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Full 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
Contents
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. 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. 3. Proofs. 3.1. Algebraic Proofs. 3.2. Proof By Inductions. 3.3. Chapter 3 Exercises. 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. 5. Pascal's Triangle Identities. 5.1 Horizontally-Oriented Identities. 5.2 Diagonally-Oriented Identities. 5.3. Binomial Expansion. 5.4. Chapter 5 Exercises. 6. Geometry. 6.1. Triangular Geometry. 6.2 Area and Perimeter Geometry. 6.3. Geometry and Proportions. 6.4. Chapter 6 Exercises. 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. 8. Answers to Chapter Exercises. 9. Appendices. 10. Index. 11. Bibliography.
