I am doing A levels and in my first year (equivalent to a junior in american system). I am very passionate about mathematics and physics but I get bored in my a level studies especially maths though I am a topper of my class. I therefore watch online university lectures like those of mit and other open courseware sites to quench my thirst of maths. My plan is to study mathematics at university and then research(I know how different maths is at university) So I want advice on how to study maths keeping in my mind my future goal. What are the high school maths topics that I should master and how do I do that? The normal school books are not interesting and are rather easy. What should I study? I am also participating in my country's national level math olympiad which leads to participation in the IMO. So should I work hard studying olympiad level maths like number theory and geometry? How much will it benefit me in mathematical career? I am finding combinatorics hard. I am more comfortable in algebra and geometry. Is that okay? How do I improve my understanding of combinatorics? I also have a copy of calculus by apostol and I like it a lot as I have some experience in proofs due to the olympiad. I have studied few topics and absolutely loved those. Should I continue to study it? Some people here suggest that it is better to approach calculus after one has mastery of algebra and other topics.