Whenever you hear a seasoned mathematician talk about group theory or hear someone try to describe group theory they often start with it’s a study of symmetry. However, as most undergrads have seen, it feels more like the study of interactions and symmetry doesn’t come in till much later.
I am aware of Dihedral groups but Atleast until undergrad they do not seem to be pivotal to group theory, other things such as the behaviour of the binary functions and arising algebraic structures seem a much more real way to coin it.
Now, I understand binary functions and algebraic structures are not very accessible terms and it seems fair They’re not used in the explanation but my point they was to just elaborate on what else it is.
Do you think ‘Study of symmetry’ is an appropriate description for group theory or is there something out there that is just as accessible but maybe more representative?
Undergrad here, please be gentle 🙂 Cheers!
EDIT: My rant is just to explore how important the idea of symmetry is and if it alone could build up group theory or are there other elements that would be better but just as accessible conceptual building blocks