103 Trigonometry Problems: From the Training of the USA Imo Team

ISBN-13: 9780817643348 / Angielski / Miękka / 2004 / 214 str.

Titu Andreescu; Zuming Feng; T. Andrees

Opis

* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions

* Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry

* A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training

Recenzje

From the reviews:

"The way chosen by the authors of this book is one that goes directly to the interested student. The theoretical facts are presnented at the beginning of each paragraph and then problems with solutions are discussed...Most of the themes are from so-called trigonometric goemetry, making the book more pleasant for the interested student. Each topic is punctured by a lot of examples. I [note] the beautiful topics on spheric trigonometry which is nowadays forgetten in schools...To conclude, I enjoyed a wonderful text in trigonometry which contains also a lot of real important mathematical ideas. I recommend it as a basic text for all students and teachers involved in high school competitions as competitors or coaches." ---Revue Roumaine de Mathématiques Pures et Appliquées

"The title of this book already says everything about the content: 103 trigonometry problems that were given in the training and testing of the US International Mathematical Olympiad team are presented along with their solutions. ... The presentation is clear, accurate and extensive. For these reasons the book is very easy to read and leads the reader to astonishing insights in an elementary field of mathematics. It is therefore also very appropriate as a textbook ... ." (St. Götz, Monatshefte für Mathematik, Vol. 149 (3), 2006)

Spis treści

* Preface * Abbreviations and Notations * Trigonometric Problems * Introductory Problems * Advanced Problems * Solutions to Introductory Problems * Solutions to Advanced Problems * Glossary * Further Reading

Blurb

103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques.

Key features:

* Gradual progression in problem difficulty builds and strengthens mathematical skills and techniques

* Basic topics include trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions

* Problem-solving tactics and strategies, along with practical test-taking techniques, provide in-depth enrichment and preparation for possible participation in various mathematical competitions

* Comprehensive introduction (first chapter) to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry expose advanced students to college level material

103 Trigonometry Problems is a cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training.

Other books by the authors include 102 Combinatorial Problems: From the Training of the USA IMO Team (0-8176-4317-6, 2003) and A Path to Combinatorics for Undergraduates: Counting Strategies (0-8176-4288-9, 2004).