International Mathematical Olympiad selection process
This article describes the selection process, by country, for entrance into the International Mathematical Olympiad.
The International Mathematical Olympiad (IMO) is an annual mathematics olympiad for students younger than 20 who have not started at university.
Each year, participating countries send at most 6 students. The selection process varies between countries, but typically involves several rounds of competition, each progressively more difficult, after which the number of candidates is repeatedly reduced until the final 6 are chosen.
Many countries also run training events for IMO potentials, with the aim of improving performance as well as assisting with team selection.
- 1 IMO Selection process by country
- 1.1 Argentina
- 1.2 Australia
- 1.3 Bangladesh
- 1.4 Brazil
- 1.5 Belgium
- 1.6 Canada
- 1.7 China
- 1.8 Colombia
- 1.9 Cuba
- 1.10 Cyprus
- 1.11 Czech Republic
- 1.12 Denmark
- 1.13 France
- 1.14 Germany
- 1.15 Greece
- 1.16 Hong Kong
- 1.17 India
- 1.18 Indonesia
- 1.19 Ireland
- 1.20 Italy
- 1.21 Japan
- 1.22 Latvia
- 1.23 Malaysia
- 1.24 Mexico
- 1.25 Netherlands
- 1.26 New Zealand
- 1.27 Norway
- 1.28 Pakistan
- 1.29 The Philippines
- 1.30 Portugal
- 1.31 Romania
- 1.32 Russia
- 1.33 South Africa
- 1.34 Spain
- 1.35 Sweden
- 1.36 Taiwan
- 1.37 Thailand
- 1.38 United Kingdom
- 1.39 United States
- 1.40 Tunisia
- 2 References
IMO Selection process by country
In Argentina, the Olimpíada Matemática Argentina is organized each year by Fundación Olimpíada Matemática Argentina. All students that took and passed the National Finals (fifth and last round of the competition) exams, usually held in November; and were born before July 1 21 years ago, are allowed to take two new written tests to be selected for IMO, usually in May. From the results of that tests, six titular students and a number of substitutes are selected to represent Argentina at the International Mathematical Olympiad.
- The Australian Mathematics Olympiad
- The Asian Pacific Mathematics Olympiad
- two IMO selection exams
The Australian Mathematics Olympiad (AMO) is held annually in the second week of February. It is composed of two four-hour papers held over two consecutive days. There are four questions in each exam for a total of eight questions. Entry is by invitation only with approximately 100 candidates per year.
A month after the AMO, the Asian 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 five questions.
The top 12 students from the AMO and APMO (along with another 12 or so junior students) are then invited to a ten-day camp held in Sydney in the April school holidays. During this camp, two four-and-a-half hour selection exams are held, each with four 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.
In 2011, there were three selection exams, each with three questions in four-and-a-half hours to better simulate the conditions of the IMO.
The selection process is organised by Bangladesh Mathematical Olympiad. There are three levels of selection in Bangladesh. In first two levels the students participate in four academic categories: primary, junior, secondary and higher secondary.
- Divisional: Currently(2011) the country is divided in 13 regions for divisional Olympiad. The number of divisions may increase later. Except Dhaka division, roughly 1000 students participate each of the divisional Olympiads and 60 are selected for the next level. In Dhaka division, where number of students are more than the others, 1600 students participate and 100 to 120 students are selected.
All problems in the divisional test are "To find" problems. The students need not to write down the solution, only the answer is necessary. The test is usually one hour long.
- National: The national Olympiad is 3-4 our test depending on the category. In this test the students must write down the solutions of the problems. Some of the winners from junior, secondary and higher secondary categories of this level are selected for the next level.
- The camps: More than one camps are arranged to select students for IMO. The selection process in the camps are not so straight forward as it is in the Olympiads. The students in the camps are closely monitored by the previous campers and coaches and four to six students are selected for IMO.
The Brazilian participants are selected in a two phase process: 1st. The contestants that are awarded medals or honorable mentions in the Brazilian Mathematical Olympiad (OBM) (Olimpíada Brasileira de Matemática)of the year before the IMO are selected to participate in a training process to the IMO. 2nd. The contestants take a series of tests, which have IMO-like level, and the top students are invited to join the Brazilian team that goes to IMO.
