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This post demonstrates how to use LaTeX math formatting in your blog posts. LaTeX is powerful for displaying mathematical notation on the web.
Inline Math Expressions
You can include inline math expressions by surrounding your LaTeX code with single dollar signs. For example, the equation for calculating the area of a circle $A = \pi r^2$ appears right within the text.
Here's another example: The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ solves the equation $ax^2 + bx + c = 0$.
Display Math Expressions
For larger equations or formulas that should be displayed on their own line, use double dollar signs:
$$\int_{a}^{b} f(x) \, dx = F(b) - F(a)$$
This is the Fundamental Theorem of Calculus. You can also add equation numbers or labels:
$$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} \tag{1}$$
$$\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \varepsilon_0 \frac{\partial \vec{E}}{\partial t} \tag{2}$$
Advanced Mathematical Notation
LaTeX can handle complex mathematical structures like matrices:
$$
A = \begin{pmatrix}
a_{11} & a_{12} & \ldots & a_{1n} \\
a_{21} & a_{22} & \ldots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \ldots & a_{mn}
\end{pmatrix}
$$
And aligned equations:
$$
\begin{align}
\nabla \cdot \vec{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \vec{B} &= 0
\end{align}
$$
Using LaTeX in Your Own Posts
To use LaTeX in your own blog posts, you need to:
- Include the MathJax scripts in the
<head> section of your HTML file (already done in this template)
- Use single dollar signs for inline math:
$your formula here$
- Use double dollar signs for display math:
$$your formula here$$
You can also use standard LaTeX syntax for symbols, like Greek letters ($\alpha$, $\beta$, $\gamma$), operators ($\sum$, $\prod$, $\int$), and more.
Examples for Machine Learning
Here are some examples relevant to machine learning and AI:
Cost function for linear regression:
$$J(\theta) = \frac{1}{2m} \sum_{i=1}^{m} (h_\theta(x^{(i)}) - y^{(i)})^2$$
Sigmoid activation function:
$$\sigma(z) = \frac{1}{1 + e^{-z}}$$
Backpropagation update rule:
$$\theta_j := \theta_j - \alpha \frac{\partial}{\partial \theta_j} J(\theta)$$
Conclusion
With LaTeX math formatting, you can clearly communicate complex mathematical ideas in your blog posts. This is especially useful for academic and technical writing.
For a complete reference on LaTeX math commands, check out the LaTeX Mathematics Wikibook.
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