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International Mathematics Olympiad (IMO)
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
 Geometry, including
 Properties of the orthocentre, Euler's line, ninepointcircle,
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
selfstudy is slowly evolving.
Contents
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.
 Official IMO web site < < < < < N E W
 A new website about the IMO, including a problem and results archive.
 Logos
 An overview of all available logos
Regulations
 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 1022 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 1022 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 1931 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 618 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 819 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 618 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 719 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 1930 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 114 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 1325 July, 2000.
 IMO 1999
[ logo
 problems day 1
 problems day 2
 results
 mailing list
]
 The 40th IMO was hosted by Romania in Bucharest on 1022 July, 1999.
 IMO 1998
[ logo
 problems
 results
]
 The 39th IMO was hosted by Taiwan in Taipei on 1021 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 1831, 1997.
There is an IMO97 mailing list.
 IMO 1996
[ logo
 the problems ]
 The 37th IMO was hosted by India in Mumbai (Bombay) on July 517, 1996.
Contact information:
Professor A.M. Vaidya
IMOCell, School of Mathematics,
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai (Bombay) 400005
India
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 1028, 1995.
 IMO 1994
[ logo
 the problems and results ]
 The 35th IMO was hosted by Hong Kong on July 1219, 1994.
 IMO 1993
[ logo
 problems day 1
 problems day 2
]
 The 34th IMO was hosted by Turkey in Istanbul on July 1219, 1993.
Journals and other info
 IMOnet
 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 Győr,
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.
 WFNMC
 The World Federation of
National Mathematics Competitions (WFNMC)
publishes a journal entitled
Mathematics Competitions.
Also see Australia below.
 M&IQ
 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''.
 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 (K7).
Look under: Events, Olympiad.
 Mental Calculation World Cup
 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 essaytype mathematical competition in the United States,
with 600 to 1,000 participants competing annually for fine prizes.
 IberoAmerican 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.
 Argentina
 The Olimpíada
Matemática Argentina (OMA) is the
Argentinian Mathematics Olympiad.
Currently, information is only available in Spanish.
 Australia
 The
Australian Mathematics Trust (AMT)
is a national nonprofit organization which conducts mathematics competitions
in Australia.
Includes information on the
WFNMC.
 Belgium
 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.
 Bulgaria
 Information about the
National Mathematical Olympiad
in Bulgaria
as part of the
Bulgarian Competitions in
Mathematics and Informatics.
 Canada
 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.
 Colombia
 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).
Email: olimpia@federman.uanarino.edu.co
 Czech Republic

 Denmark

 Estonia
 Information about the
Estonian Matemaatika Olümpiaadid
(also in the Estonian language), maintained by
Uve Nummert (uve@math.ut.ee).
Includes IMO information (in English).
 France
 Information about mathematics competitions in France,
includes French translations of IMO problem sets and
recommended French mathematics literature for IMO preparation.
 Germany
 The Verein
MathematikOlympiaden e.V.
coordinates the German Mathematics Olympiads (DeMO).
There is also information available about the
German
Mathematics Olympiad 1995.
 Ireland
 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).
 Israel

 Italy
 Information on the Italian (?) Mathematics Olympiad (in Italian).
Email contact: mvillani@cibs.sns.it
 Japan
 Information about the IMO in general (starting from 34th) and
the Mathematical Olympiad Foundation of Japan.
Maintained by Naomasa Maruyama
(maruyama@ism.ac.jp).
 Luxembourg

 Mexico
 Information (in Spanish) on the Mexican Mathematics Olympiad (OMM) and
problem sets (mostly in Spanish) of
various (regional) mathematics contests.
Email: 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
 Norway
 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).
 Panama

 Peru
 Information about Peru's math olympiad and the Cono Sur olympiads,
maintained by
Enrique Valeriano (evaleri@pucp.edu.pe).
 Poland
 Information (including problem sets) on the math olympiads
in which Polish high school students participate (in particular:
the Polish Mathematical Olympiad,
the AustrianPolish Mathematics Competition, and
the Baltic Team Contest).
Maintained by
Krzysztof Chelminski
(chel@mathematik.thdarmstadt.de)
and
Waldemar Pompe
(waldipo@mimuw.edu.pl).
 Portugal
 Olimpíadas Portuguesas de Matemática.
 Singapore
 Information about the IMO and Singapore's participation.
 Slovakia
 Mathematical olympiad in Slovakia.
 Slovenia
 Mathematical competitions in Slovenia are supervised by
DMFA.
 South Africa
 South African Mathematics Olympiad.
 Spain
 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).
 Switzerland
 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.
 Uruguay

 USA
 Information on the
USA Math Olympiad and the
IMO.
 USA: AMC
 The American Mathematics Competitions
(AMC).
 USA: USAMTS
 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 proofbased solutions.
 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.
 MathLinks.ro
 Math problem collections, a frequent (hard!) math contest, and
a large problem solving community with many online formus for discussions.
Maintained by Valentin Vornicu.
 A Large Collection of Math Contest Material
 Includes Problems in Elementary Number theory (PEN),
Topics in INequalities (TIN), and
ProblemSolving WebDirectory (PSD).
Archive maintained by
Hojoo Lee
(a.k.a. "ideahitme")
in Republic of Korea.
 PEN: Problems in Elementary Number Theory
 A forum around the numbertheory problem collection of Hojoo Lee
(see above).
 A Collection of MathOlympiadProblems
 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 19611986
 The
problems of the AllSovietUnion national mathematical competitions
(final part), 19611986 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 brainbusters, specially for those who
are tired of notveryhard 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.


 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

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