Further Mathematics offers additional challenges and opportunities for deeper study of this fascinating and universal subject. Pure mathematics and two areas of applied mathematics are studied to A-Level that will provide you with a very secure foundation for university level Mathematics, Science or Engineering. As for the Mathematics A-Level, the overarching themes of the course are mathematical argument, language and proof, mathematical problem-solving and mathematical modelling. You will study a range of core topics in pure mathematics, including proof, complex numbers, further algebra and functions, further calculus, further vectors, polar co-ordinates, hyperbolic functions, differential equations, trigonometry and co-ordinate geometry. You will also study two areas of applied mathematics: mechanics and discrete mathematics.