Applications of abstract algebra?

Question

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?

Asking questions is good, but not as good as seeking answers yourself. There are dozens of textbooks, free or not free, and numerous posts that already answer this question. You really ought to seek them first. — rschwieb, Mar 22 '16 at 03:21
Will you be studying quantum mechanics? This post from physics stack exchange may be helpful: http://physics.stackexchange.com/questions/39165/linear-algebra-for-quantum-physics — , Mar 22 '16 at 03:22

score 2 · Answer 1 · answered Mar 22 '16 at 03:08

2

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

answered Mar 22 '16 at 03:08

ngundotra

21

Ellya · Answer 2 · 2016-02-29T14:37:06.130

2

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.

edited Feb 29 '16 at 14:37

answered Apr 03 '14 at 12:36

Ellya

11,783

score 1 · Answer 3 · answered Mar 22 '16 at 11:53

1

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.

answered Mar 22 '16 at 11:53

DanielWainfleet