International Mathematical Olympiad

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The International Mathematical Olympiad (IMO) is an annual contest for high school students. It is the oldest of the international science olympiads.

The first IMO was held in Romania in 1959. Since then it has been held every year except 1980. About 80 countries send teams of (at most) 6 students each (plus one team leader, one deputy leader and observers). Teams are not officially recognized - all scores are given only to individual contestants. Contestants must be under the age of 20 and must not have any post-secondary school education. Subject to these conditions, an individual may participate any number of times in the IMO.

The paper consists of 6 problems, with each problem being worth 7 points. The total score is thus 42 points. The examination is held over two consecutive days; the contestants have 4.5 hours to solve 3 problems on each day. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. They require no knowledge of higher mathematics, and solutions are often short and elegant. Finding them, however, requires exceptional ingenuity and mathematical ability.

Each participating country other than the host country may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the 6 problems from that shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated from the contestants until the second examination has finished; the contestants are accompanied to the IMO by their deputy leaders.

Each country's marks are agreed between that country's leader and deputy leader and Co-ordinators provided by the host country (the leader of the team whose country submitted the problem in the case of the marks of the host country), subject to the ultimate decision of the Jury if any disputes cannot otherwise be resolved.

Contents

Selection process

Australia

In Australia, selection into the IMO team is determined by the Australian Mathematics Trust and is based on the results from 4 exams:

  • The Australian Mathematics Olympiad
  • The Asia Pacific Mathematics Olympiad
  • 2 IMO selection exams

The Australian Mathematics Olympiad (AMO) is held annually in the second week of February. It is composed of two 4-hour papers held over two consecutive days. There are 4 questions in each exam for a total of 8 questions. Entry is by invitation only with approximately 100 candidates per year.

A month after the AMO, the Asia Pacific Mathematics Olympiad is held (APMO) and the top 25 from the AMO are invited to sit the exam. It is a four and a half hour exam with 5 questions.

The top 12 students from the AMO and APMO (along with another 12 or so junior students) are then invited to a 10 day camp held in Sydney in the April school holidays. During this camp, two 4.5 hour selection exams are held, each with 4 questions. The top six candidates along with a reserve are then announced as part of the team based on their results in the four exams.

Cyprus

In Cyprus Four provincial competitions are held in November in every district capital. In Lefkosia is called "Iakovos Patatsos", in Lemesos is called "Andreas Vlamis", in Larnaka and Ammochostos is called "Petrakis Kyprianou" and in Pafos is called "Andreas Hadjitheoris". Afterwards 10 students from every grade (A, B and C grade) of the high-school (Lyceum) from every district are selected. Total: 4 districts * 3 grades * 10 students = 120 students.

Then a National (Pancyprian) competition is held in December and is called "Zeno". Every grade has different problems. Afterwards 10 students from every grade are selected. Total: 3 grades * 10 students = 30 students. This student are divide into two groups according to the district they come from. Group A must come from Lemesos and Pafos and Group B must come from Lefkosia, Larnaka and Ammochostos.

Each group watches about 8 to 10 four hour preparing lessons for the olympiad. Each group decides where the next lesson will be held. During the lessons Four Selection competitions are held which are considered the four parts of the Selection Competition under 15.5 which is called "Michael Georgallas". In each of the competition 5 students are eliminated. So after the 4th competition the six member of national team and the four runners-up are selected.

Denmark

In Denmark a national contest open to all high school students is held every year called "Georg Mohr-Konkurrencen"(the Georg Mohr contest) named after a Danish mathematician. The top 20 of this contest are then invited to another contest where the final team is selected.

France

The Association Animath prepares and selects the French IMO team. Students who succeed at a preselection test can get from Animath a year-long training, after which the team is selected by an IMO-like test.

Hellas

  • Θαλής (Thalis) - first round
  • Ευκλείδης (Efklidis) - second round
  • Αρχιμήδης (Archimidis) - third round

Hong Kong

In Hong Kong the International Mathematical Olympiad Preliminary Selection Contest is held every year. Students are selected to receive further training, after three phases of which 6 students will be selected as the Hong Kong team members, and 6 will be selected as reserve members.

