Colin Burdine

Colin Burdine

A renegade computer scientist interested in quantum computing, machine learning, and mathematics.

Introduction Post

1 minute read

Published:

Welcome to my blog! Here I will do my best to give occasional expositions on topics that I find interesting, profound, or meaningful. I’m not sure what kind of trajectory this blog will take, but my goal is that these posts will each serve as self-contained tutorials that provide a deep-dive into a technical topic that I find to be either relevant to my area of research or interesting in its own right. In these posts, I will do my best to make the content accessible to readers with a technical background, while not providing redundant information that would otherwise be a Google search away.

I am not sure yet if I have the time (or self-discipline) to maintain a regular upload schedule. Ideally, I am aiming to upload at least one post per month. Below are some of the topics (in no particular order) that I am thinking of posting on in the coming months:

  • Undecidable Problems (Computer Science / Mathematics)
  • Kolmogorov Complexity (Computer Science / Mathematics)
  • Transfinite Induction (Mathematics)
  • An Introduction to Machine Learning (Computer Science / Statistics)
  • An Introduction to Quantum Computing (Physics / Statistics)
  • Some interesting results from Graph Theory (Mathematics)
  • Cryptocurrency and The Bitcoin Standard (Computer Science / Finance)
  • An Introduction to Group Theory and Symmetry (Mathematics / Physics)
  • … (and some other topics, provided that I make it this far)

As I upload and document more of my personal projects on this site, I may also write a few blog posts detailing my progress on those. I will do my best to keep things sorted under different tags to avoid this blog becoming a spaghettified repository of information.

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Intro to Quantum Mechanics (Part II)

18 minute read

Published:

This is Part II of my blog post series giving an introduction to the basic principles of quantum mechanics. In this post, we will cover the importance of linearity in quantum mechanics and develop some intuition regarding the relationship between linear operators (which act on functions) and matrices (which act on vectors).

Intro to Quantum Mechanics (Part I)

15 minute read

Published:

Depending on the degree of experience you have with physics, you may or may not have encountered a few concepts from quantum mechanics in your college physics or chemistry class. Often, the way that quantum mechanics is first introduced to students is through some of the key experiments in which we observe some aspect of so-called “quantum weirdness”. Somehow, when we take a peek at the world of very tiny things, we tend to observe phenomena that we would never expect to see on the scale at which we experience the everyday world. In this multiple-part blog post, I will give a survey of the basic principles of quantum mechanics and show how it has changed our perspective on the macroscopic world.

An Introduction to Undecidability (Part 2)

7 minute read

Published:

In this post, we will pick up from where we left off in Part 1. So far, we have introduced Turing Machines (TMs) and Universal Turing Machines (UTMs). Now let’s see how they help us in proving the undecidability of the domino problem we encountered earlier.