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RMO - The Mathematical Olympiad Programme
in India, which leads to participation of Indian students in the International
Mathematical Olympiad (IMO) is organized by the Homi Bhabha Centre for Science
Education (HBCSE) on behalf of the National Board for Higher Mathematics (NBHM)
of the Department of Atomic Energy (DAE), Government of India. This programme
is one of the major initiatives undertaken by the NBHM. Its main purpose is to
spot mathematical talent among pre-university students in the country.
Stages
- Stage I: Regional Mathematical Olympiad) (RMO and pre-RMO,
- Stage II: Indian National Mathematical Olympiad (INMO),
- Stage III: International Mathematical Olympiad Training Camp (IMOTC),
- Stage IV: Pre-departure Training Camp (PDT) for IMO,
- Stage V: Participation in International Mathematical Olympiad (IMO).
Eligibility
Students from Class IX, X, XI and XII are eligible to appear for the RMO. Highly motivated and well prepared students from Class VIII may also take the RMO at the discretion of the Regional Coordinator.
Qualification and Eligibility Criteria for the Second Stage
The RMO is a 3-hour written test with 6 or 7 problems. On the basis of the performance in RMO, a certain number of students from each region is selected for Stage 2 (INMO).
Mathematical Olympiad
The Maths Olympiad Programme which leads to participation in the IMO- International Mathematical Olympiad,constitutes of the following stages:
Stage 1: Regional Mathematical Olympiad (RMO)
Regional Mathematical Olympiad is held in each region normally between September and the first Sunday of December each year. A regional coordinator makes sure that at least one centre is provided in every district of the region. RMO is a 3-hour written test which contains about 6 to 7 problems. All high-school students up to class XII are eligible to appear for RMO. To appear for RMO, interested students should get in touch with the RMO co-ordinator of their region well in advance, for enrolment and payment of a nominal fee.
Each regional coordinator has the freedom to prepare his/her own question paper or to obtain the question paper from NBHM. The regions which opt for the NBHM question paper hold this contest on the 1st Sunday of December. On Based on theirperformance in RMO, certain number of students from each region are selected to appear for the second stage. The regional coordinators charge nominal fees to meet the expenses for organizing the contests.
Stage 2: Indian National Mathematical Olympiad (INMO)
Indian National Mathematical Olympiad is held on the first Sunday of February every year at differentcentres in different regions. Just the students who are selected on the basis of RMO from various regions are eligible to appear for the INMO. It is a 4-hour written test. Its question paper is set centrally and the test is common throughout the country. Only the top 30-35 performers in INMO receive a merit certificate.
Stage 3: International Mathematical Olympiad Training Camp (IMOTC)
This is a training level for the INMO certificate awardees. They are invited for a month long training camp (for junior batch) conducted in May-June, each year. Also in addition, INMO awardees of the previous year who have satisfactorily completed the postal tuition throughout the year are again invited for a second round of training (called the senior batch).
Stage 4: International Mathematical Olympiad (IMO)
A leader and deputy leader are chosen by the NBHM from among mathematics teachers/researchers involved in the Mathematics Olympiad activity.So the team selected at the end of the camp, the leader and the deputy leader, represent India at the International Mathematical Olympiad that is normally held in July in a different member country of IMO each year. The IMO consists of two written tests held on two days with a gap of at least one day. Both the tests are of four-and-a-half-hours.
India has 25 regions along with three independent groups that conduct Regional Math Olympiad. Each region has its own Regional Coordinator, who is responsible for conducting RMO in his/her region.
They are:
Regional Coordinators have the discretion of using central RMO paper set by the HBCSE or set the examination paper themselves. Regions that choose to go with the centrally prepared RMO paper have to conduct a pre-RMO to screen students for the central RMO examination.
The format of the pre-RMO paper and criteria for short listing student for RMO is decided solely by the Regional Coordinator.
Eligibility
Only students of class IX, X, XI and XII are eligible to participate in Regional Mathematical Olympiad. However, Regional Coordinators have the discretionary power to allow any Class VIII student with exceptional mathematical talent to sit for the RMO.
