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Foreword; Preface; Contents; Goals of Mathematics Instruction; 1 Goals of Mathematics Instruction: Seven Thoughts and Seven Illustrations of Means; Abstract; 1.1 Part I: Seven Thoughts on Mathematics Instruction; 1.2 Part II: Seven Illustration of Means; Acknowledgements; References; Geometry for Competitions; 2 From a Mathematical Situation to a Problem; Abstract; 2.1 Introduction; 2.2 What Is a Mathematical Situation?; 2.3 Several Examples of Mathematical Situations; 2.4 Some Problems Arising from the Mathematical Situations of Sect. 2.3
2.5 Hints, Solutions and Comments to Some of the Problems and Examples2.5.1 Comment and Hint to Example 1.2; 2.5.2 Solution to Problem 4.1; 2.5.3 Solution of Problem 4.2; 2.5.4 Solution of the Problem 4.3; 2.5.5 Solution of the Problem 4.4; 2.5.6 Solution to Problem 4.5; 2.5.7 Solution to Problem 4.6; 2.5.8 Comments and Solution to Problem 4.7; 2.5.9 Solution to the Problems 4.8; 2.5.10 Solution to Problems 4.9.1 and 4.9.2; 2.5.11 Solution to Problem 4.10; 2.5.12 Solution to Problem 4.11; 2.5.13 Solution of the Problem 4.12; References; 3 Techniques for Solving Problems of Plane Geometry
Abstract3.1 Introduction; 3.2 Plane Geometry Problems (Moise 1990; Encyclopedia of the Solutions of Mathematics Problem 1983; Some Geometry Problems in Mathematical Olympiad Competitions 2015; Encyclopedia of Solved Problems 2016), Which Can be Solved by Analytic Geometry; 3.3 Lattice Points and Collinear Points (see Liu 1979); 3.4 Some Applications of Quadratic Equations; 3.5 Ceva's Theorem and Its Application; 3.6 Ptolemy's Theorem and Stewart's Theorem; 3.7 Erdős-Mordell Inequality; Acknowledgements; References; Combinatorics for Competitions
4 Arrangements and Transformations of Numbers on a Circle: An Essay Inspired by Problems of Mathematics CompetitionsAbstract; 4.1 Introduction; 4.2 Examples with Admissible Operations; 4.2.1 First Situation; 4.2.2 Second Situation; 4.2.3 Third Situation; 4.2.4 Fourth Situation; 4.3 Static Arrangements; 4.3.1 Example 1; 4.3.2 Example 2; 4.4 Problems to the Reader; 4.5 Conclusion; References; 5 Combinatorial Problems in the Mathematical Olympiad of Central America and the Caribbean; 5.1 Introduction; 5.2 Contest Problems; 5.2.1 Counting Problems; 5.2.2 Strategy Games
5.2.3 Configuration Problems5.2.4 Extremal Problems; 5.2.5 Miscelaneous Problems; 5.3 Shortlisted Problems; 5.4 Conclusions; References; Role of Competitions in the Classroom; 6 The Rainbow of Mathematics-Teaching the Complete Spectrum and the Role Mathematics Competitions Can Play; Abstract; 6.1 Introduction; 6.2 Defining the Rainbow; 6.3 Math Is Fun; 6.4 Math Is Useful; 6.5 Math in School. Connecting the Fun and the Usefulness; 6.6 Mathematics Competitions: Great at Connecting; 6.7 History on Top; Didactics on the Bottom; 6.8 An Example from the Rainbow: Sudoku to Graph Coloring
2.5 Hints, Solutions and Comments to Some of the Problems and Examples2.5.1 Comment and Hint to Example 1.2; 2.5.2 Solution to Problem 4.1; 2.5.3 Solution of Problem 4.2; 2.5.4 Solution of the Problem 4.3; 2.5.5 Solution of the Problem 4.4; 2.5.6 Solution to Problem 4.5; 2.5.7 Solution to Problem 4.6; 2.5.8 Comments and Solution to Problem 4.7; 2.5.9 Solution to the Problems 4.8; 2.5.10 Solution to Problems 4.9.1 and 4.9.2; 2.5.11 Solution to Problem 4.10; 2.5.12 Solution to Problem 4.11; 2.5.13 Solution of the Problem 4.12; References; 3 Techniques for Solving Problems of Plane Geometry
Abstract3.1 Introduction; 3.2 Plane Geometry Problems (Moise 1990; Encyclopedia of the Solutions of Mathematics Problem 1983; Some Geometry Problems in Mathematical Olympiad Competitions 2015; Encyclopedia of Solved Problems 2016), Which Can be Solved by Analytic Geometry; 3.3 Lattice Points and Collinear Points (see Liu 1979); 3.4 Some Applications of Quadratic Equations; 3.5 Ceva's Theorem and Its Application; 3.6 Ptolemy's Theorem and Stewart's Theorem; 3.7 Erdős-Mordell Inequality; Acknowledgements; References; Combinatorics for Competitions
4 Arrangements and Transformations of Numbers on a Circle: An Essay Inspired by Problems of Mathematics CompetitionsAbstract; 4.1 Introduction; 4.2 Examples with Admissible Operations; 4.2.1 First Situation; 4.2.2 Second Situation; 4.2.3 Third Situation; 4.2.4 Fourth Situation; 4.3 Static Arrangements; 4.3.1 Example 1; 4.3.2 Example 2; 4.4 Problems to the Reader; 4.5 Conclusion; References; 5 Combinatorial Problems in the Mathematical Olympiad of Central America and the Caribbean; 5.1 Introduction; 5.2 Contest Problems; 5.2.1 Counting Problems; 5.2.2 Strategy Games
5.2.3 Configuration Problems5.2.4 Extremal Problems; 5.2.5 Miscelaneous Problems; 5.3 Shortlisted Problems; 5.4 Conclusions; References; Role of Competitions in the Classroom; 6 The Rainbow of Mathematics-Teaching the Complete Spectrum and the Role Mathematics Competitions Can Play; Abstract; 6.1 Introduction; 6.2 Defining the Rainbow; 6.3 Math Is Fun; 6.4 Math Is Useful; 6.5 Math in School. Connecting the Fun and the Usefulness; 6.6 Mathematics Competitions: Great at Connecting; 6.7 History on Top; Didactics on the Bottom; 6.8 An Example from the Rainbow: Sudoku to Graph Coloring