Jul 26, 2010

International Mathematics Olympiad


PDATED (March 2007) Recommended literature, such as Paul Zeitz' The Art and Craft of Problem Solving
Amazon Kindle 2, Amazon's new e-reader for digital books
More about IMO:
HARD PROBLEMS: The Road to the World's Toughest Math Contest

The International Mathematics Olympiad (IMO, also known as the International Mathematical Olympiad) is an annual mathematics competition for high school students [IMO Article in Wikipedia]. It is one - in fact, the oldest - of the International Science Olympiads. The first IMO was held in Romania in 1959. The problems come from various areas of mathematics, such as are included in math curricula at secondary schools. Finding the solutions of these problems, however, requires exceptional mathematical ability and excellent mathematical knowledge on the part of the contestants.

Topics covered (see Unwritten Syllabus and Tutorials at Arkadii Slinko's Math Olympiad Website, currently being transferred):

  • Number Theory, including
    • Fundamental Theorems on Arithmetic
    • Linear and quadratic Diophantine equations, including Pell's equation
    • Arithmetic of residues modulo n, Fermat's and Euler's theorems
  • Algebra, including
    • Fundamental Theorems on Algebra, e.g. inequalities, factorization of a polynomial into a product of irreducible polynomials
    • Symmetric polynomials of several variables, Vieta's theorem
  • Combinatorics, including
    • Graph theory
  • Geometry, including
    • Properties of the orthocentre, Euler's line, nine-point-circle, Simson line, Ptolemy's inequality, Ceva and Menelaus etc.
Excluded topics:
  • Calculus (!)
  • Complex numbers (though present in the past)
  • Inversion in geometry
  • Solid geometry (though present in the past; may return)

The usual size of an official delegation to an IMO is (a maximum of) six student competitors and (a maximum of) two leaders. There is no official ``team''. The student competitors write two papers, on consecutive days, each paper consisting of three questions. Each question is worth seven marks. (The preceding information is taken from an Overview of the IMO provided by the IMO'95 host country, Canada; also see below.) A total score of 42 points is possible. Awards are determined as follows:

  • GOLD MEDAL: the top 1/12 of scores receive gold medals
  • SILVER MEDAL: the next 2/12 of scores receive silver medals
  • BRONZE MEDAL: the next 3/12 of scores receive bronze medals
  • HONORABLE MENTION: any competitor who receives a perfect score of 7 on any one question, but who does not receive a medal, is awarded an honorable mention

My report on IMO 2002 provides further details of how the IMO is run.

A list of recommended mathematics literature for self-study is slowly evolving.


Without doubt, these lists of web addreses are far from complete. If you send relevant web addresses that are not listed here, then they will be included.

General Information

Official IMO web site < < < < < N E W
A new website about the IMO, including a problem and results archive.

An overview of all available logos


Regulations Pertaining to the IMO
These Regulations define the IMO as of ?. New aspects are the IMO Advisory Board and the IMO Trust Fund.

General (but not official) IMO site

Future IMOs

IMO 2009
The 50th IMO will be hosted by Germany in Bremen on 10-22 July, 2009.

IMO 2010
The 51st IMO will be hosted by Kazakhstan in ? on ?-? ?, 2010.

IMO 2011
The 52nd IMO will be hosted by the Netherlands in ? on ?-? ?, 2011.

Past IMOs

IMO 2008 [ local files ]
The 49th IMO was hosted by Spain in Madrid on 10-22 July, 2008. (arrival day for contestants is 14 July).

IMO 2007 [ local files: logo | problems day 1, day 2 ]
The 48th IMO was hosted by Vietnam in Hanoi on 19-31 July, 2007 (arrival day for contestants is 23 July).

IMO 2006 [ local files: about | logo | problems day 1, day 2 | solutions | results ]
The 47th IMO was hosted by Slovenia in Ljubljana on 6-18 July, 2006.

IMO 2005 [ local files: | about | logo | rules | countries | problems day 1, day 2 | results ]
The 46th IMO was hosted by Mexico in Mérida, Yucatán, on 8-19 July, 2005.

IMO 2004 [ logo | rules | problems day 1, day 2 | all data | UK report incl. problems ]
The 45th IMO was hosted by Greece in Athens on 6-18 July, 2004.

IMO 2003 [ old address | English | logo | results (Excel) | problems day 1, day 2 | solutions ]
The 44th IMO was hosted by Japan in Tokyo on 7-19 July, 2003. Submission deadline for problems was 15 Feb. 2003.

IMO 2002 [ logo | problems in PDF (Dutch) | results | statistics | personal report | shortlist is confidential until IMO2003 ]
The 43rd IMO was hosted by the United Kingdom in Glasgow on 19-30 July, 2002.

