Groups are pretty awesome. Understanding group actions in particular, which amomg other things is how those guys calculated how many different states a Rubik's cube can be in, knitted things together and was my "grow up" moment in abstract algebra class.
They're also damn hard to explain! You know one when you see one, but it takes a lot of practice with different concrete examples before what they're really about begins to shine through for most of us.
For any undergrads who are tempted to skip AA and go right to category theory - don't do it, at least take the group theory course. It's a great intermediate intuition pump that makes the initial juggling you have to do with the basics of categories feel much easier.
They're also damn hard to explain! You know one when you see one, but it takes a lot of practice with different concrete examples before what they're really about begins to shine through for most of us.
For any undergrads who are tempted to skip AA and go right to category theory - don't do it, at least take the group theory course. It's a great intermediate intuition pump that makes the initial juggling you have to do with the basics of categories feel much easier.