A couple of months ago I asked a professor by e-mail to mentor me on topology during the summer. He advised me to study general topology (Hausdorff spaces, connectedness, compactness) and algebraic topology (from Hatcher) before we meet, as time permits.
Yesterday I finished chapter 2 of Munkres (I am planning to study up to chapter 3) but I have no knowledge of abstract and linear algebra. I took analysis and set theory, this is my background.
I consider myself as a beginner (if you look at my questions:-)). Although I study up to 5 hours a day, I feel I don't accomplish much. Also, I am particularly bad at finding counterexamples (perhaps because I have not taken calculus).
Coming back to my question, how much algebra do I need to cover to understand Hatcher? I have about 1 month to cover? Would you recommend some books/notes? How can I develop my skills at finding counterexamples?