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A Primer for Mathematics Competitions
Alexander Zawaira and Gavin Hitchcock
362 pages
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87 line illustrations
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234x156mm
978-0-19-953987-1
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Hardback
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30 October 2008
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- An interesting and illuminating guide to the subject
- A wealth of attractive, non-routine examples and problems, well-organised and graded, with fully worked solutions, illustrated by hundreds of diagrams.
- Development of theory is consistently motivated by carefully selected "appetiser problems".
- Can be used flexibly as a reference tool - finding problems to suit the topic, or topic to fit the problem.
The importance of mathematics competitions has been widely recognised 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 the final 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.Readership: Students and teachers in mathematics, Mathematical Olympiad competitors, and recreational mathematicians
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Alexander Zawaira, Senior Scientist, Kapa Biosystems, Cape Town, South Africa, and Gavin Hitchcock, University of Zimbabwe
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1: Geometry
2: Algebraic Inequalities and Induction
3: Diophantine Equations
4: Number Theory
5: Trigonometry
6: Sequences and Series
7: Binomial Theorem
8: Combinatorics
9: Miscellaneous Problems and Solutions
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The specification in this catalogue, including without limitation price, format, extent, number of illustrations, and month of publication, was as accurate as possible at the time the catalogue was compiled. Occasionally, due to the nature of some contractual restrictions, we are unable to ship a specific product to a particular territory. Jacket images are provisional and liable to change before publication.
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