The importance of mathematics competitions has been widely
recognized for three reasons: they help to develop imaginative
capacity and thinking skills whose value far transcends
mathematics; they constitute the most effective way of discovering
and nurturing mathematical talent; and they provide a means to
combat the prevalent false image of mathematics held by high school
students, as either a fearsomely difficult or a dull and uncreative
subject. This book provides a comprehensive training resource for
competitions from local and provincial to national Olympiad level,
containing hundreds of diagrams, and graced by many light-hearted
cartoons. It features a large collection of what mathematicians
call "beautiful" problems - non-routine, provocative, fascinating,
and challenging problems, often with elegant solutions. It features
careful, systematic exposition of a selection of the most important
topics encountered in mathematics competitions, assuming little
prior knowledge. Geometry, trigonometry, mathematical induction,
inequalities, Diophantine equations, number theory, sequences and
series, the binomial theorem, and combinatorics - are all developed
in a gentle but lively manner, liberally illustrated with examples,
and consistently motivated by attractive "appetiser" problems,
whose solution appears after the relevant theory has been
expounded.
Each chapter is presented as a "toolchest" of instruments designed
for cracking the problems collected at the end of the chapter.
Other topics, such as algebra, co-ordinate geometry, functional
equations and probability, are introduced and elucidated in the
posing and solving of the large collection of miscellaneous
problems in thefinal toolchest.
An unusual feature of this book is the attention paid throughout
to the history of mathematics - the origins of the ideas, the
terminology and some of the problems, and the celebration of
mathematics as a multicultural, cooperative human
achievement.
As a bonus the aspiring "mathlete" may encounter, in the most
enjoyable way possible, many of the topics that form the core of
the standard school curriculum.
General
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