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?
As Dave mentioned, what you want to do will be very challenging. One possibility would be to change to a different university that offers the math classes you mentioned. However, I will assume that switching schools is not an option for you. If you are very dedicated to this goal, here is one possible route.
- finish your current studies in CSE
- get a job in a town with a university that offers the math classes you desire
- start taking one class each semester as a non-degree student. I don't know about policies elsewhere, but many school in the United States have less strict admission requirements for non-degree students. Your goals for these classes should be two-fold. (1) Learn the material as well as you can. Your understanding of this material will be important for both getting into and succeeding in graduate school. (2) Impress your professors with both your ability and your desire. When you eventually apply to a masters program, you will ask some of these professors for letters of recommendation.
- apply to a masters program in mathematics. Ask for letters of recommendation from both your current professors in your CSE program and from those who know you from the math classes you take after you finish your BS.
- as you near the finish of your masters (where you have worked hard to prove yourself) apply to PhD programs
I know this is a long-term plan, but with hard work and dedication you could make it work. Here is another question Advice - MS in mathematics to increase competitiveness for PhD programs? that you may find to be helpful.