Orchid XP v8 wrote:
> I've spent a while looking at group theory. It's not "hard", it's just 
> that there are lots and lots of terms to learn, mostly with unintuitive 
> names, and the whole system of groups constructed from groups 
> constructed from groups gets confusing quite fast. Similarly, the stuff 
> with rings and fields and so forth isn't "hard", there's just lots of 
> stuff to remember...

Yeah, once you get used to it it's not to bad.  I think that proving 
things in it is a bit trickier though, as it seems to involve deep leaps 
of logical intuition more than other areas such as analysis.  It's sort 
of fun like that though, as you can actually do interesting math without 
having to acquire a ton of background knowledge.


>> Also forgot to mention that (if I recall correctly) ideas related to 
>> this play an important role in some of the operations in computer 
>> algebra systems.
> 
> Mathematica directly uses the commutivity and associativity of various 
> operators, not to mention distributivity. Indeed there are built-in 
> methods for telling Mathematica that your new function is associative 
> and/or commutative. (Distributive requires explicit transformation 
> rules...)


bases (a useful took for computer algebra systems), but indeed being 
careful about how you deal with the basic algebraic properties like 
commutativity and associativity is more fundamental to such programs.

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