Mathematical Olympiad Treasures

Description

"Mathematical Olympiad Treasures" aims at building a bridge between ordinary high school examples and exercises and more sophisticated, intricate and abstract concepts and problems in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of geometry and trigonometry, algebra, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus of "Treasures" is on engaging a wider audience of undergraduates to think creatively in applying techniques and strategies to problems in the real world. The problems are clustered by topic into self-contained sections. Unlike "Challenges," however, "Treasures" begins with elementary facts, followed by a number of carefully selected problems and an extensive discussion of their solutions. This discussion then leads to more complicated and more intellectually challenging problems as well as their solutions. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools and strategies that will be useful beyond the classroom and in a number of disciplines. "Mathematical Olympiad Treasures" reflects the experience of two experienced professors and coaches from the United States and Romanian Olympiad teams.