Stephen Siklos

This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. Warwick University also uses them, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term, Examination Paper.

The questions analyzed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, the A-level core (i.e., C1 to C4) with a few additions. A comment and a full solution follow each question. The comments direct the reader’s attention to key points and put the question in its true mathematical context.

The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must-read for any student wishing to apply to scientific subjects at the university level and for anybody interested in advanced mathematics.