I am deeply sorry if this thread or discussion topic does not belong to this forum, but I have no idea on where to post this issue of mine.
Essentially I have finished a Calculus 1 course, but kind of more "advanced", as we viewed single variable differential calculus, differential equations (from variables separable to first order linear), elementary vector calculus and multivariable differential calculus (partial derivatives, implicit differentiation and optimization). However, now that university is over for the winter break, I was planning on doing some independent study as I completely adore math (I am planning to major in math).
The question is: what should I study over the break? The topics that we are going to cover in our Calculus 2 course are integration (applications and all the like, such as arc length, curvature and solids of revolution), series and sequences (up to power series) and multiple integration. I have basic experience with integration (if finding basic antiderivatives, and substitution rules counts as experience). I am really interested in the course material and i would like to make some use of my free time to make things smoother next term (and have some fun in the process). I was thinking of studying abstract algebra (I have already covered linear algebra, even though I had bad professors) or real analysis, but I have realized that I need to grasp the material in Calculus 2 to pursue something more complicated.
Thank you very much for your insight, and once again, I am very sorry if this topic does not belong to this discussion forum.