The Belgian team is bilingual. The Dutch-speaking community selects three participants during the Vlaamse Wiskunde Olympiade. The French-speaking community selects their three participants through the Olympiade Mathématique Belge and additional tests at training weekends.
High school students must first write the Canadian Open Mathematics Challenge, which takes place around November. Should they score high enough in the COMC(normally 70+), they will be invited to write the Canadian Mathematics Olympiad (CMO), Asian Pacific Mathematics Olympiad (APMO), and unofficially write the USAMO.
The students with the top scores (conditions permitting) will make the Canadian team and travel to the location of the IMO in that year. Although the team is made up of students from all over Canada, Toronto and its suburbs have produced the most people for the team due to its high population density. The Canadian Mathematical Society is the organization which selects team leaders and members for the IMO team.
In mainland China, high school students have the annual National Highschool Mathematics Competitions, held on the second Sunday of October. A few competitors of each province with best scores, usually the top 3 to 5, will be invited to participate in the China Mathematics Olympiads. Approximately the top 20 competitors of CMO will have a training campus; and then, the 6 students with top scores will form the Chinese team. China has been very successful in recent years at the IMO.
In Colombia the selection and preparation of students for math competitions is organized by Olimpiadas Colombianas de Matemáticas. The process begins with the regional competitions which are held in October and November. The best students of these competitions are invited to the January Training Session. In early March the National Competition or Olimpiada Colombiana de Matemáticas begins. It consists of a sequence of four examinations: the classificatoria, the selectiva, the semifinal and the ronda final. The latter contains a (prior) training session and then two days of IMO-style papers.
Every Colombian high school student can take part in the first "classifying" examination but afterwards students are invited to compete according to their results on the previous examination. The three best students of the three different high school levels of the final round examination are the winners of the Colombian Math Olympiad. Although in principle students of the lower levels may be selected to go to the IMO, it generally takes many years before they can compete with students of the highest level or nivel superior. After the National Competition the twenty best students of each level are invited to the June Training Session where students undergo the IMO selection process.
In Cuba the selection process consists (depending on regional conditions of availability of resources, participants and organizers) six levels. Competitions are held to select the best candidates from each school, then from each municipality, then from each province who then are allowed to take part in the National Competition (Concurso Nacional in Spanish). The gold and silver medals (around 20 participants) take a number of further exams closer to the level of International competitions. Thirteen of these are selected to form the National Pre-Selection that trains for up to three months taking also exams out of which the best 6 are selected to form the National team. In a number of years the lack of financial support has allowed only the first member of the team to actually travel and compete in the International mathematical Olympiad.
In Cyprus Four provincial competitions and a National (Pancyprian) competition are held every year. During this procedure 30 students are selected and Four Team Selection Tests are held to determine who will be the six member of national team for IMO
- In every competition or test there are four problem usually covering geometry, number theory, algebra, and combinatorics (elementary level) and last four hours each.
After successfully completing the school and regional rounds, roughly 50 best participants are invited to the national round, where 10 best students are selected to participate in a week-long selection campus. Each day they solve a set of 3-4 problems, taken mainly from the past national olympiads of various countries. On the last day they have to find the answers (this time in form of a number) to rather large set of shorter problems under significant time-pressure. After that the team is selected and before the actual IMO, it competes in traditional Czech-Slovak-Polish Mathematical Contest where the participants can practise their skill under almost identical conditions to IMO.
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.
The Association Animath, and more precisely the Olympiade Française de Mathématiques 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.
IMO team selection in Germany is based on the main national mathematical competitions: The Bundeswettbewerb Mathematik (BWM, the former west German olympiad), the Deutsche Mathematik-Olympiade (DeMO, the former east German olympiad), and Jugend forscht (a research competition). Students successful in any of these competitions (e. g. a prize in the second round of the BWM) write two 3-hour exams at their schools, and the 16 best scorers of these exams are invited to a training program consisting of five seminars, where lectures are given and seven team selection tests are written - 4-hour exams determining the actual IMO contestants (additional tests are possible if the team is not uniquely determined after the seven exams).
- Θαλής (Thalis) - first round
- Ευκλείδης (Euklidis) - second round
- Αρχιμήδης (Archimidis) - third round
Hong Kong first joined IMO in 1988.
In Hong Kong, the International Mathematical Olympiad Preliminary Selection Contest is held every year. Around 60 students are selected to receive further training, after three phases of which six students will be selected as the Hong Kong team members, and six will be selected as reserve members. The further training is also known as phase four training.
