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Techniques for categorizing data into predefined classes

My First MDX Post

Welcome to my first MDX blog post! This is a demonstration of how MDX works with mathematical notation using LaTeX syntax.

Introduction

MDX combines the power of Markdown with JSX components, making it perfect for technical writing and documentation. Today we're testing the mathematical rendering capabilities.

Mathematical Examples

Inline Math

Here's the famous Pythagorean theorem written inline: $a^2 + b^2 = c^2$

We can also write Einstein's mass-energy equivalence: $E = mc^2$

And here's a simple quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Block Math

Let's showcase some beautiful mathematical expressions in display mode:

Euler's Identity - often called the most beautiful equation in mathematics:

e^{i\pi} + 1 = 0

The Fundamental Theorem of Calculus:

\int_a^b f'(x) \, dx = f(b) - f(a)

Maxwell's Equations - the foundation of electromagnetism:

\begin{align} \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{align}

The Schrödinger Equation:

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

Complex Mathematical Expressions

Fourier Transform:

\mathcal{F}\{f(t)\} = F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} \, dt

Gaussian Distribution:

f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Matrix Operations:

\mathbf{A} = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix}

Testing Different Notation Styles

Greek Letters and Symbols

Here are some commonly used mathematical symbols:

Greek letters: $\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \lambda, \mu, \pi, \rho, \sigma, \tau, \phi, \chi, \psi, \omega$
Special symbols: $\infty, \partial, \nabla, \sum, \prod, \int, \oint$
Relations: $\leq, \geq, \neq, \approx, \equiv, \propto$

Fractions and Roots

Inline fractions: $\frac{1}{2}$ , $\frac{x+1}{x-1}$ , $\sqrt{x}$ , $\sqrt[3]{8}$

Display fractions:

\frac{d}{dx}\left(\frac{x^2 + 1}{x^3 - 2x}\right) = \frac{(2x)(x^3 - 2x) - (x^2 + 1)(3x^2 - 2)}{(x^3 - 2x)^2}

Summations and Products

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

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

Conclusion

This MDX post demonstrates various LaTeX mathematical expressions, from simple inline equations to complex display formulas. The rendering should handle:

Basic algebraic expressions
Calculus notation
Linear algebra
Greek letters and special symbols
Fractions, roots, and exponents
Summations and products
Multi-line equations

If you can see all the mathematical expressions rendered correctly, then your MDX LaTeX setup is working perfectly!

Code Block Example

Instead of separate code blocks, let's use tabbed code blocks:

python

Highlighting code...

def hello_world():
  print("Hello, World!")
  return "Hello from Python!"

# Call the function
message = hello_world()
print(message)

You can also use the more flexible CodeTabs component:

python

Highlighting code...

def advanced_function(name, age=25):
  """
  An advanced function with default parameters
  """
  if age < 0:
      raise ValueError("Age cannot be negative")
  
  return f"Hello {name}, you are {age} years old!"

# Usage examples
print(advanced_function("Alice"))
print(advanced_function("Bob", 30))