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I'm slowly beginning a student of certain higher mathematics.

I'm trying to see if I would prefer to study Group Theory or Abstract Algebra.

I know that Abstract Algebra seems to "come before" Group Theory, in the sence that one usually learns the terminology of GT through AA.

Am I correct in thinking that AA is essentially a broader version of GT, whereas GT seems to just focus on rings and fields?

I'm basically trying to learn one of the two that will best lead to lie algebra(s), and get a pure math balance to differential geometry that I'm trying to learn now.

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Normally a group theory course focuses on $groups$. Does yours really focus on rings and fields? –  Chris Eagle Jun 17 '13 at 9:50
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Abstract algebra is more general, group theory is a part of it. It deals mainly with groups (not rings and fields; but of course they are also used in group theory). –  Martin Brandenburg Jun 17 '13 at 9:50
    
Thanks, I think I'm much more interested in Abstract Algebra than Group Theory. –  mathacka Jun 17 '13 at 9:55
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@mathacka $GT \subset AA$, but $AA \not\subset GT$. Clear now? –  Bryan Urízar Jun 17 '13 at 10:03
    
@bryanurizar that makes perfect sense –  mathacka Jun 25 '13 at 17:55
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1 Answer

No-one can give you useful advice on what courses to take without knowing the actual content of those courses. Your best bet is to ask someone at your institution, who'll know best what's involved.

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