🧮 LaTeX/MathJax Reference

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

Syntax Overview

Inline Math (within text)

Use $...$ for inline equations:

$E = mc^2$ renders as: $E = mc^2$
$x^2 + y^2 = r^2$ renders as: $x^2 + y^2 = r^2$

Display Math (centered, on its own line)

Use $$...$$ for display equations:

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

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

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

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

Uppercase

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

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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