Hello!!

This is a demo post to test out/showcase some features.

Read my entry about how this was made (coming soon…) to learn more about this blog.

Feature Overview

1. Markdown formatting

Files are render through Astro with a custom Base.

2. Code syntax highlighting

3. Latex-like math rendering with katex

4. Tag-based organization

see tags or click one of the tags on the top of this post.

Markdown features

Table of Contents

• Math Demo
  • Inline math equations
  • Another math demo
  • Block equations
• Markdown Table
• Code Demo
• Callout Demo
• Image Demo:

Table of Contents auto generated in obsidian.

Math Demo

Inline math equations

random integral, $\int_0^\infty e^{-x} dx = 1$

Another math demo

A sequence $x_{1}, x_{2}, x_{3}\dots$ of real numbers is cauchy if

$$\begin{align*} \forall \epsilon>0, \exists N \in \mathbb{N} : \forall n,m &\ge N \Rightarrow |x_{n} - x_{m}| < \epsilon \end{align*}$$

Block equations

$$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} dx$$

Markdown Table

with custom css

Table	Col 1	Col 2
Row 1	T11	T12
Row 2	T21	T22

Code Demo

Binary Search in C:

int first_true(int* arr, int n, int (*is_true)(int)){
	if(!n) return n;
	
	int lo=0, hi = n-1;
	while(lo<hi){
		int mid = lo + (hi-low)/2;
		
		if(is_true(arr[mid])){
			// go to left subarr
			// inclusive of mid
			// new subarr = [lo, mid]
			hi = mid;
		}
		else{
			// right subarr
			// skip mid
			// new subarr = (mid, hi]
			lo = mid+1;	
		}
	}
	// if lo==hi we have hit the candidate
	return is_true(arr[lo]) ? lo : n;
}

Callout Demo

Image Demo:

A screenshot of a lecture slide:

custom css for image captions

See more stuff…