Ask HN: Which areas of math are practical to programming/algorithms and why?

Discrete math first comes to mind first: lists, trees, graphs, etc. Used in basic algorithms 101, but you need some more serious probability theory for probabilistic algorithms.

Linear algebra is useful for computer graphics, but also for general "system thinking" concepts like inputs spaces, output spaces, transformations, and properties of transformations.

Basic differential calculus, meeeh, but multivariable calculus—specifically optimization—is really important in many programming contexts (e.g. machine learning).

Of course, the most important and most basic of all is the notion of a function f(x), its definition, inputs, outputs, properties, etc.

Matrix multiplication is a must-have for any graphics programming and knowledge of them is very useful for learning neural networks.

And on the more esoteric side of things, in Quantum Computing every logic gate is actually a Matrix Multiplication

Lots of areas are important. Every job I have worked has had a specific math specializations that were important. Reed-Solomon codes are used in storage and communication systems. They make use of abstract algebra (finite/Galois fields). Linear systems theory is essential for signal processing and control systems. Quaternions are important in aerospace and graphics.

I've been recently trying to make my way though Elements of Programming (https://www.amazon.com/Elements-Programming-Alexander-Stepan...) by Alexander Stepanov and Paul McJones and it makes me say abstract algebra. It's the first and only rigorous foundation of software engineering that I've seen. It basically maps abstract algebra to this somewhat simple subset of C++, introduces new algebraic objects (such as memory) and then shows this really nice correspondence between the the C++-- and the abstract algebra.

If you are not familiar with the author, Alexander Stepanov is the guy who basically figured out generic programming, was instrumental in the design of C++ templates and the C++ STL. C++ gets a lot of flak but templates are very powerful (if you disregard the complexity). I think that they are actually one of the main reasons why C++ is still relevant. Also I'm starting to think that generic programming might actually be the most powerful paradigm out there (this is just a hunch). This book doesn't take the middle road, only the low level (C++) and extreme high level (abstract algebra) and totally cuts out the middle part (aka boiler plate).

Funnily enough, this C++-like language actually translates very nicely to the modern C++ successors like Swift and Rust (or it seems, I'm in the progress of exploring this).

Has anyone here tried to explore the contents of this book in either Swift or Rust?

But remember that this is not an easy book, I've met very smart people who told me they read only a part of this and are still wrapping their heads around that.