First post -- hi, board! I'd be hoping to go into academia in maths, but I'm slightly worried about something -- is it necessary to be precocious?; i.e. is it standard for entrants to university courses to already know some (significant?) part of the course they're about to take? I ask because I would, from the research and knowledge I do have, like to take the Pure Mathematics master's at Edinburgh but I'm concerned because whilst I am quite capable in maths, and have never had any problem with course contents at school at any level, am placed in a very good top set, love maths, etc., I haven't actually got a great deal of knowledge beyond what I've been taught. I've taught myself bits and pieces of formal set theory, some linear algebra (although fairly limited -- just the basics needed to construct some basic view/world/projection/transformation matrices for some 3D rendering) and some calculus (differentiation, integration -- I'm guessing probably equivalent to a Calc-I course in the States; Higher in Scotland/AS level in England/Wales). I compare this to my other strength, Computer Science, and realise that I know absolutely nothing in comparison (where I have studied significant parts of full under-grad courses and have a fairly decent knowledge of the formalisms and more abstract mathematics-based stuff involved) and wonder if I should be better than I am in maths. I can sort of reason and say probably not -- surely it can't be the case that only the very relatively few that are not only capable in maths, but have had the time to expend on vastly forwarding their knowledge can succeed in the field? Sorry -- this is a bit rambling. In short: how much general maths knowledge should I have as I start to head up the ladder? EDIT: Oh, stage -- I'm 15, going into fifth year at high school.