Siklos S. Advanced Problems in Mathematics: Preparing for University

Cambridge: Open Book Publishers, 2015. - 188 p.This book has two aims:
The general aim is to help bridge the gap between school and university mathematics.
The more specific aim is to help you to prepare for STEP or other examinations required for University entrance in mathematics.
It used to be said that mathematics and cricket were not spectator sports; and this is still true of mathematics. To progress as a mathematician, you have to strengthen your mathematical muscles. It is not enough just to read books or attend lectures. You have to work on problems yourself. The problems are all based on STEP questions. I chose the questions either because they are ‘nice’ — in the sense that you should get a lot of pleasure from tackling them. STEP (Sixth Term Examination Paper) is an examination used by Cambridge University as part of its procedure for admitting students to study mathematics. STEP is used for conditional offers not just by Cambridge, but (at the time of writing) also by Warwick University for almost all of its Mathematics offers, and to a lesser extent by some other English universities. Many other university mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.