I'm currently learning abstract algebra in high school. The subject itself is extremely interesting because of its generality. I have found that it includes a lot of concepts that I have thought about before. For example, the whole concept of generalizing operations on sets and dealing with identity and inverse elements.
What I'm now wondering: Can you give any concrete examples on what abstract algebra can be used for? I'm talking about being more specific about which field it is used in. For example, I will be taking a lot of physics at university, what concrete examples am I likely to run into?
Best Answer
I know that field theory is part of coding theory and cryptography, which are responsible for technological security. Field theory is part of abstract algebra.