Moonracer

Sorry for the late reply. Midterm week was pretty hellish. I'm not sure what areas to research yet. I like anything visual, like geometry. i thought about topology, but have heard the concepts are very challenging to grasp. I also really enjoyed a discrete math course that I took last semester, so possibly number theory, combinatorics, or probability. As far as coursework I have only had a couple of semesters of calculus and a graduate course in discrete math. I'm guessing that I would still need to take multivariable calculus, linear algebra, and maybe differential equations (not to mention the GRE subject test) before applying to PhD programs.

I'm currently a MS computer science degree student at a top 20 school. I'd like to switch to a PhD in pure math. I know that research matters the most at top-ranked math depts. My question is that is research in machine learning or artificial intelligence acceptable or do you need to show research in a pure math subject? Would computer science math (combinatorics, number theory, etc.) be acceptable?

I got into a top 20 MSCS with worse qualifications than you. Was an average college student with 3.0 gpa and an anthropology major no less. Fell into web development from the HTML and CSS picked up in college. Worked as a web developer for 10 years then decided to apply to grad school. I took 4 comp sci courses covering basics. Also took calc, discrete math and probability. Did well in all. Good references from profs and my boss. GRE Q: 160, V:167. Treated the MSCS application like I was applying for PhD. Talked about those researchers whose work was most interesting to me. Convey your passion for comp sci in your SoP. Let the committee see exactly what excites you about it. But try to make sure the researchers you have selected are interested in the same things too! There are fine variations even in a specific field. The more perfectly your interests align with a researcher's the better. Make it up and be very specific if you have to, you can always switch topics after you get in.

Cinoadam, I was in the same situation as you, but I managed to get accepted to a top 20 MSCS program. I got in using this method: 1. Took 4 computer science courses covering the basics at a good top 50 school. 2. Took a discrete math / probability class. I had 2 semesters of calculus already. 3. Got a decent GRE quant score. 4. Got strong letters from professors and my boss. 5. Looked at the strengths of the department, found a couple of researchers in AI who I especially admired, read and discussed several of their published papers (why they were interesting, etc). Then talked about what I specifically wanted to get out of the program--work as a robotics software engineer and develop a robotic prototype to assist scuba divers. I treated the application like it was for a PhD program even though I was under-qualified. I talked about what I wanted to study and why (robotics because it's amazing). My grades in the comp sci and math classes were all A's or B+. My references talked about my potential to do research and I hinted at it too in the SoP. Basically, schools want intellectual titans. If you come off sounding like you want to and can do cutting-edge research with faculty there, they are more likely to take you over someone who treats the MSCS as a terminal professional degree.