51th Mathematical Olympiad

The 51st International Mathematical Olympiad will take place in Astana, Republic of Kazakhstan from the 6th until the 12th of July, 2010.A Mathematical Olympiad is a problem solving competition open to all "mathletes". The aim of the competition is to test innate problem solving skills. The problems are restricted to those that require minimal background and high ingenuity. Since one of the goals of such olympiads is to identify talent at a young age, these olympiads are usually restricted to students not yet admitted to any undergraduate programme.The content ranges from extremely difficult precalculus problems to problems on branches of mathematics not conventionally covered at school and often not at university level either, such as projective and complex geometry, functional equations and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle at play that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity.The selection process differs by country, but it often consists of a series of tests which admit fewer students at each progressing test. Awards are given to a top percentage of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more so than individual scores. Contestants must be under the age of 20 and must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO.
Scoring and format
The paper consists of six problems, with each problem being worth seven points, the total score thus being 42 points. No calculators are allowed. The examination is held over two consecutive days; the contestants have four-and-a-half hours to solve three problems per 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 such as calculus and analysis, and solutions are often short and elementary. However, they are usually disguised so as to make the process of finding the solutions difficult. Prominently featured are algebraic inequalities, complex numbers, and construction-oriented geometrical problems.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 six problems from the shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated and observers.Each country's marks are agreed between that country's leader and the deputy leader and coordinators 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 decisions of the chief coordinator and ultimately a jury if any disputes cannot be resolved.
Selection process
The selection process for the IMO varies greatly by country. In some countries, especially those in east Asia, the selection process involves several difficult tests of a difficulty comparable to the IMO itself. The Chinese contestants go through a camp, which lasts from March 16 to April 2. In others, such as the USA, possible participants go through as series of easier standalone competitions that gradually increase in difficulty. In the case of the USA, the tests include the American Mathematics Competitions, the American Invitational Mathematics Examination, and the United States of America Mathematical Olympiad, each of which is a competition in its own right. For high scorers on the final competition for the team selection, there also is a summer camp, like that of China.
The former Soviet Union and other eastern European countries' selection process consists of choosing a team several years beforehand, and giving them special training specifically for the event. However, such methods have been discontinued in some countries.
Awards
The participants are ranked based on their individual scores.
• Subsequently the cutoffs (minimum score required to receive a gold, silver or bronze medal) are chosen such that the ratio of medals awarded approximates 1:2:3.
• Participants who do not win a medal but who score seven points on at least one problem 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.
• The rule that at most half the contestants win a medal is sometimes broken if adhering to it causes the number of medals to deviate too much from half the number of contestants. This last happened in 2006 when the choice was to give either 188 or 253 of the 498 contestants a medal.
The selected students in first round will now participate in the second stage Indian National Mathematical Olympiad (INMO). Homi Bhabha Centre for Science Education is the nodal centre of the country for olympiad programmes in mathematics and science, including astronomy.The mathematics olympiad is conducted in five stages under the aegis of the National Board of Higher Mathematics (NBHM) for class 11th & 12th. Students from 23 places will participate in the second stage on the basis of the results of RMO. 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 six problems from the shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated and observed.