The IMO Compendium

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics.

The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world.

Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off. 

• IMO
• International Mathematical Olympiad
• Mathematical Problem-Solving
• Mathematics Competition

"The International Mathematical Olympiad, or IMO is the premier international competition for talented high school mathematics students. … This book collects statements and solutions of all of the problems ever set in the IMO, together with many problems proposed for the contest. … serves as a vast repository of problems at the Olympiad level, useful both to students … and to faculty looking for hard elementary problems. No library will want to be without a copy, nor will anyone involved in mathematics competitions … ."

—(Fernando Q. Gouvêa, MathDL, March, 2006)

• , Department of Mathematics, University of Toronto, Toronto, Canada

  Dušan Djukić

• , Department of Mathematics, University of Belgrade, Belgrade, Serbia

  Vladimir Janković

• , Department of Mathematics, Duke University, Durham, USA

  Ivan Matić

• , Science Department, Texas A&M University, Doha, Qatar

  Nikola Petrović

The authors of this volume have published the first edition with Springer in 2006. The first edition has gone through 3 printings and 2510 print sales. Links to the first edition can be found on the IMO website.

Each of the authors are from Serbia and all were medalists in the mathematical olympiads. Dusan Djusic is an expert in number theory and took part in 3 IMOs. He won 2 silver medals and 1  gold. He has also participates in 2 Balkan IMOs and medaled in each.

Ivan Matic's area of research is partial differential equations and won a silver medal at the 1999 IMO along with a number of awards in other competitions.

Vladimir Jankovic's areas of study are extreme problems in optimal control. He was awarded 2 silver medals at the IMOs in 1969 and 1970 and has been the main gatekeeper for the shortlist problems from IMOs of years past.

Nikola Petrovic took part in 3 IMOs and 2 Balkan IMOs and has been awarded silver and bronze medals.

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