A Primer for Mathematics Competitions (Oxford Mathematics) 1st Edition by Alex Zawaira (PDF)

Description

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 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.

User’s Reviews

Editorial Reviews: About the Author Alexander Zawaira was born in Zimbabwe in 1978. He studied Mathematics and Biochemistry at the University of Zimbabwe where Dr Gavin Hitchcock was one of his teachers. He won a Beit Trust Scholarship to study at Oxford University (England) where he obtained a PhD in Structural Biology. His research interests focus on bridging the gap between bioinformatics and “wet-lab” biochemistry by deriving and experimentally investigating hypotheses from bioinformatics analyses. He is also interested in the general application of mathematics in biology.Gavin Hitchcock was born in Zimbabwe in 1946. He won scholarships to study mathematics at the Universities of Oxford and Keele, where he took his PhD with a thesis in general topology. He is Senior Lecturer in the Department of Mathematics, University of Zimbabwe, and his research interests are in topology and the history of mathematics. He is internationally known for his writings concerned with the communication of mathematical ideas and their history through theatre and dialogue. He spearheads the mathematical talent search and mathematical Olympiad training programmes in Zimbabwe, and is editor of Zimaths Magazine. He mounts workshops in Zimbabwe and neighbouring countries for teachers, for learners, and for parents, on such topics as “touching and seeing mathematics”, “using the history of mathematics to enliven teaching”, and “creative problem solving”. He also conducts seminars on creative problem solving for workers and for management in commerce and industry.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐First I must make it abundantly clear that this book is not meant for preparation for competitions such as the IMO and Putnam. For those there is Arthur Engel and many Oympiad Compendiums. This book’s function is to take a average top-of-the-class math student and to expose him/her to Olympiad mathematics. All the classic topics are covered: geometry, inequalities, diophantine equations, trigonometry, binomial theorem, sequences and series – and lastly number theory. Each topic is introduced very simply and succintly. The topic grows in complexity, to a level that is well beyond that expected of High School mathematics.This book is not at all a heuristic guide to problem solving, or mathematics. It clearly states a great deal of useful mathematical techniques that are not common (Congruence notation, the more obscure Geometry theorems Cevas etc) and many others. Then it shows you where the techniques can and should be applied, and often will give invaluable tips on topic-specific steps. This is perfect for potential math olympians who have through more challenging school-curriculum problems developed their problem-solving ability and incorporated many heuristic principles already. It must be made clear that the topics introduced are not substantial enough for the IMO and most national competitions, no Vectors and no real topic on functional equations or any functions whatsoever. However, it will definitely take your normal mathematical knowledge and broaden it a thousand-fold. Buy this book if you want to enter the highly complicated field of math olympics. That more than often is just too inaccessible to potential mathematicians because of the vast differece between what they are accustomed to and the difficulty of questions. If you are already competing on a National Level, then I would discourage you buying this book – simply because chances are that you will know everything already and that therefore the problems too will seem too simplistic. There is a delibrate focus on the notion of proof (especially focused in the geometry section), helping students understand the notion behind it – and also exposing them to the idea that is woefully neglected in current school systems.I must mention that the book also includes a very substantial section on Combinatorics. This section of Math Olympiads; I would put on par with number theory as being equally alien to many math students. Therefore this section will be invaluable for nearly all mathematics students. There are many theorems and formulas that are logicly developed from highly simplistic models.This book is a triumph, finnaly an introduction that is accessible to those who are not yet well versed in the oftentimes bizarre procedures expected in Mathematical Olympiads.

⭐Beautiful book. Wonderfully pedagogic and broad. There’s a lot of value in this for anyone wanting to know some real math., not just as competitors. I have a PhD in physics, which commonly has some high level math talent. And I learned some new things just in the first few pages.

⭐There are 3 levels of Math:1) 1 technique for 1 type of problems: Math Olympiad problems2) 1 technique for 1 family of problems: Algorithmic-type of problems, (eg. Ancient Chinese ‘Nine Chapters of Arithmetics), which could be programmed and solved by computer (e.g. Mechanical Proof of Geometry by Prof Wu WenJun, China)3) No fixed technique for all kind of problems: New Math where the problems could be cross-boundary among 4,000+ (?)of math sub-fields. e.g. Fermat Last Theorem used all the Number Theories and the obscure Elliptic Function, which escaped the imagination of the past great mathematicians (eg. Gauss, Euler, etc) in the past 380 years, until Andrew Wiles adopted it in 1994.This Primer book is for the first level. Written by a former IMO Medallist, it covers 8 chapters each with one set of toolchest for 1 type of competition math problems e.g. Inequality, Binomial, Geometry, Combinatorics, etc.The authors also link the text to the Cambridge GCE O and A level, which will enrich high school student’s Math knowledge thru these competition math problems.I recommend this book to those who have keen interest in Math, aspire to participate in Math competitions, but need a less intimidating primer to get into the doorstep of IMO.

⭐This is an outstanding book. The alternative (mainly UKMT) books will have you believe that answers (to BMO questions) can be extracted from nowhere by clever manipulation of elementary maths. Pleasingly, this book lays out the methods needed to answer such questions, without relying on divine intervention.

⭐Has been very helpful.

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