The aim of 16-19 Mathematics has been to produce a course which, while challenging, is accessible and enjoyable to all students. The course develops ability and confidence in mathematics and its applications, together with an appreciation of how mathematical ideas help in the understanding of the world and society in which we live. This unit develops: * an intuitive, informal idea of isomorphism; * an appreciation of the importance of symbolism and notation in mathematics; * an appreciation of abstract algebra as a unifying thread linking many branches of mathematics; * an awareness of the advantages of studying generalities in abstract mathematics; * an awareness of the importance and central role of proof in mathematics; * familiarity with some of the great unsolved problems of mathematics.