Latvia

In Latvia a national contest open to all high school students takes place each year. The best participants of regional contests are allowed to participate in the national olympiad held in Riga. The top students are further tested to select the national team.

Malaysia

The first selection round is based on the Olimpiad Matematik Kebangsaan, OMK (National Mathematical Olympiad) and around 30 candidates are selected to join two or three of training camps. The final 6 candidates are selected from the results of some more tests and exams (including the APMO) in these training camps.

Generally, no one knows the exact criteria on how the team is selected since the exam results in the training camps are not disclosed. However, it is known to the public is that the team must consist of a certain number of Bumiputeras. There have been cases where even the top three in the OMK were not selected as one of the member of the camp.

In fact, private school students are not allow to take part in the international olympiad training camps of Malaysia(Even you are Albert Einstein ot Gauss).

Portugal

In Portugal, there are four selection steps. The three first are the exams of the Portuguese Mathematics Olympiad and the last is composed of several exams made by Projecto Delfos, who also prepares the students for international competitions.

Romania

In Romania those that enter the Romanian National Team on Mathematical Olympiad are selected from 3 rounds: City, County and National. A team (plus reserve) is selected from the first 9 topped on the National Olympiad.

United Kingdom

In the UK those that enter the British Mathematical Olympiad are reduced to around 20 for a 'training session' held in Trinity College, Cambridge. A squad (team plus reserve) of around 9 is selected from examinations during these sessions and a final team is selected after a further training session held at Oundle School.

United States

In the United States, the team is selected through the American Mathematics Competitions, which are open to all high school students.

Awards

The participants are ranked based on their individual scores.

  • Gold medals will be awarded to the top 1/12 of the contestants.
  • Silver medals will be awarded to the next 2/12.
  • Bronze medals will be awarded to the next 3/12.
  • Participants who don't win a medal but who score 7 points on at least one problem will get an honorable mention.

Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem. This last happened in 2005, 1995 and 1988, but was more frequent up to the early 1980s.

Current and future IMOs

Past IMOs

Sources differ about the cities hosting some of the early IMOs. This may be partly because leaders are generally housed well away from the students, and partly because after the competition the students did not always stay based in one city for the rest of the IMO. The exact dates cited may also differ, because of leaders arriving before the students, and at more recent IMOs the IMO Advisory Board arriving before the leaders.

Results for the 2005 IMO

Results by Medals for the 2005 IMO

  1. China | (5 gold, 1 silver)
  2. USA , Russia | (4 gold, 2 silver)
  3. Romania | (4 gold, 1 silver, 1 bronze)
  4. Korea | (3 gold, 3 silver)
  5. Taiwan | (3 gold, 2 silver, 1 bronze)
  6. Japan | (3 gold, 1 silver, 2 bronze)
  7. Iran | (2 gold, 4 silver)

Results by points for the 2005 IMO

  1. China (235)
  2. United States of America (213)
  3. Russian Federation (212)
  4. Iran (201)
  5. Korea (200)
  6. Romania (191)
  7. Taiwan (190)
  8. Japan (188)
  9. Hungary, Ukraine (181)
  10. Bulgaria (173)
  11. Germany (163)
  12. United Kingdom (159)
  13. Singapore (145)
  14. Vietnam (143)
  15. Czech Republic (139)
  16. Hong Kong (138)
  17. Belarus (136)
  18. Canada (132)
  19. Slovakia (131)

External links

es:Olimpiada Internacional de Matemáticas fr:Olympiades de mathématiques it:Olimpiadi Internazionali della Matematica ja:国際数学オリンピック ru:Международная Математическая олимпиада sl:Mednarodna matematična olimpijada sv:Matematikolympiaden zh:国际数学奥林匹克竞赛 fi:Kansainväliset matematiikkaolympialaiset

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