I am graduating from mathemetics bachelor program and I've been accepted for masters degree in mathematics. But I am not sure to pursue math, hence I am looking for other field I can do research. I am going to study potenial theory in the masters degree in math so I am good at analysis, particularly in measure theory. I also took some statistics courses, java and matlab. Moreover, I really like computers so I educated myself on some other stuff(I do some game modding and photoshop)Some friends of mine suggested machine learning but they are undergrad and they don't really know the subject well. So my question is what fields/areas of computer science I can work on for PhD and what should I learn.Or in this respect can I work on CS(Phd) as a math grad?(I've read the similar questions but they are only similar. So I appreciate any help.)Edit: In Math M.S program I only have one none-technical elective and I will get some undergrad CS lectures(additional). So, as @RB suggested, I am asking for the areas that require realtively less CS and more math. But note that I am willing to study/work hard.
Which areas of TCS are better for a math bachelor?
soft question;advice request;career
It had been argued that Theoretical Computer Science is a branch of mathematics, so it seems to me that any answer to this question would necessarily be primarily opinion-based. That said, in your place (and this is an uninformed opinion) I would steer clear of subfields in which a tremendous volume of technical work has been done, and in which coding plays a greater role. The barrier to entry in such subfields will be quite high for a math major. So for example, I would be cautious of anything related to computer vision and speech recognition. I would also be cautious of subfields in which the objective is perhaps a bit fuzzy, such as AI and machine learning. More controversially, I think that perhaps you should steer clear of quantum computation for this reason.Conversely, subfields in which the objective is well-defined and in which coding plays a lesser role have a lower entry barrier for a math major. For example, complexity theory, graph algorithms, information theory (perhaps especially for you!), concurrency, cryptography, and maybe even things like clustering and compressed sensing. 