Introduction to Math Olympiad Problems

Description

Introduction to Math Olympiad Problems aims to introduce high school students to all the necessary topics that frequently emerge in international Math Olympiad competitions. In addition to introducing the topics, the book will also provide several repetitive-type guided problems to help develop vital techniques in solving problems correctly and efficiently. The techniques employed in the book will help prepare students for the topics they will typically face in an Olympiad-style event, but also for future college mathematics courses in Discrete Mathematics, Graph Theory, Differential Equations, Number Theory and Abstract Algebra. Features: Numerous problems designed to embed good practice in readers, and build underlying reasoning, analysis and problem-solving skills Suitable for advanced high school students preparing for Math Olympiad competitions Cover Half Title Title Page Copyright Page Contents Preface Author Bio Acknowledgments Chapter 1: Introduction 1.1. Patterns and Sequences 1.2. Integers 1.3. Geometry 1.4. Venn Diagrams 1.5. Factorial and Pascal's Triangle 1.6. Graph Theory 1.7. Piecewise Sequences 1.8. Chapter 1 Exercises Chapter 2: Sequences and Summations 2.1. Linear and Quadratic Sequences 2.2. Geometric Sequences 2.3. Factorial and Factorial–Type Sequences 2.4. Alternating and Piecewise Sequences 2.5. Formulating Recursive Sequences 2.6. Solving Recursive Sequences 2.7. Summations 2.8. Chapter 2 Exercises Chapter 3: Proofs 3.1. Algebraic Proofs 3.2. Proof by Induction 3.3. Chapter 3 Exercises Chapter 4: Integers' Characteristics 4.1. Consecutive Integers 4.2. Prime Factorization and Divisors 4.3. Perfect Squares 4.4. Integers' Ending Digits 4.5. Chapter 4 Exercises Chapter 5: Pascal's Triangle Identities 5.1. Horizontally Oriented Identities 5.2. Diagonally Oriented Identities 5.3. Binomial Expansion 5.4. Chapter 5 Exercises Chapter 6: Geometry 6.1. Triangular Geometry 6.1.1. Isosceles Triangles 6.1.2. 30–60–90 Triangles 6.1.3. 45–45–90 Triangles 6.1.4. Additional Right Triangles 6.2. Area and Perimeter Geometry 6.3. Geometry and Proportions 6.4. Chapter 6 Exercises Chapter 7: Graph Theory 7.1. Degrees of Vertices and Cycles 7.2. Regular Graphs 7.3. Semi-Regular Graphs 7.4. Hamiltonian Cycles 7.5. Chapter 7 Exercises Chapter 8: Answers to Chapter Exercises 8.1. Answers to Chapter 1 Exercises 8.2. Answers to Chapter 2 Exercises 8.3. Answers to Chapter 4 Exercises 8.4. Answers to Chapter 5 Exercises 8.5. Answers to Chapter 6 Exercises 8.6. Answers to Chapter 7 Exercises Chapter 9: Appendices 9.1. Venn Diagram 9.2. Angular Geometry 9.3. Right Triangles 9.4. Isosceles Triangles 9.5. Equilateral Triangles 9.6. Area of Figures 9.7. Patterns (Sequences) 9.8. Alternating Patterns (Sequences) 9.9. Summation Properties 9.10. Finite Summations 9.11. Laws of Exponents 9.12. Factoring Methods 9.13. Binomial Expansion Bibliography Index