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🧮 LaTeX/MathJax Reference

NoteDiscovery supports LaTeX mathematical notation powered by MathJax 3. Write beautiful equations in your notes using familiar LaTeX syntax.

Syntax Overview

Delimiter	Type	Behavior
$...$	Inline	Flows with text, not centered
`$...$`	Inline	Same as $...$ (LaTeX standard)
`$$...$$`	Display	Own paragraph, centered, larger
`\[...\]`	Display	Same as `$$...$$` (LaTeX standard)

Inline Math (within text)

Inline math flows with your text: $E = mc^2$ renders as E = mc^2

Display Math (centered, on its own line)

Display math gets its own centered paragraph:

$$
x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
$$

Or using LaTeX-style delimiters:

\[
x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
\]


x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}

Basic Examples

Superscripts and Subscripts

Superscripts use ^:

$x^2$ → x^2
$e^{i\pi}$ → e^{i\pi}

Subscripts use _:

$x_1$ → x_1
$a_{ij}$ → a_{ij}

Combined:

$x_1^2$ → x_1^2
$\sum_{i=1}^{n} i^2$ → \sum_{i=1}^{n} i^2

Fractions

Simple fractions: $\frac{a}{b}$ → \frac{a}{b}

Complex fractions:


\frac{\frac{1}{x}+\frac{1}{y}}{x+y} = \frac{x+y}{xy(x+y)} = \frac{1}{xy}

Square Roots

$\sqrt{2}$ → \sqrt{2}
$\sqrt[3]{8}$ → \sqrt[3]{8} (cube root)
$\sqrt{x^2 + y^2}$ → \sqrt{x^2 + y^2}

Greek Letters

Lowercase

$\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \lambda, \mu, \pi, \sigma, \tau, \phi, \chi, \psi, \omega$

\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \lambda, \mu, \pi, \sigma, \tau, \phi, \chi, \psi, \omega

Uppercase

$\Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Phi, \Psi, \Omega$

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

Calculus

Integrals

Definite integral:

$$
\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}
$$


\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}

Multiple integrals:

$$
\iiint_V f(x,y,z) \, dx \, dy \, dz
$$


\iiint_V f(x,y,z) \, dx \, dy \, dz

Derivatives

First derivative: $\frac{df}{dx}$ → \frac{df}{dx}

Partial derivatives: $\frac{\partial f}{\partial x}$ → \frac{\partial f}{\partial x}

Gradient:

$$
\nabla f = \frac{\partial f}{\partial x}\mathbf{i} + \frac{\partial f}{\partial y}\mathbf{j} + \frac{\partial f}{\partial z}\mathbf{k}
$$


\nabla f = \frac{\partial f}{\partial x}\mathbf{i} + \frac{\partial f}{\partial y}\mathbf{j} + \frac{\partial f}{\partial z}\mathbf{k}

Limits

$$
\lim_{x \to \infty} \frac{1}{x} = 0
$$


\lim_{x \to \infty} \frac{1}{x} = 0

Summations and Products

Summation

Inline: \sum_{i=1}^{n} i = \frac{n(n+1)}{2}

Display:

$$
\sum_{k=1}^{\infty} \frac{1}{k^2} = \frac{\pi^2}{6}
$$


\sum_{k=1}^{\infty} \frac{1}{k^2} = \frac{\pi^2}{6}

Product

$$
\prod_{i=1}^{n} i = n!
$$


\prod_{i=1}^{n} i = n!

