Mathematical Olympiad Challenges

[...]... Romania, Russia, South Korea, Ukraine, United Kingdom, and Vietnam Also included are problems from international competitions such as the IMO, Balkan Mathematical Olympiad, Ibero-American Mathematical Olympiad, Asian-Pacific Mathematical Olympiad, Austrian-Polish Mathematical Competition, Tournament of the Towns, and selective questions from problem books and from the following journals: Kvant (Quantum),... Matematika v Skole (Mathematics in School), American Mathematical Monthly, and Matematika Sofia More than 60 problems were created by the authors and have yet to be circulated Mathematical Olympiad Challenges is written as a textbook to be used in advanced problem-solving courses or as a reference source for people interested in tackling challenging mathematical problems The problems are clustered in... include a glossary of definitions and fundamental properties used in the book Mathematical Olympiad Challenges has been successfully tested in classes taught by the authors at the Illinois Mathematics and Science Academy, the University of Michigan, the University of Iowa, and in the training of the USA International Mathematical Olympiad Team In the end, we would like to express our thanks to Gheorghe... national mathematical competitions, such as the AMC 8 (formerly the American Junior High School Mathematics Examination), AMC 10 (the American Mathematics Contest for students in grades 10 or below), and AMC 12 (formerly the American High School Mathematics Examination), the American Invitational Mathematics Examination (AIME), the United States Mathematical Olympiad (USAMO), the W L Putnam Mathematical. .. we have found that participants in mathematics Olympiads have often gone on to become first-class mathematicians or scientists and have attached great significance to their early Olympiad experiences For many of these people, the Olympiad problem is an introduction, a glimpse into the world of mathematics not afforded by the usual classroom situation A good Olympiad problem will capture in miniature the...Foreword Why Olympiads? Working mathematicians often tell us that results in the field are achieved after long experience and a deep familiarity with mathematical objects, that progress is made slowly and collectively, and that flashes of inspiration are mere punctuation in periods of sustained effort The Olympiad environment, in contrast, demands a relatively... of insight that heralds the start of a successful solution Like a well-crafted work of fiction, a good Olympiad problem tells a story of mathematical creativity that captures a good part of the real experience and leaves the participant wanting still more And this book gives us more It weaves together Olympiad problems with a common theme, so that insights become techniques, tricks become methods, and... craft of a skilled Olympiad coach or teacher consists largely in recognizing similarities among problems Indeed, this is the single most important skill that the coach can impart to the student In this book, two master Olympiad coaches have offered the results of their experience to a wider audience Teachers will find examples and topics for advanced students or for their own exercise Olympiad stars will... moves away from routine exercises and memorized algorithms toward creative solutions to unconventional problems The second consists in spreading problem-solving culture throughout the world Mathematical Olympiad Challenges reflects both trends It gathers essay-type, nonroutine, open-ended problems in undergraduate mathematics from around the world As Paul Halmos said, “problems are the heart of mathematics,”... solutions in the book Titu Andreescu American Mathematics Competitions R˘ zvan Gelca a University of Michigan April 2000 Problems Chapter 1 Geometry and Trigonometry T Andreescu and R Gelca, Mathematical Olympiad Challenges, DOI: 10.1007/978-0-8176-4611-0_1, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009 3 4 Chapter 1 Geometry and Trigonometry 1.1 A Property of Equilateral Triangles . international competitions such as the IMO, Balkan Mathematical Olympiad, Ibero-American Mathematical Olympiad, Asian-Pacific Mathematical Olympiad, Austrian-Polish Mathematical Com- petition, Tournament. (Mathematics in School), American Mathematical Monthly,and Matematika Sofia. More than 60 problems were created by the authors and have yet to be circulated. Mathematical Olympiad Challenges is written as. American Invitational Mathematics Examination (AIME), the United States Mathematical Olympiad (USAMO), the W. L. Putnam Mathematical Competi- tion, and a number of regional contests such as the