Applications of abstract algebra? 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?
 A: 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.
A: Charles C Pinter's Abstract Algebra book gives numerous different examples of real-world applications of abstract algebra. The examples are mostly real world applications:


*

*coding theory 

*crystallographic structures

*games
etc

A: I've given two talks (which can be found here) in reference to applications of group theory. 
https://faraadarmwoodblog.files.wordpress.com/2014/11/symmetry-groups-talk-21.pdf
https://faraadarmwoodblog.files.wordpress.com/2014/11/gttalk.pdf
A great source is this text: http://abstract.ups.edu/download/aata-20130816.pdf
A: On a historical note, the interactions of a certain family of sub-atomic particles was found to be describable by all but 1 of the members of a finite group named the Eight-Fold Way. This suggested there should be another particle corresponding to the missing group member. It  was sought for,and found, and its properties did match  the group-structure model.
