I have personally used the previous editions of this book over many years and

with pupils of a broad range of ability. I have always admired it for its common

sense approach to the subject, for the large number and great variety of its

examples and for the scope and grading of its exercises. In recent years, however,

it has become increasingly clear that drastic revision was needed to take account

of the many changes which have appeared in A-level syllabuses since the book

was first written. At the time of writing the common core syllabus is about to

appear at A-level and this new edition, and its companion volume, have been

prepared with this in mind.

Although many of the new chapters are concerned with so-called modern

topics, I make no apology for retaining the traditional style of the earlier

editions. Indeed, I hope that readers will feel that the book conforms to the spirit

of paragraph 582 of the Cockcroft Report, which says

Syllabus changes during the last ten years have lessened the dif-

ferences between the content of modern and traditional syllabuses

and many feel it is no longer appropriate to distinguish between them

We support the view that the distinction should no longer be

maintained.

This new edition of Pure Mathematics, Books 1 and 2, contains all the topics

which are in the common core syllabus and the symbols used throughout are

those adopted by the Examining Boards. The pure mathematics content of most

single subject syllabuses is included and, while it cannot be guaranteed that all

double subject syllabuses are covered, the books will provide a sound course of

study for most of them. These books are also suitable for the pure mathematics

content of most AS level syllabuses.

The book has not been designed to be read straight through chapter by

chapter in numerical order, and most readers will probably prefer to develop

several branches simultaneously. Indeed, later sections of some chapters are

better delayed for a second reading; where a natural break occurs this has been

indicated in the text. New chapters and material have been incorporated

without unduly disturbing the overall contents of previous editions, and, to

make it easier to locate a particular topic, an index has now been provided.

Another new f~ature of this edition is an appendix on Algebra revision which