My code in some of my projects is ad-hoc due the time restraints of having homework and lectures, but I do not waste the opportunity to add a new concept I wanted to try in basic Python or C++/Rust. I will try better implementations for HPC when the time permits.

For example these 2024 repos of linear programming simply have Simplex methods, but not the more interesting interior-point methods:

• Simplex in Rust
• Simplex in Python
• Dual Simplex in Rust
• Big-M Simplex Method in Rust

These are simply because I was taking Operations Research and doing these calculations by hand and I wanted a way to check on my work. I have plans to refactor these into a single Rust library project with an idiomatic way to select the method to use, like traits. I was using a crate for arrays back then, I wonder if it's up to date today, if I should write my own matrix math library, or use a different crate.

Since I got an interest for optimization methods in general now, I might write a few more general convex programming methods, though I might be more inclined to use a different language.

In 2020 I wrote a Fortran program to numerically test some (proven) hypothesis of Hermite polynomials regarding the Hermite differential equation ($\ddot{x}(t) - 2\dot{x}(t) t + \lambda x(t) = 0$). I hadn't taken either mathematical or numerical analysis, so it was challenging to get what was asked of me done, but it got done. I even wrote some code in Python to get a few graphs of what was happening. Through the years the estimation aspect of mathematics has become one of my favorite topics, be it with noisy data or truncating a series to finite steps.

I like having the formal definitions burned into my mind, they give you a "target" to identify when a complex problem arises. If not for the theorems and applications, the language (and thus thinking) you get from it alone is worth it. For example I have these notes that are simply the basics of the respective theory:

• Linear Algebra Notes in Spanish.
• Introduction to Measure Theory Notes.

The advanced parts I'd be interesting in going through only as much as another topic also uses them, as they are not as ubiquitous as the basic theory. I might write such notes in the future.

My way of going through books nowadays is more "exploratory" than sitting strictly through the classical "definition-theorem-proof" loop. While I used to sit with a notebook to truly learn the language in the past. Nowadays I grab theoretical books on applications like optimization and skim to see the major concepts. Now I only sit with a notebook when the language is ubiquitous in current papers I'm more interested in getting a basic grasp.