Imo Problems, Theorems, And Methods: Algebra

The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics. In the algebra volume, the IMO algebra problems are organized into five chapters: "Equation Problems," "Function Problems," "Sequence Problems," "Inequality Problems," and "Other Algebra Problems." Each chapter begins with an introduction to the relevant foundational knowledge and methods, followed by a reclassification and reorganization of past IMO problems. Multiple elegant solutions are provided for some of the problems, along with a statistical analysis of their difficulty. The book concludes with a record of past IMO participation and award information, as well as an index of algebra problems, facilitating further study and convenient reference. This series is suitable for researchers in mathematical competitions, mathematics educators, and contestants.

Jinhua Chen is a doctoral candidate in Mathematical Education at East China Normal University, with research interests in mathematics competitions and gifted education. He serves as an external mentor for mathematics competition courses at several high schools. Chen attended the Affiliated High School of South China Normal University and Guangdong Olympic School during his secondary education. He has excelled in various competitions, including the Chinese High School Mathematics League, the American Mathematics Competition 12, the Chinese College Mathematics Competition, and the COMAP Mathematical/Interdisciplinary Contest in Modeling.

Bin Xiong is a professor and doctoral supervisor at the School of Mathematical Sciences, East China Normal University, director of the Shanghai Key Laboratory of Core Mathematics and Practice, and director of the International Mathematical Olympiad Research Center. He is an expert with special allowance from the State Council, awarded the Shanghai May Day Labor Medal, and recognized as a model teacher and educator in Shanghai. More than 100 papers have been published both domestically and internationally, and over 150 books have been edited and co-authored. He served as the leader and head coach of the Chinese team at the International Mathematical Olympiad more than 10 times and received the Paul Erdos Award for International Mathematics in 2018.