Do you prefer Topology or Algebra?

[TLRDX91]

To all who have taken an introduction course to topology and abstract algebra, which did you prefer and why? Does the preference of one course over the other reflect a certain from of intuition that we rely on for reasoning or heuristics for problem solving?

For these classes, I used textbooks by Munkres and Gallian. Quite frankly, I found topology a lot more abstract and conceptually difficult but after a long while it started clicking and made sense after a few months of study. On the other hand, abstract algebra was a lot more straight forward from the get-go and the problem were fairly easy. Overall, the challenge of learning topology was what made it appealing to me but it's style of thinking is alien to me.

 

[micromass]

What about algebraic topology?? Does that classify as topology or algebra?

 

[jedishrfu]

I preferred Abstract Algebra it extended what I already learned in basic algebra and made it easier to do proofs.

Topology was so abstract, I got lost in the definitions and couldn't understand the practical nature of it. To be fair I was a physics major out of water taking topology because I thought it'd be cool to learn. I guess I thought I'd be learning something about rubbersheet topology.

One of my math profs encouraged me to take it, saying if you throw enough mud at the wall some of it will stick. He hoped I'd switch to math since in general most of my courses were math oriented. My topology class had mostly junior level math majors and I was very weak in proofs but I squeaked by. Later I took abstract algebra still weak in proofs but at least I could see some practicality to it.

In our college, Abstract Algebra was taught as a precursor to topology so that may be a clue as to how you should approach them. In my case, they let me in since I had several other higher level courses under my belt.