I am starting on math later than many of my peers and hence have little to no experience in competitive problem solving. Is this a disadvantage during the study of the more abstract mathematics that one encounters in college? Should I put emphasis on improving my problem solving skills along with my coursework?
To put things into better perspective, I am a physics undergraduate who will be moving to math for graduate study (a masters degree to be more specific).
Experience or skill in solving olympiad style problems is not necessarily related to ability to pursue mathematical research. For one, the timeframe is very different, and so are the types of problems and the tricks that olympiad takers are expected to know. However, problem solving skills are very useful to have in any type of research as problems will undoubtedly crop up.