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Coordinate Geometry and Complex Numbers

Posted By: arundhati
Coordinate Geometry and Complex Numbers

P.S. MacIlwaine, Charles Plumpton, "Coordinate Geometry and Complex Numbers"
1984 | ISBN-10: 0333362535 | 88 pages | PDF | 8 MB

Preface
Advanced level mathematics syllabuses are once again undergoing changes in
content and approach following the revolution in the early 1960swhich led to
the unfortunate dichotomy between 'modem' and 'traditional' mathematics.
The current trend in syllabuses for Advanced level mathematics now being
developed and published by many GCE Boards is towards an integrated
approach, taking the best of the topics and approaches of modem and tradi-
tional mathematics, in an attempt to create a realistic examination target
through syllabuses which are maximal for examining and minimal for teaching.
In addition, resulting from a number of initiatives, core syllabuses are being
developed for Advanced level mathematics consisting of techniques of pure
mathematics as taught in schools and colleges at this level.
The concept of a core can be used in several ways, one of which is mentioned
above, namely the idea of a core syllabus to which options such as theoretical
mechanics, further pure mathematics and statistics can be added. The books
in this series are core books involving a different use of the core idea. They are
books on a range of topics, each of which is central to the study of Advanced
level mathematics, which together cover the main areas of any single-subject
mathematics syllabus at Advanced level.
Particularly at times when economic conditions make the problems of
acquiring comprehensive textbooks giving complete syllabus coverage acute,
schools and colleges and individual students can collect as many of the core
books as they need to supplement books they already have, so that the most
recent syllabuses of, for example, the London, Cambridge, AEB and 1MB GCE
Boards can be covered at minimum expense. Alternatively, of course, the whole
set of core books gives complete syllabus coverage of single-subject Advanced
levelmathematics syllabuses.
The aim of each book is to develop a major topic of the single-subject
syllabuses givingessential book work, worked examples and numerous exercises
arising from the authors' vast experience of examining at this level. Thus, as
well as using the core books in either of the above ways, they are ideal for
supplementing comprehensive textbooks by providing more examples and
exercises, so necessary for the preparation and revision for examinations.
In this book, we cover the requirements of the non-specialist mathematician
in coordinate geometry and complex algebra in accordance with the core
syllabus of pure mathematics now being included by GCE Examining Boards
at Advanced level and meeting the requirements of the polytechnics and
universities for entrants to degree courses in mathematics-related subjects.
In the use of coordinates, the importance of technique, that is the choice of a
suitable method to tackle a problem, has been stressed. The statement and
proof of standard properties of conics has been kept to a minimum, or covered
by worked examples. While inevitably lacking experience, the student should
try to acquire and appreciate good technique, so that more difficult problems
can be tackled confidently. Only the most elementary knowledge of coordinates
has been assumed, and important basic results are listed for easy reference.
In the section on complex algebra no previous knowledge is assumed; the
intention is to show the usefulness of complex numbers rather than give a
rigorous development of their properties from a set of axioms. On the other
hand, in accordance with modern attitudes, the underlying structure of the
complex field has been indicated so that the student can pursue this aspect
further if desired.
Plenty of examples are provided throughout the book , both as exercises and
as part of the text; the worked examples sometimes make comparisons between
good and bad methods.
P. S. W. MacIlwaine
C. Plumpton