Questions about abstract algebra

Hey everyone!

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!

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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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