I am in my final year of high school, I am doing the highest level of maths available but I don't find it difficult at all, so I was wondering whether or not I should cover some university level mathematics before doing bachelor of science (Advanced) next year. For this BSc I am allowed to do two majors (1 major replaces electives) over 3 years, the available majors are physics, chemistry, maths, nanotech, medical science, computer science, biology erc... so I am thinking about doing physics and maths. The topics I will cover by the end of high school (October 2013) are curve sketching, complex numbers, polynomials, advanced calculus, mechanics, conics, series and induction, inequalities, circle geo, combinations and permutations, binomial theorem, probability, trig, parametric equations and more... so which topics should I study during the 2013 December holidays before uni starts? I am thinking differential equations because we don't study those in HS, what else? By the way the university website doesn't say what topics are covered in first semester for physics and maths so I have no idea what to study?