Learn You Galois Fields for Great Good (00)

Summary

Learn you Galois Fields for Great Good (00) Navigation | first | next Introduction This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science. This is a project I've been excited about for many years now, but have been too busy to dedicate the adequate effort to meet my perfectionism standards (yay perfectionism!). Backstory Many moons back I was self-learning Galois Fields for some erasure coding theory applications. I was quite disappointed with the lack of accessible resources for computer scientists. Many resources assumed either: Its beyond your skill level so let's oversimplify ("it's hard, don't worry about it"), or You had prior Pure Math studies in Abstract Algebra ("it's easy, just use jargon jargon jargon") Unfortunately, Abstract Algebra is not standard subject matter in most computer science curriculums. Often computer science mathematics start and end with Discrete Math. If you're lucky, maybe you've also been exposed to Linear Algebra. So, ultimately, I ended up self-learning Abstract Algebra from a pure math textbook. But for the great majority of computer scientists, there has to be a better way. This series intends to fill this gap. This is the gentle step-by-step approach with applications implemented with actual code. It's the intro I wanted when I was starting out. What is this subject? Abstract algebra is a beautiful subject. It's the idea that the numbers you're familiar with don't matter. The numbers are just arbitrary labels. What matters is the relationships they have with other numbers when you add or multiply them. If the numbers don't matter, then we can swap those labels for different labels and all the normal math rules will still work. For example, we could create an algebra that allows us to add or multiply colors: And this is what makes the subject abstract and confusing. How can you just say that numbers don't m...