Syllabus for Mathematics Olympiads-
Syllabus for Mathematics Olympiads (regional, national and international) is class 9th to 12thstandard mathematics.
The typical areas of problems are: number theory,algebra, geometry, and combinatorics.
The topics covered under these areas are: number systems, geometry, arithmetic of integers,quadratic equations and expressions, co-ordinate geometry, trigonometry,systems of linear equations, factorisation of polynomials, permutations and combinations,inequalities, probability theory,elementary combinatorics, number theory, complex numbers, elementary graph theory and , infinite series.
The syllabus does not include statistics and calculus.
Though the syllabus is roughly spread over class IX to class XII levels, still the problems under each topic are of an exceptionally high level in difficulty and sophistication as compared to the text book problems.
The difficulty level keeps increasing from RMO to INMO to IMO.
Books for preparation of Mathematical Olympiads
The following books treats the topic which are covered in the different levels of the olympiad and also are a rich source of problems-
S. No. | Book | Author | Publication |
1 | Challenge and Thrill of Pre-College Mathematics | V. Krishnamurthy, C. R. Pranesachar, K. N. Ranganathan and B. J. Venkatachala | New Age International Publishers |
2 | Mathematical Challenges from the Olympiads* | C. R. Pranesachar, S. A. Shirali, B. J. Venkatachala, and C. S. Yogananda | Prism Books Pvt. Ltd. |
3 | Problem Primer for the Olympiad | C. R. Pranesachar, B. J. Venkatachala, and C. S. Yogananda | Prism Books Pvt. Ltd., #1865, 32nd. Cross, BSK II Stage, Bangalore 560 070. or 49, SardarSankar Road, Kolkata 700029. Phone: 24633890/24633944. |
4 | An Excursion in Mathematics | M. R. Modak, S. A. Katre, V. V. Acharya | BhaskaracharyaPratisthan, 56/14 Erandavane, Damle Path, Pune 411 004 |
5 | International Mathematical Olympiad, Vol I, 1959-1975 | IstvanReiman | Anthem Press (Indian Edition available) |
6 | International Mathematical Olympiad, Vol II, 1976-1990 | IstvanReiman | Anthem Press (Indian Edition available) |
7 | International Mathematical Olympiad, Vol III, 1991-2004 | IstvanReiman | Anthem Press (Indian Edition available) |
8 | Mathematical Circles | D. Fomin, S. Genkin& I. Itenberg | First Reprinted Edition, University Press, New Delhi, 2000 |
9 | Problem-Solving Strategies | Arthur Engel | Springer |
10 | A Primer On Number Sequences | S. A. Shirali | University Press |
11 | First Steps In Number Theory--- A Primer On Divisibility | S. A. Shirali | University Press |
12 | Functional Equations---A Problem Solving Approach | B. J. Venkatachala | Prism Books Pvt. Ltd |
*(Contains problems and solutions of International Mathematical Olympiad from 1986-1994)
Apart from the above listed books dedicated for the Olympiad purpose, the following books listed below form the recommended topic-wise reading for the various math competitions. From the given reads, some are elementary, and some are not so elementary.