The Indian National Mathematics Olympiad (or INMO) is held every year. This is an invitational exam, and only students who qualify the Regional Mathematics Olympiad (or RMO) are invited to appear for it. Students qualifying the INMO get to attend the IMO Training Camp at the Homi Bhabha Centre for Science Education at the Tata Institute of Fundamental Research, where further selection tests are used to identify the top six students who will represent the country. The students are also trained by some of the top mathematicians of India. The camp usually runs throughout the month of May. There are two batches of students in the camp, the seniors and juniors. If a student has come to the camp for the first time, he/she is a junior. There can be atmost 6 juniors from class 12. For those who have been to the camp at least once, the INMO is not necessarily required, and they are selected based on their performance in certain postal problem sets.
In Indonesia, National Mathematical Olympiad is held as a part of National Science Olympiad (Olimpiade Sains Nasional), and has been held annually since 2002. About 100-120 students who pass the province-level test will be eligible to participate in the National Mathematical Olympiad, which is held in August or September. About thirty students are chosen to get into the first training camp, which is held at October through November. About half of them will go to second training camp and participate in the Asian Pacific Mathematics Olympiad. At the end, six students are selected to represent the country. The selection depends on the results of regular tests held every week in every training camp, IMO simulation test and APMO.
In Ireland, the top scorers in the Junior Certificate (a state exam taken around the age of 15-16) are invited by the various universities to take part in the Irish Mathematical Olympiad. The IrMO is held simultaneously in May in each of these universities. The test consists of two three-hour papers, each containing five questions, run on the same day. The top six students are selected for the national team.
In Italy, the Mathematical Olympiad is held every year; the full selection process is made up of four stages:
- the so-called Archimedean games, held as a multiple-choice test in all participating high schools in November
- the regional stage, held as a mixed test (multiple choice, numerical answers and proof-writing) in ca. 100 sites in February
- the national stage, held in Cesenatico at the beginning of May, composed of six problems requiring a full proof
- the team selection test, held in Pisa at the end of May after a five-day stage, composed of two sessions each containing three problems requiring a full proof.
The six-person team competing in the IMO is determined by summing up the scores of four different competitions: the senior national stage, held each September in Pisa, the Balkan selection test held each February in Pisa (also selecting the team competing in the BMO and in the RMM) composed by two papers with three problems, four and a half hours each, and then the national stage and the May stage held in Pisa.
In Japan, Japan Mathematical Olympiad(JMO) is held every year. JMO has two rounds: the first one in January and the second one in February. The best 20 scorers in JMO are invited to the spring training camp in March. The top six students in several tests at this camp are selected for the national team.
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.
The selection is based on the Olimpiad Matematik Kebangsaan, OMK (National Mathematical Olympiad) and the subsequent training camps. Top OMK performers are selected to attend the training camps, and the final IMO representatives are selected based on the students' performance in the camps and race.
The selecting process in Mexico has 3 stages and is organized by the Mexican Mathematical Olimpiad. At first stage, each of the 31 states and the Distrito Federal select a team of up to 6 students (10 in the case of the Distrito Federal) which will represent the state in the national contest. The contest is held once at year, in the month of November. According to the results of this contest, at least 16 students are selected, who will continue to the second stage of the selecting process, the national trainings, which are held from November to April in which the group of 16 students gets reduced to approximately 10. In May the third stage of the contest is held, in which the six students that will represent Mexico in the next IMO. In similar process the teams for the Centroamerican and Caribbean Mathematical Olimpiad (OMCC) and Iberoamerican Mathematical Olimpiad (OIM) are selected. In March the test for the APMO is solved.
In the Netherlands the selecting process consists of three rounds.
- The first round takes place on high schools. It contains 8 multiple-choice questions, and 4 open questions.
- The second round takes place at the Eindhoven University of Technology. It contains 5 open questions.
- Then there is a training and at the end of the training the students make a test: the best 6 students will go to the IMO. The test contains 5 open questions.
The first selection is based on the September Problems, where the top 24 students are selected and invited to a residential one week training camp. At the end of the camp, approximately 12 students are selected as a squad. The squad receives regular assignments to complete every few weeks as well as sitting the British Maths Olympiad, Australian Maths Olympiad and the APMO. The final six candidates plus one reserve are later selected based on results of the assignments and these tests.
