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A Primer for Mathematics Competitions (Oxford Mathematics (Paperback Unnumbered))

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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.

There are 3 levels of Math:
1) 1 technique for 1 type of problems: Math Olympiad problems
2) 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.