# Hello there!

I am Hai, also known as `hozy`

. You can also look
at my resumé.

I am currently a Computer Science student at the City University of Hong Kong. In the past, I have had some—albeit not in-depth—experience developing websites and cross-platform mobile applications. Right now, I am exploring C# and .NET, as well as learning Rust and Julia.

Even though my major is Computer Science, I like to learn about mathematics and physics as well, striving to self-study whenever possible. In particular, I am keenly interested in the intersection between mathematics and theoretical computer science, i.e., topics such as formal language and automata theory, computability and complexity theory, formal verification, and symbolic computation. I like to learn from textbooks and other text-based media.

This website contains a miscellany of things that I have learnt or encountered. I hope you will find something interesting here.

## Recent Posts

- A Measure Theory Surprise
The class of Borel sets in the Euclidean space is not closed under linear transformation.

- The spectral theorem and the singular value decomposition
Turning a matrix into a diagonal matrix simplifies many problems and thus is of particular interest. We take a look at the spectral theorem, which captures the diagonalizability of self-adjoint operators, and the singular value decomposition, which generalizes it to non-square matrices.

- Deriving Dynkin’s theorem from the monotone class theorem
Dynkin’s theorem is an extensively applicable result in measure theory. Here, we prove the theorem in a more roundabout way, using the monotone class theorem.