历届国际数学奥林匹克摘要——1959～2004年国际数学奥林匹克预选试题集 The IMO compendium 文字版[PDF]

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资源信息： 中文名: 历届国际数学奥林匹克摘要——1959～2004年国际数学奥林匹克预选试题集 原名: The IMO compendium 别名: 历届国际数学奥林匹克摘要 作者: Dusan Djukic Vladimir Jankovic Ivan Matic Nikola Petrovic 图书分类: 科技 资源格式: PDF 版本: 文字版 出版社: Springer Science+Business Media, Inc. 书号: 978-0387-24299-6 发行时间: 2005年 地区: 美国 语言: 英文 概述:

　 内容介绍 　　国际数学奥林匹克是世界中学生最高级别的数学竞赛活动，至今已成功举办50届。而此书收集了1959～2004年绝大多数历届数学竞赛试题的备选题的资料，并附有完整的解答，其收藏价值就已经可见一斑，更是高手登顶的必经之路。对于竞赛教练来说，更是当仁不让的杀手锏。 　　可惜的是，这份资料是英文的。不过对于现在的国内中学生来说，读懂这些资料并非难事。 内容截图

下面的英文介绍来自原书，下划线和加粗是我做的。 The IMO Compendium Olympiad problems have been published in many books [65]. However, the remaining shortlisted and longlisted problems have not been systematically collected and published, and therefore many of them are unknown to mathematicians interested in this subject. Some partial collections of shortlisted and longlisted problems can be found in the references, though usually only for one year. References [1], [30], [41], [60] contain problems from multiple years. In total, these books cover roughly 50% of the problems found in this book. The goal of this book is to present, in a single volume, our comprehensive collection of problems proposed for the IMO. It consists of all problems selected for the IMO competitions, shortlisted problems from the 10th IMO and from the 12th through 44th IMOs, and longlisted problems from nineteen IMOs. We do not have shortlisted problems from the 9th and the 11th IMOs, and we could not discover whether competition problems at those two IMOs were selected from the longlisted problems or whether there existed shortlisted problems that have not been preserved. Since IMO organizers usually do not distribute longlisted problems to the representatives of participant countries, our collection is incomplete. The practice of distributing these longlists effectively ended in 1989. A selection of problems from the first eight IMOs has been taken from [60]. The book is organized as follows. For each year, the problems that were given on the IMO contest are presented, along with the longlisted and/or shortlisted problems, if applicable. We present solutions to all shortlisted problems. The problems appearing on the IMOs are solved among the other shortlisted problems. The longlisted problems have not been provided with solutions, except for the two IMOs held in Yugoslavia (for patriotic reasons), since that would have made the book unreasonably long. This book has thus the added benefit for professors and team coaches of being a suitable book from which to assign problems. For each problem, we indicate the country that proposed it with a three-letter code. A complete list of country codes and the corresponding countries is given in the appendix. In all shortlists, we also indicate which problems were selected for the contest. We occasionally make references in our solutions to other problems in a straightforward way. After indicating with LL, SL, or IMO whether the problem is from a longlist, shortlist, or contest, we indicate the year of the IMO and then the number of the problem. For example, (SL89-15) refers to the fifteenth problem of the shortlist of 1989. We also present a rough list of all formulas and theorems not obviously derivable that were called upon in our proofs. Since we were largely concerned with only the theorems used in proving the problems of this book, we believe that the list is a good compilation of the most useful theorems for IMO problem solving. The gathering of such a large collection of problems into a book required a massive amount of editing. We reformulated the problems whose original formulations were not precise or clear. We translated the problems that were not in English. Some of the solutions are taken from the author of the problem or other sources, while others are original solutions of the authors of this book. Many of the non-original solutions were significantly edited before being included. We do not make any guarantee that the problems in this book fully correspond to the actual shortlisted or longlisted problems. However, we believe this book to be the closest possible approximation to such a list. 　　下面只提供简单明了的目录，因为重复的大多是年份。 目录: 1 Introduction (2节) 2 Basic Conceptions and Facts (5节) 3 Problems (45节，对应45个年份) 4 Solutions (45节，与[3]对应) 附录、后记、引用