Abstract Algebra (12): Algebra in the Wild — Cryptography, Coding Theory, and Beyond

Thu, 23 Sep 2021 09:00:00 +0000

For eleven articles, we have built algebra from the ground up: groups, rings, fields, Galois theory, modules, representations, categories. At times, the material may have felt like pure abstraction — beautiful, perhaps, but detached from the “real world.” This final article corrects that impression. The structures we have studied are not just mathematically elegant; they are the backbone of technologies and theories that shape modern life. By the end of this article, the question “is abstract algebra useful?” should feel about as well-posed as “is calculus useful?” — the answer is so overwhelmingly yes that the question itself sounds quaint.

Cryptography on Chen Kai Blog

Abstract Algebra (12): Algebra in the Wild — Cryptography, Coding Theory, and Beyond