Towards Higher Mathematics: A Companion

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

Introduction; 1. Complex numbers; 2. Induction; 3. Vectors and matrices; 4. More on matrices; 5. Techniques of integration; 6. Differential equations; 7. Hints to selected exercises; Bibliography; Index.

Richard Earl is currently Director of Undergraduate Studies in the Mathematical Institute, University of Oxford, and a Tutor in Mathematics at Worcester College. From 2003–13, he was Admissions Coordinator and Schools Liaison Officer in the department and has over a decade's experience setting the MAT (Oxford's Mathematics Admissions Test). He has won several teaching awards within the University for his teaching and lecturing. This book grew out of a residential week he ran for several years in Oxford for new students who had not had the chance to study Further Mathematics at A-Level.