Dear all,

I am a graduate student in a Germany university. Today, I took my first ever oral exam on algebraic topology and I failed it. According to university policy, I have two re-takes. I have not decided yet, but I suppose the next one would be around same date next month.

I am in fact an aspiring combinatorialist and theoretical computer scientist, so I’m interested in extremal combinatorics, graph theory, and algorithms. I never felt clicked with topology — I took a general topology course as an undergraduate in an US university, at the end, I think my grade is B or something. (I’m feeling like Szemeredi in Moscow… though I’m no where near as good as he is.)

So my question is: How should I study so that I at least pass this course? With respects for topologists, when studying for the exams, I sometimes just find topology to be really boring and do not want to study... There is a note for this course. We covered topological spaces, basic category theory, fundamental groups and covering spaces, as well as basic abélien group theory.

Thank you for your time!