Tab Article

The needs of those taking Pure Mathematics at Advanced Level in the recently introduced General Certificates of Education have set the standard for this book. The contents should also prove suitable for candidates preparing themselves for the Intermediate Examination of London University, the Qualifying Examination for the Mechanical Science Tripos at the University of Cambridge and for several of the examinations set by the Civil Service Commission.
The starting point is the Ordinary Level for the General Certificates and I have included in a single volume the appropriate parts of Algebra, Trigonometry, Calculus and Geometry. With so wide a field of study, the order in which the subjects appear is not necessarily the order in which they should be read. I believe that an early start should be made with the Calculus and the chapters on this subject may well be studied concurrently with those on Algebra and Trigonometry. I have included a large number of worked examples and graded the exercises in a way which will, I hope, make the book equally suitable for class or private study.
In preparing this book, I have made great use of the reports of the Teaching Committees of the Mathematical Association. In particular, I have found their recent reports on the Teaching of Trigonometry and Calculus Quite invaluable and I wish to acknowledge my debt to them. Only very occasionally have I differed from their recommendations and here, of course, I bear full responsibility.
Among nearly 1600 examples and exercises, I .have included a large number taken from recent papers set by the various examining bodies. My thanks are due to the Senate of the University of London, the Oxford and Cambridge Schools Examination Board, the Joint Matricu- lation Board of the Universities of Manchester, Liverpool, Leeds, Sheffield and Birmingham and the Syndics of the Cambridge University Press for permission to use their Questions. My thanks are also due to many friends and colleagues who read the manuscript and offered constructive criticism. I am particularly grateful to Dr. E. T. Davies, Professor of Mathematics, University of Southampton, Dr. D. R. Dickinson, Senior Mathematics Master, Bristol Grammar School, Mr. F. L. Heywood, Senior Mathematics Master, Manchester Grammar School and Mr. H. K. Prout, Head of the Department of Mathematics, Royal Naval College, Dartmouth, all of whom made most useful suggestions when the book was in its first draft.