Books on Geometry
S. No. | Book | Author | Publication |
1 | Modern Geometry | Durrel M. A., | Macmillan & Co., London |
2 | Geometry Revisited | H. S. M. Coxeter and S. L. Greitzer | Mathematical Association of America |
3 | Plane Trigonometry | S. L. Loney | Macmillan & Co., London |
Books on Number Theory
S. No. | Book | Author | Publication |
1 | An Introduction to the Theory of Numbers | I. Niven& H. S. Zuckerman | Wiley Eastern Ltd. New Delhi |
2 | Elementary Number Theory | David Burton | Universal Book Stall, New Delhi |
3 | An introduction to the theory of numbers | G. H. Hardy & Wright | Oxford University Publishers |
Problem Books
- I M O Problem Collections
S. No. | Book | Author | Publication |
1 | International Mathematical Olympiad 1959-1977 | S. L. Greitzer | MAA Pubications |
2 | International Mathematical Olympiad 1978-1985 | M. S. Klamkin | MAA Pubications |
- General Problems
S. No. | Book | Author | Publication |
1 | USA Mathematical Olympiads 1972-1985 | M. S. Klamkin | MAA Pubications |
2 | Selected problems and Theorems in Elementary Mathematics | D. O. Shklyarshky, N. N. Chensov and I. M. Yaglom |
|
3 | 250 Problems in Elementary Number Theory | W. Sierpenski | American Elsevier |
4 | Problems in Plane Geometry | I. R. Sharygin | MIR Publishers |
Books for General Reading
S. No. | Book | Author | Publication |
1 | Higher Algebra | S. Barnard & J.M. Child | Macmillan & Co., London, 1939; reprinted Surjeet Publishers, Delhi, 1990 |
2 | The Theory of Equations, Vol. 1 (13th Edition) | W. S Burnside & A.W. Panton | S. Chand & Co., New Delhi, 1990 |
3 | Elementary Number Theory, Second Edition | D. M. Burton | Universal Book Stall, New Delhi, 1991 |
4 | Introductory Combinatorics | RA. Brualdi | Elsevier, North-Holland, New York, 1977 |
5 | Geometry Revisited | H.S.M. Coxeter& S.L. Greitzer | New Mathematical Library 19, The Mathematical Association of America, New York, 1967 |
6 | Modern Geometry | C.V. Durell | Macmillan & Co., London, 1961 |
7 | Higher Algebra | H.S. Hall & S.R Knight | Macmillan & Co., London; Metric Edition, New Delhi, 1983 |
8 | Mathematical Gems Part I (1973), Part II (1976), Part III (1985) | R Honsberger | The Mathematical Association of America, New York |
9 | Geometric Inequalities | N.D. Kazarinoff | New Mathematical Library 4, Random House and The L.W. Singer Co., New York, 1961 |
10 | Inequalities | P.P. Korovkin | Little Mathematics Library, MIR Publishers, Moscow, 1975 |
11 | An Introduction to the Theory of Numbers | Fifth Edition, Wiley Eastern, New Delhi, 2000 | |
12 | Applied Combinatorics | A.W. Tucker | Second Edition, John Wiley & Sons, New York, 1984 |
13 | High School MathematicsPart II | G.N. Yakovlev | MIR Publishers, Moscow, 1984 |
Students who clear INMO but are not selected for International Math Olympiad (IMO) receive postal problems during the period of July to December. Based on their responses, they might be invited to the pre-departure training camp for IMO directly or asked to sit for INMO again (without having to sit for the Regional Math Olympiad).
Exam Structure
RMO has six or seven problems that students have to solve in three hours. The syllabus for RMO basically covers pre-degree college mathematics. The major areas covered in the syllabus are algebra, geometry, number theory and combinatorics. Calculus and statistics are not within the scope of the exam but students are allowed to use approaches based on them to solve problems.
The questions generally have high difficulty level and sophistication which only increase from RMO to INMO to IMO.
One should go through Regional Mathematical Olympiad past year papers as well as Regional Mathematical Olympiad sample papers to fully understand what is to be expected in the exam.
Syllabus
The syllabus for Mathematical Olympiad (regional, national and international) is pre-degree college mathematics. The areas covered are arithmetic of integers, geometry, quadratic equations and expressions, trigonometry, co-ordinate geometry, system of linear equations, permutations and combination, factorisation of polynomial, inequalities, elementary combinatorics, probability theory and number theory, finite series and complex numbers and elementary graph theory. The syllabus does not include calculus and statistics. The major areas from which problems are given are number theory, geometry, algebra and combinatorics. The syllabus is in a sense spread over Class XI to Class XII levels, but the problems under each topic involve high level of difficulty and sophistication. The difficulty level increases from RMO to INMO to IMO.
For more information, Visit http://olympiads.hbcse.tifr.res.in/subjects/mathematics