In Norway, the Niels Henrik Abels Matematikkonkurranse is held each year. The first selection, usually in September, consist of a multiple-choice exam with 20 problems. One is given 5 points for each correct answer, 1 point for each unanswered problem and 0 point for a wrong answer. Approximately 10% of the competing students are selected for the second selection, which is held in February. The examination consist of 10 problems, giving 10 points for each correct answer, who are integers between zero and one thousand. 20 students are then selected for a final four-hour-long examination consisting of four problems. While usually the 3 best students are automatically chosen for the final team, the rest 3 are decided by their results in the Nordic Mathematical Contest, which they will compete in afterwards.
In Pakistan, selection for the IMO participants is quite similar to that in other countries. The process starts one and a half year before a particular IMO; and a test (also known as NMTC - National Mathematics Talent Contest) is taken by the high school students which is organized by the Higher Education Commission of Pakistan. The test is held in January and the results are announced by April or May. About fifty students out of a 4000 are selected which are called by Abdus Salam School of Mathematics, Government College University, Pakistan - usually in September. The fifty selectees are taught at the school for a week or two and are then tested at the last two days of the camp. This process, involving the top 50, is known as First Camp. Based on the performance in the test, about 20 students are further selected for the Second Camp, and the rest are dropped. These 20 students are joined by 30 students (from NMO - National Mathematics Olympiad) in the Second Camp. Ten students from the 50 are then selected, again based on their performance in a test. Third Camp is the final camp, and 5 are screened out of these 10. These would be the finalised participants for IMO.
Alternatively, high school students from all over Pakistan take NMO (National Mathematics Olympiad) which is organized by Abdus Salam School itself. About 30 are selected which join the NMTC top 20 students in Second Camp. This test is held after the result of the First Camp of NMTC is announced. Students who do not qualify the First Camp of NMTC can still take the NMO if they wish to come to the Second Camp.
Sometimes, the selection process may involve more than three camps and the number of students selected per camp can vary from the figures provided above.
- Official site of Science Olympiads in Pakistan, in English
- Official site of the Abdus Salam School of Mathematical Sciences, the home institution for the training/selection of IMO in Pakistan, in English
The selection process starts with the Philippine Mathematical Olympiad (PMO), which includes a regional level, an area level, and a national level. The top twenty students in the national level of PMO will be invited to a one-month training camp. The top students (at most six) in the selection tests given during this training camp will make up the IMO team.
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.
In Romania those that enter the Romanian National Team on Mathematical Olympiad are selected from four rounds: School, City, County and National. In the case of Bucharest, being some 5 times larger than the largest county, as well as having larger schools, the rounds are: school, sector (a borough, roughly), city and national. From the first two rounds the advancing pupils are chosen using a minimum grade threshold (usually 8.00/10.00). From the city/county round advance the top five (fewer in certain cases), with a playoff round organised if necessary. The national round offers fifteen medals (five of each colour). A team (plus reserve) is selected from the medal winners, usually following a playoff round.
Russia has very extensive system of selecting and training participants for IMO. Different aspects of solving mathematical problems are studied and revealed: combinatorics, logics, structural arrangement and proofs. All problems are evaluated from 7 points. Top participants obtain certificates of 3 degrees ("1st", "2nd" and "3rd diploma") and often additional "commendable certificates". Totally up to half of participants (in the last 3 rounds) gain diplomas.
The official rounds (each picking about 1/3 top of the previous) are: School, Borough, Region, Okrug (a district, roughly) and national. More details:
- School round (Russian: Школьный этап, I stage) is a public stage - every interested pupil of 4-11 grade can participate. Completely organized by every school this competition aimed more at popularisation than at selection.
- Borough round (Russian: Школьный этап, II stage) for some schools (specifically ones that has winners of region round) is equal to the School round.
- Region round (Russian: Областной этап, III stage) is the first which brings together participants in one place to live for some days. It has two rounds on its own. In Moscow they are separated with process of selection, but in less populated regions pupils take part in both. In present days problems for all rounds starting with region round are created by special central committee. There are juries in each region of roughly constant membership. Winners of the region rounds usually have privileges for high-school entering.