IMO 2001, Scoring Site [ logo | problems in PDF | problems and solution as Mathematica Notebook | results | mailing list | shortlist | book ]
The 42nd IMO was hosted by the United States of America in Washington DC on 1-14 July, 2001.

IMO 2000 [ logo | regulations | problems day 1 | problems day 2 | problems in PDF | results | medals | mailing list ]
The 41st IMO was hosted by South Korea in Taejon on 13-25 July, 2000.

IMO 1999 [ logo | problems day 1 | problems day 2 | results | mailing list ]
The 40th IMO was hosted by Romania in Bucharest on 10-22 July, 1999.

IMO 1998 [ logo | problems | results ]
The 39th IMO was hosted by Taiwan in Taipei on 10-21 July, 1998.

IMO 1997 [ logo | problems day 1 | problems day 2 | results ]
The 38th IMO was hosted by Argentina in Mar del Plata on July 18-31, 1997. There is an IMO97 mailing list.

IMO 1996 [ logo | the problems ]
The 37th IMO was hosted by India in Mumbai (Bombay) on July 5-17, 1996.
Contact information:
Professor A.M. Vaidya
IMO-Cell, School of Mathematics,
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai (Bombay) -400005

Telephone:91(022) 2152971, 2152311, 2188654
Telefax: 91 (022) 2152110/2152181
Email: imo@tifrvax.tifr.res.in or imo@math.tifr.res.in

IMO 1995 [ logo | regulations | the problems ]
The 36th IMO was hosted by Canada in Toronto on July 10-28, 1995.

IMO 1994 [ logo | the problems and results ]
The 35th IMO was hosted by Hong Kong on July 12-19, 1994.

IMO 1993 [ logo | problems day 1 | problems day 2 ]
The 34th IMO was hosted by Turkey in Istanbul on July 12-19, 1993.

Journals and other info

The network for the participants to the IMO. Has information on three mailing lists (for IMO'99, IMO2000, and IMO problems).

IMO News at MAA
The Mathematical Association of America (MAA) carries some information on the IMO and publishes books with IMO problems.

IMO Scores
This site has some statistics about scores at IMO 1993 an on (except 1994). Maintained by Joseph Myers.

KöMaL - Mathematical and Physical Journal for Secondary Schools
More than one hundred years ago, Dániel Arany, a high school teacher from the city of Gyõr, decided to found a mathematical journal for high school students. His goal was "to give a wealth of examples to students and teachers". The journal's first edition appeared on January 1, 1894.

MathPro Press
MathPro Press specializes in the publication of compendiums and indexes of mathematics problems.

The World Federation of National Mathematics Competitions (WFNMC) publishes a journal entitled Mathematics Competitions. Also see Australia below.

The Mathematics and Informatics Quarterly is an international journal which:
  • Publishes articles, notes, problems and solutions in school mathematics and informatics.
  • Is devoted to teachers and students, who are interested in mathematics and informatics clubs, olympiads and competitions.

In the World of Mathematics
This new quarterly journal is aimed at pupils, students, and teachers interested in mathematical problems and puzzles as well as in the history of mathematics and its new trends.

SIPROMA Bulletin (in Spanish)
SIPROMA is the ``Sociedad Iberoamericana para la Promoción de la Matemática''.

International Mathematics Competitions

Kangourou Sans Frontières / Kangaroo without Frontiers: International Mathematics Competition (French site)
Kangourou Sans Frontières (KSF) is an international mathematics competition for various levels of students. History and Rules (old)

Mathematical Olympiads for Elementary and Middle Schools
Created in 1977 by Dr. George Lenchner, an internationally known math educator, the Math Olympiads went public in 1979. In the year 2000, over 120,000 students from 5,000 teams worldwide participated in the Olympiads, representing 26 countries.

International Living Maths Mathletics Olympiad <<<<< N E W
Living Maths (South Africa) organizes the International Living Maths Mathletics Olympiad for ages 6 to 13 (K-7). Look under: Events, Olympiad.

Mental Calculation World Cup

Regional Mathematics Competitions

Asian Pacific Mathematics Olympiad
Problems in English and French.

Balkan Math Olympiad
No link yet.

Bay Area Mathematical Olympiad
The Bay Area Mathematical Olympiad (BAMO) is a contest for high school students sponsored jointly by the Mathematical Sciences Research Institute (MSRI), the American Institute of Mathematics (AIM), the University of California at Berkeley (UCB), and the University of San Francisco (USF).

Colorado Mathematical Olympiad
The Colorado Mathematical Olympiad (CMO) is the largest essay-type mathematical competition in the United States, with 600 to 1,000 participants competing annually for fine prizes.

