Initial Blog Post

This is my first blog post. I’m excited to start sharing my thoughts and experiences here. Stay tuned for more content!

Let’s try some math here using Latex:

Block equation: \(E = mc^2\)

Inline equation: The famous equation $E = mc^2$ revolutionized physics.

More complex examples:

Matrix equation: \(\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax + by \\ cx + dy \end{pmatrix}\)

Calligraphic fonts with \mathcal{}: \(\mathcal{L} = \frac{1}{2}m\dot{x}^2 - V(x)\)

Blackboard bold fonts with \mathbb{}: \(\mathbb{R}, \mathbb{C}, \mathbb{Z}, \mathbb{N}, \mathbb{Q}\)

Combined usage: \(\mathcal{H}: L^2(\mathbb{R}) \to L^2(\mathbb{R})\)

Cross-referencing Examples

Consider the famous equation in Equation (1): \(E = mc^2 \tag{1}\)

We can refer back to Equation (1) later in the text.

For numbered equations, you can also use: \(\begin{equation} F = ma \label{eq:newton} \end{equation}\)

And reference it as Newton’s second law (Equation 2).

Using Markdown anchors

You can create anchors and link to them:

Theorem 1: The fundamental theorem of calculus states…

Later, you can reference Theorem 1.

Code Examples

Here’s a Python code block demonstrating syntax highlighting:

import numpy as np
import matplotlib.pyplot as plt

def fibonacci(n):
    """Generate Fibonacci sequence up to n terms."""
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    
    fib_sequence = [0, 1]
    for i in range(2, n):
        fib_sequence.append(fib_sequence[i-1] + fib_sequence[i-2])
    
    return fib_sequence

# Generate and plot Fibonacci sequence
n_terms = 15
fib_nums = fibonacci(n_terms)

plt.figure(figsize=(10, 6))
plt.plot(range(len(fib_nums)), fib_nums, 'bo-', linewidth=2, markersize=6)
plt.title('Fibonacci Sequence')
plt.xlabel('Term Index')
plt.ylabel('Fibonacci Number')
plt.grid(True, alpha=0.3)
plt.show()

print(f"First {n_terms} Fibonacci numbers: {fib_nums}")

Image Examples

Local image (stored in assets/images/):

External image:

Local image with caption:

"Your LLM agent is dividing a by b" by Andrej Karpathy.