- Okrug round (Russian: Окружной, зональный этап, IV stage) is an intermediate before the final round. Problems usually corresponds to non-trivial mathematical facts, often to recent discoveries or their particular cases. Singular schools (e.g. Saint Petersburg Lyceum 239) have the right to present their pupils directly to okrug round.
- National round (Russian: Всероссийский этап, V stage) aimed at selection the most prominent pupils for participation in IMO. For this sake about 14 top of national round from 10th and 11th grades (usually "1st diplomas") are combined in following summer and winter "gatherings" for special training and further selection.
In South Africa those who would be members of the team must pass through a nationwide talent search by correspondence, after which the top fifty or so are selected for a camp (usually in the December holidays) at Stellenbosch University. A number of rounds of monthly problem sets are issued by the University of Cape Town which are taken into consideration, along with the camp marks to select the top fifteen/sixteen to go to a final selection camp at Rhodes University, Grahamstown or more recently the University of the Free State, Bloemfontein in April. A final training camp takes place at the University of Cape Town or more recently, the University of Pretoria just before the IMO. The Asian Pacific Mathematics Olympiad has been used informally as a test, along with an IMO selection test written at the schools of the top fifteen in the event of indecision.
In Spain there are two rounds. The first one is held in each university district. There are two written tests, in which six or eight problems are to be solved, depending on the region. The first three participants in each district go to the national round. This one also consists of two written tests, three and half hours long each, with a total of six problems. The top six scorers go onto the International Olympiad.
In Sweden, a mathematics contest called "Skolornas Matematiktävling" is held every autumn. Those who qualify to the finale are invited to participate in a correspondence course in problem solving as well as the Nordic Mathematical Contest. From the combined results of the qualification round, the correspondence course and the finale and NMC, the six highest achievers of the Swedish finalists are invited to join the Swedish IMO team.
In Taiwan, the selection process consists of three sessions, starting from April to the mid of May. Students who rank among the top 25 in the APMO can participate the first session. During each session students will be tested by six IMO-style problems, and top six students will be selected as the members of the Taiwanese IMO team. The training sessions will be held during May and June.
In Thailand, the selection of the IMO representatives is the responsibility of the organization "The Promotion of Academic Olympiad and The Development of Science Education Foundation". There are many branches of this organization around the country. At the end of August, a 30-question exam is open to all high school students to select 200 students to join a camp in each branch of the country in October for promoting mathematics skills, known in Thailand as "POSN Camp 1". The topics include Algebra, Geometry, Number Theory, Combinatorics and Inequality. After the camp, an exam is given in each of the preceding topics to evaluate the skills. A number of students, usually 50 or 100, are selected to join another camp in March, known in Thailand as "POSN Camp 2". The topics include Algebra, Geometry, Number Theory and Combinatorics in an advanced level, and Functional Equation. After the camp, an exam is given and 18 students are selected from each branch of the country to compete in the Thailand Mathematical Olympiad. Anyone with gold medal will continue to the camp known as "IPST Camp 1", and an exam is given, and some are selected to "IPST Camp 2", finally, only 6 students will compete in the International Mathematical Olympiad.
In the UK, selection is through competitions and training camps under the auspices of the United Kingdom Mathematics Trust, starting with the multiple-choice Senior Mathematical Challenge (SMC). The SMC is followed by the British Mathematical Olympiad (BMO), held in two rounds, but candidates who did not take part in the SMC or did not achieve the qualifying score may enter the BMO on payment of an entry fee and so be considered for the IMO team. After the two rounds of the BMO, 20 potential team members, chosen primarily based on BMO results, are invited to a training and selection camp held in Trinity College, Cambridge, during which further examinations are held, allowing the number of potential team members to be reduced to eight or nine. A final camp is subsequently held at Oundle School, after which six students are chosen as the team and the remaining two or three as reserves. In addition to this formal selection process, there is further training during the year for a squad of potential team members, including the 'Advanced Mentoring Scheme', practice exams and an annual training camp in Hungary; information from exams at the Hungary camp may be considered in selection where available.
In the United States, the team is selected through the American Mathematics Competitions, which are open to all high school students. Top scorers on the USAMO go to a training camp, where the top 25 or so (the number varies from 18 to almost 30) non-seniors from the result of a TSTST are tested over the course of the year with the APMO, RMM, USA TST, and next year's USAMO.
No official selection process takes place. Contestants are selected based on mere recommandations.