First of all, a little background: I'm a computer engineering student, currently on my second year of study. I've always been fond of mathematics but my interest has grown a lot since last year, mainly because of my first formal take on it at my mathematical analysis class.
Since then, I've been considering switching to a math major but I still have my doubts. Anyway, I decided to start learning maths on my own as well. I've taken a mathematical analysis (proof oriented, single-variable calculus) course, a linear algebra course (once again, proof oriented) and I'm taking a multivariable calculus course right now. I'm working on my own on abstract algebra (using Herstein's Topics in Algebra) and introductory topology (just started with Topology Without Tears by Morris).
I may remark that studying with textbooks on my own is considerably harder than taking a course; I seem to be progressing really slowly with those (I try to do every exercise though), compared to my performance inside a course, where I normally don't have problems at all.
So basically, my question is a bit broad: What do you think I should focus on? I'm mostly interested in pure math, since I have a few applied math courses later on my major. Book recommendations and general advice are welcome as well.
PS: English isn't my first language and I realize the above is a bit rusty, feel free to edit it if you find errors.