I am a Bangladeshi student studying CSE in the best university of my country. At the beginning of my second year in my university, an interest towards pure math grew in my mind. But my university does not offer courses in Abstract algebra, Real Analysis, Topology, Complex Analysis, Algebraic geometry, etc. I have seen this related post, but the advice there doesn't help me because there is no computer scientist in my university whose research interests lie between CS and Pure Math.
I met a few of my professors to discuss about my situation. Some of them asked me to study math by myself and also to try to study a paper by mathematicians under whom I want to work, then to write a paper which demonstrates I understand all (at least most of) the things written in the paper, and later send it to them asking if they are interested in taking me as student. They also asked me to get prepared for Math GRE. But is it possible to switch to pure math if I do so? If not, how I can go to a pure math grad school?