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Bamdad R. Yahaghi, ""

Preface

International mathematical competitions have gained great popularity in recent years. They provide the first test for a young person’s mathematical prowess, and success in these competitions often translates into gaining admittance to the best research institutions for graduate work. For this reason some colleges and even high schools have organized special classes for training mathematically talented students for these competitions. The purpose of this text is to provide a selection of mathematical problems that are not only suitable for special college level (and occasionally even at high school level) courses designed for these competitions, but can significantly improve the level of mathematical sophistication of students who

are intrigued by and envision a career in mathematics in general.

I was asked by the Iranian Mathematical Society (IMS) to prepare a problem book on the basis of college level competitions in Iran. Since Iranian students have done quite well in international competitions and their success to some extent reflects the training that they received in special courses, I decided to make the book available to a wider audience. The problems (and their solutions) that are presented in this book are from national mathematical competitions in Iran at college level from 1973 to 2007. I provided my own solutions to most of the problems and also

utilized solutions from the files of the IMS, which contained approximately about 40% of all the solutions.

I should point out that I have not edited the problems of the competitions and they are direct translations from Persian into English. Unfortunately, there were some typos and mistakes in the original version. The errors have been corrected and except for trivial typographical ones, the corrections are so indicated as footnotes throughout Chapter One. Some comments on the problems also appear in footnotes.

I am indebted, and hence express my deepest gratitude, to the colleagues who contributed in different ways to these competitions and to this book — either as members of the Scientific Committee for the competitions, or proposed problems or assisted in finding elegant solutions. Unfortunately, some of those colleagues have left us; may they rest in peace. I am thankful to my dear friend Dr. Hossein

Hajiabolhassan who constantly encouraged me and helped me with the preparation of the book. I would like to thank Professor Alireza Jamali, Professor Ebad Mahmoodian, the outgoing President of the IMS, Dr. Rashid Zaare-Nahandi, and Messrs. M. Shokoohi and M. Abdi-Zadeh and the administrative assistants at the main office of the IMS for their assistance in gaining access to the existing solution files of the IMS. I am grateful to Ms. Anahita Samie for drawing the figures for this book...

Bamdad R. Yahaghi

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