#19 Math Formulas & Scientific Notation
Input math formulas in the editor — from basic arithmetic to AI matrix operations, all rendered instantly into beautiful mathematical typography.
Two Ways to Insert
Method 1: π Button
Click the π button in the toolbar to insert a sample formula $E=mc^2$, then edit it to match your content.
Method 2: Direct Input
Wrap your formula in $...$: type $ at the start, enter your formula, then type $ at the end — it auto-renders as a formatted image.
| You type | Result |
|---|---|
$x + y = z$ |
$x + y = z$ |
$E=mc^2$ |
$E=mc^2$ |
$\pi \approx 3.14159$ |
$\pi \approx 3.14159$ |
Edit Formulas
Click a rendered formula → switches to edit mode → make changes and click elsewhere to confirm.
Basic Examples
Fractions & Roots
| Syntax | Result |
|---|---|
$\frac{a}{b}$ |
$\frac{a}{b}$ |
$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$ |
$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$ |
$\sqrt{x}$ |
$\sqrt{x}$ |
$\sqrt{a^2 + b^2}$ |
$\sqrt{a^2 + b^2}$ |
$\sqrt[3]{x}$ |
$\sqrt[3]{x}$ |
Exponents & Logarithms
| Syntax | Result |
|---|---|
$e^{x}$ |
$e^{x}$ |
$2^{10} = 1024$ |
$2^{10} = 1024$ |
$\log_2 x$ |
$\log_2 x$ |
$\ln e = 1$ |
$\ln e = 1$ |
Greek Letters
| Syntax | Result | Common Use |
|---|---|---|
$\alpha, \beta, \gamma$ |
$\alpha, \beta, \gamma$ | Angles, coefficients |
$\theta$ |
$\theta$ | Parameters, angles |
$\sigma$ |
$\sigma$ | Standard deviation, Sigmoid |
$\mu$ |
$\mu$ | Mean value |
$\lambda$ |
$\lambda$ | Learning rate, regularization |
$\nabla$ |
$\nabla$ | Gradient operator |
$\partial$ |
$\partial$ | Partial derivative |
Intermediate Examples
Summation & Product
$\sum_{i=1}^{n} x_i = x_1 + x_2 + \cdots + x_n$
$\prod_{i=1}^{n} x_i = x_1 \cdot x_2 \cdots x_n$
Limits & Derivatives
$\lim_{x \to 0} \frac{\sin x}{x} = 1$
$\frac{d}{dx} e^x = e^x$
$\frac{d}{dx} \ln x = \frac{1}{x}$
Integration
$\int_0^{\infty} e^{-x}\, dx = 1$
$\int_a^b f(x)\, dx = F(b) - F(a)$
Advanced: AI / ML Matrix Operations
Matrices & Vectors
Define a matrix:
$\mathbf{A} = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}$
Matrix multiplication:
$\mathbf{C} = \mathbf{A} \cdot \mathbf{B}, \quad c_{ij} = \sum_{k} a_{ik} b_{kj}$
Transpose: $(\mathbf{A}^T)_{ij} = a_{ji}$
Linear Layer (Forward Pass)
$\mathbf{y} = \mathbf{W} \mathbf{x} + \mathbf{b}$
Where $\mathbf{W} \in \mathbb{R}^{m \times n}$, $\mathbf{x} \in \mathbb{R}^{n}$, $\mathbf{b} \in \mathbb{R}^{m}$.
Loss Functions
Mean Squared Error (MSE):
$L_{MSE} = \frac{1}{N} \sum_{i=1}^{N} (y_i - \hat{y}_i)^2$
Cross-Entropy:
$L_{CE} = -\frac{1}{N} \sum_{i=1}^{N} y_i \log(\hat{y}_i)$
Activation Functions
Sigmoid:
$\sigma(x) = \frac{1}{1 + e^{-x}}$
Softmax:
$\text{softmax}(x_i) = \frac{e^{x_i}}{\sum_{j=1}^{K} e^{x_j}}$
ReLU:
$\text{ReLU}(x) = \max(0, x)$
Gradient Descent
Basic update rule:
$\theta_{t+1} = \theta_t - \eta \nabla_\theta L(\theta_t)$
Adam optimizer update:
$m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t$
$v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2$
$\theta_{t+1} = \theta_t - \frac{\eta}{\sqrt{\hat{v}_t} + \epsilon} \hat{m}_t$
Backpropagation
Chain rule:
$\frac{\partial L}{\partial \mathbf{W}} = \frac{\partial L}{\partial \mathbf{y}} \cdot \mathbf{x}^T$
Weight update:
$\mathbf{W} \leftarrow \mathbf{W} - \alpha \frac{\partial L}{\partial \mathbf{W}}$
Attention (Transformer)
$\text{Attention}(\mathbf{Q}, \mathbf{K}, \mathbf{V}) = \text{softmax}\!\left(\frac{\mathbf{Q}\mathbf{K}^T}{\sqrt{d_k}}\right)\mathbf{V}$
KaTeX Cheat Sheet
| Effect | Syntax |
|---|---|
| Fraction | \frac{numerator}{denominator} |
| Square root | \sqrt{x} |
| Superscript | x^{2} |
| Subscript | x_{i} |
| Summation | \sum_{i=1}^{n} |
| Integral | \int_a^b |
| Vector | \mathbf{v} |
| Matrix | \begin{pmatrix} a & b \\\\ c & d \end{pmatrix} |
| Partial derivative | \frac{\partial f}{\partial x} |
| Approximately | \approx |
| Element of | \in |
| Real numbers | \mathbb{R} |
Full syntax reference: KaTeX Supported Functions