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The IMO Compendium [Djukić] - mklabgr - 08-17-2026
Full title:The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2009
Authors: Dušan Djukić, Vladimir Janković, Ivan Matić & Nikola Petrović
Publication date: 2011
Publisher: Springer New York
Edition: 2nd edition
Series:Problem Books in Mathematics
Length: xiv + 809 pages
The IMO Compendium is an enormous collection of problems associated with the International Mathematical Olympiad, covering the period from the first IMO in 1959 through 2009. Rather than being a conventional textbook, it is essentially a historical archive and advanced problem-solving laboratory. It gathers both problems actually selected for the IMO and many problems proposed during the selection process, making material that was once scattered through old manuscripts and national archives available in a systematic collection. The second edition adds 143 problems beyond the first edition's 1959–2004 coverage. All four authors are themselves former mathematical-olympiad medalists.
The book is particularly valuable because it combines an exceptionally large problem collection with complete solutions. After a short introduction and a section reviewing basic concepts and facts, roughly 320 pages are devoted to problems, followed by more than 440 pages of solutions. The problems span the traditional Olympiad areas—algebra, geometry, number theory and combinatorics—and demand ingenuity rather than advanced university mathematics. This makes the book useful not only for students training seriously for mathematical competitions, but also for teachers looking for challenging classroom material and mathematicians who enjoy elementary problems with surprisingly deep solutions.
Its greatest strength is therefore not that it teaches a fixed collection of techniques step by step, but that it provides an environment in which mathematical problem-solving ability can be developed through sustained practice. Working through the problems chronologically also gives the reader something resembling a 50-year history of Olympiad mathematics, revealing recurring ideas, changing styles and the remarkable creativity possible with relatively elementary mathematics. For anyone seriously interested in Olympiad problem solving, it functions less like a book to read from beginning to end and more like a long-term reference and training manual. The Mathematical Association of America specifically recommended that undergraduate mathematics libraries consider acquiring it.
Key Takeaways
- Comprehensive scope: IMO and proposed problems covering 1959–2009.
- Huge training resource: more than 800 pages of problems, mathematical background and solutions.
- Problem-solving focused: emphasizes creativity, proof and mathematical insight rather than routine calculation.
- Broad usefulness: excellent for Olympiad students, competition coaches, mathematics teachers and recreational problem solvers.
- Historical value: documents roughly half a century of the development of international mathematical competition problems.
- Second edition: adds 143 new problems to the original 1959–2004 collection.
The IMO Compendium — Springer Nature
The IMO Compendium — Goodreads