This book is intended as a teacher's manual and as an independent-study handbook for students and mathematical competitors. Based on a traditional teaching philosophy and a non-traditional writing approach (the stair-step method), this book consists of new problems with solutions created by the authors. The main idea of this approach is to start from relatively easy problems and "step-by-step" increase the level of difficulty toward effectively maximizing students' learning potential.
In addition to providing solutions, a separate table of answers is also given at the end of the book. A broad view of mathematics is covered, well beyond the typical elementary level, by providing more in depth treatment of Geometry and Trigonometry, Number Theory, Algebra, Calculus, and Combinatorics.
Hayk Sedrakyan is an IMO medal winner Professor of mathematics in Paris, France and a professional Math Olympiad Coach in Greater Boston area, Massachusetts, USA. He has defended his PhD thesis in mathematics in UPMC- Sorbonne University, Paris, France. Hayk is a Doctor of Mathematical Sciences in USA, France and Armenia. He has received 3 Master's degrees in mathematics from Germany, Austria, Armenia and has spent a small part of his PhD studies in Italy. Hayk has authored several scientific mathematical research articles and several books on the topic of problem solving and Olympiad style mathematics published in USA and South Korea. Nairi Sedrakyan is involved in national and international Olympiads of mathe- matics, having been the President of Armenian Mathematics Olympiads and IMO problem selection committee member. He is the author of one of the hardest prob- lems ever proposed in the history of International Mathematical Olympiad (5th problem of 37th IMO). He has been the Leader of Armenian IMO Team, jury mem- ber of IMO, jury member and problem selection committee member of Zhautykov International Mathematical Olympiad (ZIMO), jury member and problem selection committee member of International Olympiad of Metropolises, the President of In- ternational Mathematical Olympiad Tournament of the Towns in Armenia. He is also the author of a large number of problems proposed in these Olympiads and has authored several books on the topic of problem solving and Olympiad style math- ematics published in USA, Russia, South Korea and Armenia. For his outstanding teaching Nairi Sedrakyan received the title of the best teacher of the Republic of Armenia and has been awarded with a special gift from the Prime Minister.
Geometry and Trigonometry.- Number Theory.- Algebra.- Calculus.- Combinatorics.- Hints.- Solutions.- Answers.