Today was my first day in my algebra course, and it was pretty cool and unlike anything I’ve seen before! We didn’t get into much obviously but I had a few questions that I thought maybe would promote some discussion:
1.) we talked about isomorphisms and while I understand how to verify that some mapping indeed is isomorphic from, say, (Z,+) onto (Z,*), I was wondering what this means in terms of the properties or structure of the sets/binary operators? Is there an underlying reason we care whether an isomorphism exists/what the mapping is?
2.) What is the most fun topic/section you learned while in the course or what blew your mind the most. What can I look forward to?
3.) What was the hardest topic in your course and what made it so tricky?
Thanks you guys!