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.

he 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

Syllabus : The syllabus for Mathematics Olympiads (regional, national and international) is pre-degree college mathematics. The syllabus is spread over class IX to class XII levels, but the problems under each topic are of an exceptionally high level in difficulty and sophistication . The difficulty level increases from RMO to INMO to IMO

Number Theory, including

### Topics covered

1. Fundamental Theorems on Arithmetic
2. Linear and quadratic Diophantine equations, including Pell’s equation
3. Arithmetic of residues modulo n, Fermat’s and Euler’s theorems

Algebra, including

1. Fundamental Theorems on Algebra, e.g. inequalities, factorization of a polynomial into a product of irreducible polynomials
2. Symmetric polynomials of several variables, Vieta’s theorem

Combinatorics, including

1. Graph theory
2. Geometry, including
3. Properties of the orthocentre, Euler’s line, nine-point-circle, Simson line, Ptolemy’s inequality, Ceva and Menelaus etc.

Excluded topics:

1. Calculus
2. Complex numbers (though present in the past)
3. Inversion in geometry
4. 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:

1. GOLD MEDAL: the top 1/12 of scores receive gold medals
2. SILVER MEDAL: the next 2/12 of scores receive silver medals
3. BRONZE MEDAL: the next 3/12 of scores receive bronze medals
4. 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

A Mathematical Olympiad is a problem solving competition open to all “Mathletes”. One main purpose of this activity is to support mathematical talent among high school students in the country.

The Mathematics Olympiad activity was undertaken by National Board of Higher Mathematics (NBHM) from 1986 onwards and is currently run in collaboration with the Homi Bhabha Centre for Science Education, Mumbai.

The Mathematics Olympiad Programme leading to participation in the International Mathematical Olympiad consists of the following stages:

Stage-1 : Regional Mathematical Olympiad (RMO) is held in each region normally between September and the first Sunday of December each year. The RMO is meant primarily for students of Class XI and XII, but currently they allow bright students of Class IX & X to appear for the RMO. As special cases, exceptionally talented students from Class VIII may be allowed to appear at the discretion of the Regional Coordinator.

Stage-2 : Indian National Mathematical Olympiad (INMO) is held in January / February each year at various centres in different regions. Only students selected on the basis of RMO from different regions are eligible to appear for INMO.

Stage-3 : International Mathematical Olympiad T raining Camp (IMOTC), On the basis of performance in INMO , the top 35 students in the merit list are selected for stage-3. All the 35 students are invited to a month long training camp (junior batch) conducted in May- June, each year. In addition, INMO awardees of the previous year that have satisfactorily gone through postal tuition throughout the year are invited again for a second round of training (senior batch).

Stage-4 : Pre-departure T raining Camp for IMO, On the basis of a number of selection tests through the Camp, a team of the best six students is selected from the combined pool of junior and senior batch participants. All the six students go through another round of training and orientation for about 10 days prior to the departure for IMO.

Stage-5 : International Mathematical Olympiad (IMO), The six-member team selected at the end of the Camp accompanied by a leader and a deputy leader represent the country at the IMO, held in July each year in a different member country of IMO. IMO consists of two written tests held on two days with a gap of at least one day. Each test is of four-and-a-half-hours duration.

### Awards

The participants are ranked based on their individual scores. Medals are awarded to the highest ranked participants, such that slightly less than half of them receive a medal. 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

### Contact information:

Dr. A. K. Mathur
Dept of Mathematics
University of Rajasthan
Jaipur 302 004
Ph.: (0141) 2708392 (O), 2550377 (R)
Mobile : 09314529855
e-mail: tagorebiotechcollege@rediffmail.com