Description
Book SynopsisIntroduction 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
Trade Review"The book presents a selected set of mathematical and geometrical topics useful for preparing for high school math competitions, Olympiads, SAT tests, and some college courses. Repetitive exercises and hands-on practice help to students to elaborate an efficient know-how capability in problem solving.
[. . .] The book is interesting, innovative, and can serve as a good addition to the regular high school algebra and geometry manuals."
- Technometrics, Volume 65, 2023 - Issue 2
"This book has two principal goals: Preparing students for typical problems they will face in i) Olympiad-style events, and ii) future college mathematics courses in Discrete Mathematics, Graph Theory, Differential Equations, Number Theory, and Abstract Algebra. For each topic, the book introduces the topic with a remarkably easy pace and then proceeds to provide numerous practice problems to ensure mastery of the necessary skills. Traditional book solutions to exercises and a bibliography are provided. Therefore, this book targets i) advanced high school students preparing for Math Olympiad competitions, ii) college students taking relevant courses who want supplementary explanations and extra practice, iii) college instructors of relevant courses who want supplementary reference material for their courses.
[. . .] As already indicated, this is excellent reference material for a university discrete mathematics course."
- MAA Reviews"The book presents a selected set of mathematical and geometrical topics useful for preparing for high school math competitions, Olympiads, SAT tests, and some college courses. Repetitive exercises and hands-on practice help to students to elaborate an efficient know-how capability in problem-solving.
[. . .] The book is interesting, innovative, and can serve as a good addition to the regular high school algebra and geometry manuals."
- Technometrics
Table of Contents1. 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.
