A Potpourri Of Algebra
Experience has taught me that there are two distinct phases in the grasping of Mathematical Olympiad. First and foremost, one has to understand the content which is being taught during Mathematical Olympiad lessons or through reference materials. This includes all the relevant theorems of the four major topics in MO: Algebra, Geometry, Combinatorics and Number Theory. Achieving this first step should not take the student too much time as it does not take much effort to learn such knowledge that is readily available to general students of mathematics. Of much higher priority is the second phase whereby students internalise the usage and application of these learned knowledge. One must understand and appreciate various creative methods of applying learnt theorems in order to excel in MO competitions. These notes aim to facilitate your second preparatory step in mastering the Mathematical Olympiad. Algebra is a major topic in Junior Section, be it in the first round or the second round. Recently participants have complained that questions in the SMO Junior Section are becoming more challenging and ”unapproachable”. This is mainly due to the fact that the problems which are appearing in recent SMO papers are fresh and some students have no experience of dealing with such questions. Nonetheless, a strong foundation in algebra plus the application of suitable strategies will help you solve these problems. Note my usage of the term ”strategies” instead of ”theorems”. A good MO student usually thinks in terms of strategies to tackle the problem instead of theorems used to solve the problem. I have organised past year SMO problems as well as problems from other countries according to the strategies used to solve the problems. Hopefully this will improve your manipulation skills in solving algebra problems.
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November 2017 -
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