting in Markdown documents. The first is inline, which means that the notation is included in the paragraph or sentence, with the flow of text.

The second method is as separate code blocks, so that the notation is shown in it’s own paragraph.

Inline LaTeX mathematical notation is wrapped in single-dollar signs. For example, for the square of "x", just type $x^2$, which is then formatted as $x^2$.

Alternatively, code blocks of LaTeX begin and end with two dollar signs, wrapped inside triple backticks. For example…

1
2$$3\displaystyle\sum_{k=3}^5 k^2=3^2 + 4^2 + 5^2 =50 4$$
5


The above is rendered as:

$$\displaystyle\sum_{k=3}^5 k^2=3^2 + 4^2 + 5^2=50$$

## Cheat Sheet

### Arithmetic

NotationExampleInlineCode Block
Addition$a+b$$a+b$$$ a+b $$
Subtraction$a-b$$a-b$$$ a-b $$
Various Forms of Multiplication$a \times b$
$a \ast b$
$a \cdot b$
$a \times b$
$a \ast b$
$a \cdot b$
$$ a \cdot b $$
Various Forms of Division$a \colon b$
$a / b$
$a \div b$
$\frac{a}{b}$
$a \colon b$
$a / b$
$a \div b$
$\frac{a}{b}$
$$ a \div b $$
Remainder / Modulo$5 \mod 2 = 1$$5\mod 2=1$$$ 5\mod 2=1 $$
Negative Value$-a$$-a$$$ -a $$
Plus or Minus, Minus or Plus$\pm a$
$\mp a$
$\pm a$
$\mp a$
$$ \pm a $$
Squared, Cubed, nth-Power$a^2$
$a^3$
$a^n$
$a^2$
$a^3$
$a^n$
$$ a^3 $$
Square Root, Cube Root, nth-Root$\sqrt{a}$
$\sqrt[3]{a}$
$\sqrt[n]{a}$
$\sqrt{a}$
$\sqrt[3]{a}$
$\sqrt[n]{a}$
$$ \sqrt[3]{a} $$

### Equality

NotationExampleInlineCode Block
Equals$3=1+2$$3=1+2$$$ 3=1+2 $$
Not Equals$3 \neq 4$$3\neq4$$$ 3\neq4 $$
Identical / Equivalent To$a \equiv b$$a \equiv b$$$ a \equiv b $$
Proportional To$a \propto b$$a \propto b$$$ a \propto b $$
Approximately Equal To$\sin(0.01) \approx 0.01$$\sin(0.01) \approx 0.01$$$ \sin(0.01) \approx 0.01 $$

### Comparison

NotationExampleInlineCode Block
a Less Than b
a Greater Than b
$a < b$
$a > b$
$a<b$
$a>b$
$$ a<b $$
a Less Than or Equal To b
a Greater Than or Equal To b
$a \leq b$
$a \geq b$
$a \leq b$
$a \geq b$
$$ a \leq b $$
a Much Smaller Than b
a Much Larger Than b
$a \ll b$
$a \gg b$
$a \ll b$
$a \gg b$
$$ a \ll b $$

### Algebra

NotationExampleInlineCode Block
Factorial$5 ! = 5 \times 4 \times 3 \times 2 \times 1$$5!=5 \times 4 \times 3 \times 2 \times 1$$$ 5!=5 \times 4 \times 3 \times 2 \times 1 $$
Absolute Value$| -5 | = 5$$|-5|=5$$$ |-5|=5 $$
Function Of$f(x) = 2x^2$$f(x)=2x^2$$$ f(x)=2x^2 $$
Change or Difference$\Delta x = x_1 - x_0$$\Delta x = x_1 - x_0$$$ \Delta x = x_1 - x_0 $$
Pi$\pi = 3.14159…$$\pi = 3.14159...$$$ \pi $$
Euler’s Constant$e = 2.71828…$$e = 2.71828...$$$ e = 2.71828... $$
Sum$\displaystyle\sum_{k=3}^5 k^2 = 3^2 + 4^2 + 5^2 = 50$$\displaystyle\sum_{k=3}^5 k^2=3^2 + 4^2 + 5^2 =50$$$ \displaystyle\sum_{k=3}^5 k^2=3^2 + 4^2 + 5^2 =50 $$
Series Product$\displaystyle\prod_{x=2}^4 x^2 = 2^2 \times 3^2 \times 4^2 = 576$$\displaystyle\prod_{x=2}^4 x^2 = 2^2 \times 3^2 \times 4^2 = 576$$$ \displaystyle\sum_{k=2}^4 k^2=2^2 \times 3^2 \times 4^2 = 576 $$
Brackets & Parentheses$[\ldots]$ $(\ldots)$$[\ldots] (\ldots)$$$ [\ldots] (\ldots) $$

