Mathematical Olympiad Treasures

ISBN-13: 9780817682521 / Angielski / Twarda / 2011 / 253 str.

Andreescu

Opis

Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience toapply techniques and strategies to real-worldproblems.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 that will be useful beyond the classroom and in a number of disciplines."

Spis treści

I Problems.-

1 Algebra.- 2 Geometry and Trigonometry.- 3 Number Theory and Combinatorics.- II Solutions.- 4 Algebra.- 5 Geometry and Trigonometry.- 6 Number Theory and Combinatorics

Blurb

"I took great pleasure in reading Mathematical Olympiad Treasures, by Titu Andreescu and Bogdan Enescu. This book is the fruit of the prodigious activity of two well-known creators of mathematics problems in various mathematical journals.... In all the chapters, the reader can find numerous challenging problems. All featured solutions are interesting, given in increasing level of difficulty; some of them are real gems that will give great satisfaction to any math lover attempting to solve the problems—or even extend them. I believe strongly that Mathematical Olympiad Treasures will reveal the beauty of mathematics to all students, teachers, and all math lovers." 

—MAA Online (Review of the First Edition)

"...this is one of a long recent series of challenging secondary math books, coauthored by Dr. Titu Andreescu and published by Birkhäuser, a series that has definitely enriched the literature on secondary mathematics—a credit to the coauthor and to the wisdom of the editor."

—Zentralblatt MATH (Review of the First Edition)

This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for solving real-world problems, with new sections, revisions, and many more Olympiad-like problems at various levels of difficulty.

The problems are clustered by topic into three self-contained chapters. The book begins with elementary facts, followed by carefully selected problems and detailed, step-by-step solutions, which then lead to more complicated, challenging problems and their solutions. Reflecting the vast experience of two professors and Mathematical Olympiad coaches, the text will be invaluable to teachers, students, and puzzle enthusiasts. The advanced reader is challenged to find alternative solutions and extensions of the proposed problems.