I couldn't think of a better forum to ask this question. I am a first year cs graduate student. I couldn't really pursue theoretical cs during my undergrad, but as part of our PhD qualifiers, i had to take computability and complexity theory, advanced algorithms, and i loved those courses. More than the computational aspects, i enjoyed the theoretical aspects and rigorous proofs. This kindled a lot of interest in me and I checked out Enderton's set theory, which i liked. Right now I am going through Spivak's Calculus in order to refresh my knowledge for a real analysis course next semester. Lately, i have been feeling that i would love learning and doing pure math more than applied CS. I know theoretical CS is an option, but i feel i would enjoy pure math more.
So my question is, whether introductory graduate level courses on algorithms and complexity theory involve enough rigor and abstract concepts (computability and complexity theory) that i am not underestimating pure math. I would really appreciate sincere inputs. I am thinking of taking standard analysis, algebra, topology sequence next year and find a professor to work with.