### Angles

NotationExampleInlineCode Block
Angle$\angle$$\angle$$$ \angle $$
Degree, Arc Min, Arc Sec$30\degree45\rq30\rq\rq$$30\degree45\rq30\rq\rq$$$ 30\degree45\rq30\rq\rq $$
Radians$360\degree = 2\pi rad$$360\degree = 2\pi rad$$$ 360\degree = 2\pi rad $$

### Probability & Statistics

NotationExampleInlineCode Block
Probability of Event A$P(A)$ or $\Pr(A)$$P(A)$ or $\Pr(A)$$$ P(A) $$
Intersection Prob. of A & B$P(A \cap B)$$P(A \cap B)$$$ P(A \ca pB) $$
Union Prob. of A or B$P(A \cup B)$$P(A \cup B)$$$ P(A \cup B) $$
Conditional Prob. of A Given B$P(A | B)$$P(A|B)$$$ P(A|B) $$
Median$\tilde{x}$$\tilde{x}$$$ \tilde{x} $$
Population Mean$\mu , \overline{x} , \langle x \rangle$$\mu , \overline{x} , \langle x \rangle$$$ \mu , \overline{x} , \langle x \rangle $$
Standard Deviation$\sigma$$\sigma$$$ \sigma $$
Varience$\sigma^2$$\sigma^2$$$ \sigma^2 $$

### Linear Algebra

#### Linear Algebra: Vectors

NotationExampleInlineCode Block
Vectors$\mathbf{v} \overline{v} \vec{v}$$\mathbf{v}\overline{v}\vec{v}$$$ \mathbf{v} \overline{v} \vec{v} $$
Row Vector$v = \begin{pmatrix} 1 & 2 & 3 \end{pmatrix}$$v=\begin{pmatrix}1&2&3\end{pmatrix}$$$ v = \begin{pmatrix} 1 & 2 & 3 \end{pmatrix} $$
Column Vector$w = \begin{pmatrix} 4 \cr 5 \cr 6 \cr \end{pmatrix}$$w=\begin{pmatrix}4\cr5\cr6\cr\end{pmatrix}$$$ w=\begin{pmatrix} 4 \cr 5 \cr 6 \cr \end{pmatrix} $$
Dot Product$\mathbf{v} \cdot \mathbf{w}$
$(v,w)$
$\left< v|w \right>$
$\mathbf{v} \cdot \mathbf{w}$<br>$(v,w)$<br>$\left<v | w\right>$$$ \mathbf{v}\cdot\mathbf{w} (v,w) \left<v|w \right> $$
Cross Product$v \times w$$v \times w$$$ v \times w $$
Length of v$|v|$$|v|$$$ |v| $$
Norm of v$||v||$$||v||$$$ ||v|| $$

#### Linear Algebra: Matrices

NotationExampleInlineCode Block
Matrix, 2 By 3$A=\begin{bmatrix} 1 & 2 & 3 \cr 4 & 5 & 6 \end{bmatrix}$$A=\begin{bmatrix}1&2&3\cr4&5&6\end{bmatrix}$$$ A= \begin{bmatrix} 1 & 2 & 3 \cr 4 & 5 & 6 \end{bmatrix} $$
Product$A \cdot B$$A \cdot B$$$ A \cdot B $$
Hadamard Product$A \circ B$$A \circ B$$$ A \circ B $$
Kronecker Product$A \otimes B$$A \otimes B$$$ A \otimes B $$
Transposed Matrix$A^T$$A^T$$$ A^T $$
Hermitian Matrix or
Conjugate Transpose
$A^\dag$
$A^\ast$
$A^\dag$
$A^\ast$
$$ A^\dag A^\ast $$
Inverse Matrix$A^{-1}$$A^{-1}$$$ A^{-1} $$
Determinant$|A|$$|A|$$$ |A| $$
Norm$||A||$$||A||$$$ ||A|| $$

### Calculus

NotationExampleInlineCode Block
Example Function:
$y = \frac{x^2}{4}$
$y = \frac{x^2}{4}$$y = \frac{x^2}{4}$$$ y = \frac{x^2}{4} $$
Integration
(Limits: 1 to 4)
$A = \int_1^4 \frac{x^2}{x} dx$$A = \int_1^4 \frac{x^2}{x} dx$$$ A = \int_1^4 \frac{x^2}{x} dx $$
Differentiation
First Derivative
With Respect To $x$
$\frac{df}{dx}$$\frac{df}{dx}$$$ \frac{df}{dx} $$
Partial Derivative
With Respect To $x$
$\frac{\partial f}{\partial x}$$\frac{\partial f}{\partial x}$$$ \frac{\partial f}{\partial x} $$
First and Second Derivative
of Function
$f\rq$
$f\rq\rq$
$f\rq$
$f\rq\rq$
$$ f\rq f\rq\rq $$
First and Second Derivative
With Respect To Time
$\dot f$
$\ddot f$
$\dot f$
$\ddot f$
$$ \dot f \ddot f $$

### Complex Numbers

NotationExampleInlineBlock