Hi there, I'm currently finishing my A-Level exams (UK system) and provided I achieve my offer will be going to university in autumn to studying single honours mathematics (4 Yr MMath/Msci). I'm going to have a 3 month gap between my last exam and starting university, so I obviously want to make good use of my time. While I obviously want to enjoy myself a little and I have to work to earn more money I'd like to keep learning throughout the summer. By mathematics background is that of two A-Levels in maths. I've studied up to things such as: De Moivres theorem, maclaurin and taylor series, vectors(mostly just the equations of planes/lines), proof by induction, differentiation and integration of inverse trig/hyperbolic functions and reduction formulae etc. [I can easily provide a link to the syllabus i've been following if that is necessary] Basically my question is: What should I try to learn in the time that I have? Obviously my background is mostly manipulative mathematics (or so I hear) so would it be best to try to learn some analysis or should I try to extend my calculus knowledge to partial differentiation etc.? Thanks for any advice.