The present book is a collection of all problems proposed at Balkan Mathematical Olympiads (BMO), also containing some of the problems discussed during these contests by the jury. It is not only a collection of elementary problems but a page of history - the history of BMO, one of the first reginoal mathematical competition for highschool students.
As it is already accepted, International Mathematical Olympiads (IMO), which was created in 1959, had an important contribution to development of mathematical education of young students all around the world. They extended the area of problems used in mathematical education of young people and also improved their quality. Many mathematicians realized how important is to use some parts of their research problems as elementary educational problems.
All problems are presented with complete solutions. Many problems have several alternative solutions and we also present some extensions. The reader can follow the real increasing of the quality of problems as an illustration of the improvement of mathematical preparation of students. An additional preparatory addendum, containing notions and classical useful results has been added to the end of the book. Află mai mult
Bulgaria is a country with long traditions in mathematical competitions. There are numerous regional competitions connected with important dates in Christian calendar or in Bulgarian history. These competitions range in format and difficulty and give opportunity to all students in lower and secondary school to test their abilities in problem solving. Great many of them being fascinated by problem solving in such competitions start working hard in order to acquire new knowledge in mathematics.
The most important and prestigious national competitions in Bulgaria are Winter Mathematical Competitions, Spring Mathematical Competitions and National Olympiad. The organization of these competitions is responsibility of the Ministry of Education and Science, the Union of Bulgarian Mathematicians and the local organizers. The problems for the competitions are prepared by so called Team of extra curricula research - a specialized body of the Union of Bulgarian Mathematicians.
This book contains all problems for grades 8 to 12 from the above mentioned national competitions in the period 2003-2006. The problems from all selection tests for BMO and IMO are also included. Most of the problems are regarded as difficult IMO type problems. The book is intended for undergraduates, high school students and teachers who are interested in olympiad mathematics. Află mai mult