I am trying to teach myself set theory, number theory and logic before I engage in mathematics. I have been able to get through Calculus but I think that it was just by repeating different types of problems (i.e., memorization). I really want to understand the mathematics in a pure format as I think the applied format will come from that easier. I am not interested in being a mathematician but will need a lot of math in what I will be studying and thought it would be good to have a solid foundation in mathematics. Would these subjects be a good place to start before trying geometry/precalculus and the rest of the traditional mathematics sequence?
I am hoping the logic based approach will help me be more creative when I actually have to conduct some type of research that requires a great level of innovativeness.