Matrices and Vectors

Basic Matrix

$$
\begin{bmatrix}
a & b \\\ 
c & d
\end{bmatrix}
$$


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

Larger Matrix

$$
A = \begin{bmatrix}
1 & 2 & 3 \\\ 
4 & 5 & 6 \\\ 
7 & 8 & 9
\end{bmatrix}
$$


A = \begin{bmatrix}
1 & 2 & 3 \\\ 
4 & 5 & 6 \\\ 
7 & 8 & 9
\end{bmatrix}

Identity Matrix

$$
I = \begin{pmatrix}
1 & 0 & 0 \\\ 
0 & 1 & 0 \\\ 
0 & 0 & 1
\end{pmatrix}
$$


I = \begin{pmatrix}
1 & 0 & 0 \\\ 
0 & 1 & 0 \\\ 
0 & 0 & 1
\end{pmatrix}

Determinant

$$
\det(A) = \begin{vmatrix}
a & b \\\ 
c & d
\end{vmatrix} = ad - bc
$$


\det(A) = \begin{vmatrix}
a & b \\\ 
c & d
\end{vmatrix} = ad - bc

Advanced Features

Systems of Equations

$$
\begin{cases}
x + y = 5 \\\ 
2x - y = 1
\end{cases}
$$


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

Aligned Equations

$$
\begin{aligned}
f(x) &= (x+1)^2 \\\ 
&= x^2 + 2x + 1
\end{aligned}
$$


\begin{aligned}
f(x) &= (x+1)^2 \\\ 
&= x^2 + 2x + 1
\end{aligned}

Continued Fractions

$$
\phi = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots}}}
$$


\phi = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots}}}

Mathematical Symbols

Operators

Symbol	LaTeX	Result
Plus-minus	$\pm$	`\pm`
Multiply	$\times$	`\times`
Divide	$\div$	`\div`
Not equal	$\neq$	`\neq`
Less/Greater	$\leq, \geq$	`\leq, \geq`
Approx	$\approx$	`\approx`
Infinity	$\infty$	`\infty`

Set Theory

Symbol	LaTeX	Result
Element of	$\in$	`\in`
Not element	$\notin$	`\notin`
Subset	$\subset$	`\subset`
Union	$\cup$	`\cup`
Intersection	$\cap$	`\cap`
Empty set	$\emptyset$	`\emptyset`

Logic

Symbol	LaTeX	Result
And	$\land$	`\land`
Or	$\lor$	`\lor`
Not	$\neg$	`\neg`
Implies	$\implies$	`\implies`
If and only if	$\iff$	`\iff`
For all	$\forall$	`\forall`
Exists	$\exists$	`\exists`

Famous Equations

Euler's Identity

 e^{i\pi} + 1 = 0

Einstein's Mass-Energy Equivalence

 E = mc^2

Pythagorean Theorem

 a^2 + b^2 = c^2

Schrödinger Equation

 i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)

Maxwell's Equations

$$
\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\\ 
\nabla \cdot \mathbf{B} &= 0 \\\ 
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\\ 
\nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}
\end{aligned}
$$


\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\\ 
\nabla \cdot \mathbf{B} &= 0 \\\ 
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\\ 
\nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}
\end{aligned}

Tips

1. Preview Mode

Always use Split View or Preview Mode to see your equations rendered in real-time.

2. Escaping Dollar Signs

If you need a literal dollar sign (not math), escape it: $\\$100$ renders as \\$100

3. Complex Expressions

For very long equations, consider breaking them across multiple lines using aligned or split environments.

4. Matrix & Multi-line Formatting

IMPORTANT: Use 3 backslashes + space (\\\ ) for line breaks to enable multi-line formatting:

✅ Good (readable multi-line format):
$$
\begin{bmatrix}
a & b \\\ 
c & d
\end{bmatrix}
$$

❌ Bad (only 2 backslashes - won't work):
$$
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
$$

The Secret: Use \\\ (three backslashes + trailing space) at the end of each row, then add a newline. This allows for readable multi-line equations!

5. Debugging

If an equation doesn't render:

Check for matching delimiters ( $...$ or $$...$$)
Ensure backslashes are correct (\frac not /frac)
Look for unescaped special characters
For matrices/line breaks, use \\\ (three backslashes + space) not \\
Make sure there's a trailing space after \\\ before the newline

6. Performance

MathJax renders efficiently, but very equation-heavy notes (100+ equations) may take a moment to typeset.

Resources

For more LaTeX commands and symbols, see:

MathJax Documentation
LaTeX Math Symbols
Detexify - Draw a symbol to find its LaTeX command

💡 Tip: Copy and paste examples from this note to quickly start using math in your own notes!

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