Problem Solving Methods and Strategies in High School Mathematical Competitions

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【簡介】 This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking. It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools. The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu. The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results. 【目錄】 Methods of Reduction Proofs by Contradiction Inductive Methods The Drawer Principle Inclusion–Exclusion Principle Extreme Principle Parity Area Methods Thinking Globally Proper Representations Combine Numbers and Figures Correspondence and Pairing Recurrence Colouring Assignment Methods Calculate in Two Ways Stepwise Adjustment Methods of Construction Invariants and Monovariants Graph Theory Method Solutions for the Exercises

Engaging Young Students in Mathematics through Competitions — World Perspectives and Practices vol.2

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The two volumes of "Engaging Young Students in Mathematics through Competitions" present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Volume II contains background information on connections between the mathematics of competitions and the organization of such competitions, their interplay with research, teaching and more. It will be of interest to anyone involved with mathematics competitions at any level, be they researchers, competition participants, teachers or theoretical educators. The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018. Sample Chapter(s) Introduction Chapter 1.1: From the Lifting-the-Exponent-Lemma to Elliptic Curves with Isomorphic Groups of Points: How Olympiad Mathematics Influences Mathematical Research Readership: Students, teachers, researchers, and general public interested in mathematics competition problems.