Ibero-American Mathematics Olympiad
Home page (in Spanish) of the Olimpíadas Iberoamericanas de Matemática (OIM).

The Math League (USA & Canada)
The Math League is dedicated to bringing challenging mathematics materials to students, and specializes in math contests (for high schools in the USA and Canada), books, and computer software.

National Mathematics Competitions

The Olimpíada Matemática Argentina (OMA) is the Argentinian Mathematics Olympiad. Currently, information is only available in Spanish.

The Australian Mathematics Trust (AMT) is a national non-profit organization which conducts mathematics competitions in Australia. Includes information on theWFNMC.

Information about the Mathematics Olympiads in Belgium:

Brazil [ also see here ]
Information about the Brazilian Mathematics Olympiad (OBM=Olimpíada Brasileira de Matemática). All material in Portuguese only.

Information about the National Mathematical Olympiad in Bulgaria as part of the Bulgarian Competitions in Mathematics and Informatics.

Information about the Canadian Mathematics Competition (CMC) maintained by Ruth Malinowski (cmc@math.uwaterloo.ca).

The Canadian Mathematical Society also has an Olympiads Home Page.

The WWW Home Page for the Colombian Olympiads (in Spanish), covering Mathematics, Phyisics, and Informatics, maintained by Fernando Vega Salamanca (fvega@zulima.uanarino.edu.co).
E-mail: olimpia@federman.uanarino.edu.co

Czech Republic


Information about the Estonian Matemaatika Olümpiaadid (also in the Estonian language), maintained by Uve Nummert (uve@math.ut.ee). Includes IMO information (in English).

Information about mathematics competitions in France, includes French translations of IMO problem sets and recommended French mathematics literature for IMO preparation.

The Verein Mathematik-Olympiaden e.V. coordinates the German Mathematics Olympiads (DeMO). There is also information available about the German Mathematics Olympiad 1995.

Information on Irish participation in the International Mathematical Olympiads and (eventually) copies of Irish Maths Olympiad questions and photographs. Contact: Gordon Lessells (gordon.lessells@ul.ie).


Information on the Italian (?) Mathematics Olympiad (in Italian). E-mail contact: mvillani@cibs.sns.it

Information about the IMO in general (starting from 34th) and the Mathematical Olympiad Foundation of Japan. Maintained by Naomasa Maruyama (maruyama@ism.ac.jp).


Information (in Spanish) on the Mexican Mathematics Olympiad (OMM) and problem sets (mostly in Spanish) of various (regional) mathematics contests. E-mail:omm@hp.fciencias.unam.mx. Maintained by Felipe Lemaitre Carabias (iker@hardy.fciencias.unam.mx).

There is also an unofficial page for the Mexican Mathematical Olympiad (in Spanish), maintained by Pedro Sánchez.

Pierre Fermat Math Competition (in Spanish: Concurso de Matemáticas Pierre Fermat).

The Netherlands
Information about the Dutch Mathematics Olympiad (now also in English), maintained by Tom Verhoeff (Tom.Verhoeff@acm.org).

New Zealand
Information about the New Zealand Math Olympiads

The Niels Henrik Abels Mathematics Competition selects students for partiticipation in the IMO. This site also contains problem sets of the Norwegian Mathematical Olympiad and the IMO, including some solutions and results. Maintained by Einar Andreas Rødland (einara@math.uio.no).


Information about Peru's math olympiad and the Cono Sur olympiads, maintained by Enrique Valeriano (evaleri@pucp.edu.pe).

Information (including problem sets) on the math olympiads in which Polish high school students participate (in particular: the Polish Mathematical Olympiad, the Austrian-Polish Mathematics Competition, and the Baltic Team Contest). Maintained by Krzysztof Chelminski (chel@mathematik.th-darmstadt.de) and Waldemar Pompe (waldipo@mimuw.edu.pl).

Olimpíadas Portuguesas de Matemática.

Information about the IMO and Singapore's participation.

Mathematical olympiad in Slovakia.

Mathematical competitions in Slovenia are supervised by DMFA.

South Africa
South African Mathematics Olympiad.

Information and problem sets (in Spanish) for the math olympiads in which Spanish high school students participate, including the Spanish Mathematics Olympiad (Olimpiada Matemática Española = OME). Maintained by Cristobal Sánchez Rubio (csanchez@platea.pntic.mec.es).

Unoficcial Spanish Math Olympiad page maintained by Ramon Esteban Romero (Ramon.Esteban@uv.es).

Information about the Swiss participation in the IMO in English, French, German, Italian.

