Do you recommend I take a course in Abstract Algebra before or after a course in Linear Algebra? I have never taken any abstract mathematics courses before. So this would be my first one.
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1It really depends on the material they each cover, together with your background and aptitudes. – May 09 '14 at 00:19
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I'd suggest you to take a course in number theory or discrete mathematics first. Your number theoretic knowledge will come to your help a lot in abstract algebra, but that's only my opinion. – math.n00b May 09 '14 at 00:23
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The point of abstract algebra is to recognise when two apparently different situations are "essentially the same". To understand the abstractions it is very helpful to be familiar with a good number of the examples which prompt the abstraction - that is, the examples which we are going to say are all "somehow the same".
IMO there are two areas which are relatively easy to understand and which lead smoothly into abstract algebra. One is linear algebra (leading into vector spaces) and the other is number theory (leading into groups and integral domains, and later into rings and fields). So I think you will find it advantageous to study both of these topics before beginning on abstract algebra (or perhaps concurrently with abstract algebra).
For a bit of amplification of this in the vector space scenario you might like to read my answer to this question.
