I'd recommend Linear Algebra before taking Abstract Algebra. What is Intermediate Analysis at your uni? Topology is good to take early - any time after Calc III, I'd say.
So I'm currently enrolled in Calc III and a sort of intro to abstract math class, but I'm trying to make up my mind on classes for next semester. Linear Algebra and Probability Theory are on the schedule now, but I have options (I think) for the others as well. I'd prefer not picking up two as I have other requirements to take care of, and the first two certainly open doors for more classes.
any ideas?
Intermediate Analysis is described as dealing with sequences, series, metric spaces, continuity and differentiation. The assigned book is Walter Rudin's book which I've leafed through a little. It does have a pre-req of linear, but they seem lenient about pre-reqs becoming co-reqs if you are comfortable taking them at the same time. actually all of the courses have a pre-req of linear.
I would go ahead and treat Linear, then, as a full pre-requisite for Intermediate Analysis. Rudin will make more sense, I think, if you've had linear algebra. You also want to make sure that you've had some sort of proofs course (could be your linear algebra course, depending on how it's taught) to get ready for Rudin.
That sounds like the sort of thing you should have under your belt. If you've had Calc III, your proofs course, and Linear, then I'd say you're ready for Rudin. Have fun!
I'd recommend reading this review of Rudin's book on Amazon. Rudin has some issues, but I would recommend this guy's learning style for learning Rudin. The review in question is the one entitled "Book should be called 'Tada! You're a mathematican!' ", by Bolzano Bourbaki.