Collection of Problems

The IMO Compendium is the ultimate collection of challenging high school level mathematics problems. It is an invaluable resource, not only for students preparing for competitions, but for anyone who loves and appreciates math. Training for mathematical olympiads is enjoyed by talented students throughout the world. Olympiads have become one of the primary ways to recognize and develop talented youth with a potential to excel in areas that require abstract thinking. Although the problems appearing at IMO do not involve advanced mathematics, they must be difficult and their solutions must arise from creative and clever insights rather than tedious calculations.

The IMO Compendium is the ultimate collection of challenging high school level mathematics problems. It is an invaluable resource, not only for students preparing for competitions, but for anyone who loves and appreciates math. Training for mathematical olympiads is enjoyed by talented students throughout the world. Olympiads have become one of the primary ways to recognize and develop talented youth with a potential to excel in areas that require abstract thinking. Although the problems appearing at IMO do not involve advanced mathematics, they must be difficult and their solutions must arise from creative and clever insights rather than tedious calculations.

The Russian version of A collection of problems in probability theory contains a chapter devoted to statistics. That chapter has been omitted in this translation because, in the opinion of the editor, its content deviates somewhat from that which is suggested by the title: problems in pro­ bability theory. The original Russian version contains some errors; an attempt was made to correct all errors found, but perhaps a few stiII remain. An index has been added for the convenience of the reader who may be searching for a definition, a classical problem, or whatever.

The extensive application of modern mathematical teehniques to theoretical and mathematical physics requires a fresh approach to the course of equations of mathematical physics.