Department of Atomic Energy
Government of India.
Mathematics Olympiad activity on a national level has been one of the major initiatives
of NBHM (National Board for Higher Mathematics) since 1986. The activity aims to spot
mathematical talent among High School children. NBHM, with Homi Bhabha Centre for
Sciencec Education (HBCSE), also has taken on the responsibility of selecting and training
the Indian team for the International Mathematical Olympiad every year.
For the purpose of the Olympiad contests, the country has been divided in to about 25 regions.
The selection process for participation in the International Mathematical Olympiad
(IMO) consists of the following stages:
Stage 1: Regional Mathematical Olympiad (RMO): RMO is currently held on the
first Sunday of October each year in each of the regions in the country. The Regional coordinator
each region holds the charge of conducting RMO in the region. All school students
from Class XI are eligible to appear in RMO. Students from Class XII may also appear
in RMO, but the number of students selected from Class XII is at most 6. Exceptionally
brilliant students from lower standards may also appear for RMO subject to the approval
of the Regional Coordinator. RMO is a 3-hour written test containg 6 or 7 problems. On
the basis of the performance in RMO, students are selected for the second stage.
The Regional Coordinators may charge a nominal fee to meet the expenses in organising
Stage 2: Indian National Mathematical Olympiad (INMO): INMO is currently
held on the third Sunday of January each year at the regional centres in all regions. Only
those students who are selected in RMO are eligible to appear in INMO. This contest is
a 4-hour written test. The evaluation of these papers is centralised, and is undertaken by
the IMO Cell of NBHM. The top 75 contestants in INMO receive Merit Certificates.
Stage 3: International Mathematical Olympiad Training Camp (IMOTC): The
top 30-35 INMO certificate awardees are invited to a month long training camp inMay/June
each year. The training camp is organised by HBCSE, Mumbai. The number of students
from Class XII who are selected for IMOTC is at most 6. In addition to these 35 students,
a certain number of INMO awardees of previous year(s) who have satisfactorily undergone
postal tuition over the year are also invited to a second round of training. A team of six
students is selected from the combined pool of junior and senior batch participants, based
on a number of selection tests conducted during the camp, to represent India in the International
Stage 4: International Mathematical Olympiad (IMO): The six member team selected
at the end of IMOTC, accompanied by a leader and a deputy leader represent India
at IMO, that is normally held in July each year in one of the chosen for the years IMO.
IMO consists of two 4-and-a-half hour tests held on two consecutive days. The normal
schedule between departure and return of the team takes about two weeks. The students
of Indian team who win gold, silver and bronze medals at IMO receive from NBHM a cash
prize of RS. 5000/-, Rs. 4000/- and Rs. 3000/- respectively. MHRD (Ministry of Human
Resource Development) finances international travel of the 8-member Indian delegation
to IMO, while NBHM (DAE) finances the entire in-country programme and takes care of
other expenditure connected with international participation. The six students representing
India at IMO automatically qualify for Kishore Vaigyanik Protsahan Yojana (KVPY)
scholarship (Rs 3000/- per month and some contingency) instituted by Department of Science
and Technology, Government of India.
Syllabus for Mathematical Olympiad: The syllabus for Mathematical Olympiad (regional,
national and international) consists of pre-degree college mathematics. The difficulty
level increases from RMO to INMO to IMO. Broadly the syllabus for RMO and
INMO is: Algebra (basic set theory, principle of Mathematical Induction,inequalities (AMGM
and Cauchy-Schwarz), theory of equations (remainder theorem, relation between roots
and coefficients, symmetric expressions in roots, applications of the Fundamental theorem
of algebra and its applications), functional equations); Geometry (similarity, congruence,
concurrence, collinearity, parallelism and orthogonality, tangency, concyclicity, theorems
of Appollonius, Ceva, Menelaus and Ptolemy, special points of a triangle such as circumcentre,
in-centre, ex-centres, ortho-centre and centroid); Combinatorics (Basic counting
numbers such as factorial, number of permutations and combinations, cardinality of a
power set, problems based on induction and bijection techniques, existence problems, pigeonhole
principle); Number theory (divisibility, gcd and lcm, primes, fundamental theorem
of arithmetic (canonical factorisation), congruences, Fermat’s little theorem, Wilson’s theorem,
integer and fractional parts of a real number, Pythagorean triplets, polynomials with
integer coefficients). An idea of what is expected in mathematical olympiad can be had
from the earlier question papers (see http://www.isid.ac.in/˜ rbb/olympiads.html) and the
1. Problem Primer for Olympiads, by C R Pranesachar, B J Venkatachala and C S
Yogananda (Prism Books Pvt. Ltd., Bangalore).
2. Challenge and Thrill of Pre-College Mathematics, by V Krishnamurthy, C R Pranesachar,
K N Ranganathan and B J Venkatachala (New Age International Publishers,
3. An Excursion in Mathematics, Editors: M R Modak, S A Katre and V V Acharya
(Bhaskaracharya Pratishthana, Pune).
4. Problem Solving Strategis, Arthur Engel (Springer-Verlag, Germany).
5. Functional Equations, B J Venkatachala (Prism Books Pvt. Ltd., Bangalore).
6. Mathematical Circles, Fomin and others (University Press, Hyderabad).
Reference to many other interesting books may be found in An Excursion in Mathematics.
Nurture Programme: The INMO awardees who choose Mathematics as one of the subjects
in their undergraduate studies are eligible for a scholarship by NBHM (which is at
present Rs 1500/= per month) throughout their undergraduate studies. If they further
pursue their studies to masters, they continue to get scholarship (enhanced). Even the students
who do not pursue Mathematics in their undergraduate studies are eligible for certain
benefits under a novel programme instituted by NBHM, called Nurture Programme. Under
this programme, each batch of students (selected from among the INMO awardees through
their responses to a few sets of postal problems) is assigned to an institution. The coordinator
in that institution gives out some reading material which the students can go through
during their leisure time while pursuing their undergraduate studies. At the end of each
year, during summer, they are invited to that institution for a contact programme with
working Mathematicians. Based their performance, they may be recommended to a scholarship
given by NBHM. This programme continue for four years. Thus, even those who
pursue under-graduate studies in some other discipline can still get training in Mathematics
and use it in their further pursuit of knowledge.