Math circles are periodic math programs that attract middle and high school students to mathematics by exposing them to intriguing and intellectually stimulating topics, rarely encountered in classrooms. The concept of a “math circle" has been modeled after experiences in Russia, Bulgaria, Romania, and other countries. It is a way to stimulate, encourage and help gifted and interested pre-college students to study and solve mathematics problems, sometime with the involvement of mathematicians and/or mathematics faculty from universities. The main purpose of a math circle is to inspire in students an understanding of and a lifelong love for mathematics. The book under review presents materials used during the course of one year in a math circle organized by mathematics faculty at Moscow State University, and also used at the mathematics magnet school known as Moscow School Number 57. This volume contains 28 Problems Sets. Each problem set has a similar structure: it combines review material with a new topic, offering problems in a range of difficulty levels. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation. Some are within the reach of most mathematically competent high school students, while others are difficult even for a mathematics professor. Many mathematically inclined students have found that tackling these problems, or even just reading their solutions, is a great way to develop mathematical insight. The problems and the accompanying material are well suited for math circles. They are also appropriate for problem-solving classes and practice for regional and national mathematics competitions. In summary, this is an excellent resource for those interested in math circles, including students and parents (they can just skip the organizational part and go directly to the presentations and problems). For those interested in starting and running a math circle, I think it is an invaluable resource.
Reviewer: Vicenţiu D. Rădulescu (Craiova)