I am an engineering student(EE) , and I am familiar with high school math as well as the applied mathematics(thats what typically taught in an engineering degree). I am curious how much mathematical knowledge do I need to to prove the solutions/ideas and its correctness. I am familiar with basic proving techniques like, direct proof through the logic, proof by induction, proof by contradiction. But I have only studied them for the class so I cant really say I am well versed with them and may get stuck while proving some good problems.

My aim is to reach to expert or candidate master level. So which type of mathematical concepts frequently occurs in the problems of these rating ranges, and what level of mathematical maturity and proofs do I need for them so that I can efficiently solve these problems to reach to my desired level.

Thanks.