United Kingdom
Information about the British Mathematical Olympiad (BMO). The UK IMO Register offers a lot of historic information about the UK's participation in the IMO. Do browse the Leaders's Reports.
Related: United Kingdom Mathematics Trust (UKMT), a registered charity which conducts a number of mathematical enrichment activities via schools.


Information on the USA Math Olympiad and the IMO.
The American Mathematics Competitions (AMC).

The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to any US middle or high school student. It is a great contest for students aspiring to Olympiad problem solving, since many of the problems require proof-based solutions.

Archives and Link Collections

The IMO Collection =====NEW=====
Here you will find a large collection of olympiad problems from all over the world. You will also find all the information regarding The IMO Compendium, the most complete collection of problems proposed to the International Mathematical Olympiads.

The Art of Problem Solving
The Art of Problem Solving contains a variety of resources for avid students of mathematics in middle and high school. There are many free resources (in addition to a Forum) such as articles, a LaTeX tutorial, and online Math Jam sessions. Olympiad problem solvers from all over the world participate in problem discussions. The site also sells a set of problem solving textbooks and has an online school.

Includes IMO Problems and Solutions, with authors.

Mathematical Problem Solving Advice by Prof. Shapiro
This website covers some general techniques for solving mathematical problems. It intends to grow into an interactive website. Maintained by Harold Shapiro.

Math problem collections, a frequent (hard!) math contest, and a large problem solving community with many on-line formus for discussions. Maintained byValentin Vornicu.

A Large Collection of Math Contest Material
Includes Problems in Elementary Number theory (PEN), Topics in INequalities (TIN), and Problem-Solving Web-Directory (PSD). Archive maintained by Hojoo Lee(a.k.a. "ideahitme") in Republic of Korea.

PEN: Problems in Elementary Number Theory
A forum around the number-theory problem collection of Hojoo Lee (see above).

A Collection of Math-Olympiad-Problems
Archive maintained by Hans Vernaeve (Hans.Vernaeve@rug.ac.be) in Belgium.

Arkadii Slinko Mathematics Olympiad Site (gradually being transferred)
Provides: a collection of problems, tutorials, training material, articles, a Monthly Internet Mathematics Olympiad, and information on the New Zealand Math Olympiads.

Math Competitions Archive
Kiran Kedlaya (MIT, USA, kray@post.com) has a Math Competitions Archive with some of the recent (back to 1991) IMO problem sets in various formats, and information about the USA Mathematical Olympiad (USAMO). He now has a separate Math Problem Directory.

Math Competition on the Web
Archive and links maintained by Naoki Sato (ensato@hotmail.com) in Toronto, Canada.

OMAP: Online Math Problems
Database of problems that appeared on various national and international math competitions around the world, including detailed info about the Putnam Math Competition. Maintained by meeroh@mit.edu.

Soviet Union 1961-1986
The problems of the All-Soviet-Union national mathematical competitions (final part), 1961-1986 were translated into English and put on the Web by Vladimir Pertsel (voldemar@sagantec.co.il). There is also a plain ASCII version, and a compressed archive with everything: HTML, ASCII, and GIF pictures. [The original page and original archive are still available.]

Olympiad Math Madness
A collection of mathematical brain-busters, specially for those who are tired of not-very-hard problems. Maintained by jefflock@geocities.com.

Mathematics Olympiad Lecture Notes
By Greg Gamble (gregg@maths.uwa.edu.au).

20,000 Problems Under the Sea: Mathematical Treasures on the Web
Online reference to mathematical problems.

Kalva Homepage
Problem collections maintained by John Scholes.

Le Thai Hoang's Math Olympiad
Le Thai Hoang's Math Olympiad Page contains many math problem sets, including shortlists for IMO from 1983 to 1998.

Nick's Mathematical Puzzles
A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided, along with answers, fully worked solutions, and links to related mathematical topics. Many of the puzzles are elementary in their statement, yet challenging. New puzzles are added on a regular basis.
A key feature of the site is the detailed exposition, from first principles, of the puzzle solutions. Some of the puzzles are used to showcase particular mathematical concepts. See, for example, puzzle 56, which introduces a partition identity, and puzzle 63, where Ptolemy's Theorem permits a surprisingly simple solution. Further references are provided with many of the solutions.


Mathematics on WWW

AIMS [ Activities Integrating Math & Science ]
AMS [ American Mathematical Society ]
EMS [ European Mathematical Society ]
GAMS [ Guide to Available Mathematical Software ]
IMU [ International Mathematical Union ]
MAA [ Mathematical Association of America ]
Math Archives
PSTC [ Problem Solving Task Centres ]
PSU [ Penn State University ]
SIAM [ Society for Industrial and Applied Mathematics ]

Miscellaneous Links

No comments: