Mathematical Olympiad Prepared By: Mr. Jagat Singh National Coordinator KVS Mathematical Olympiad

OVERVIEW Mathematical Olympiad is the only school level mathematical problem solving contest held annually. It is conducted by different organizations to identify, encourage, promote and nurture the talent in Mathematics at State, Regional, National and International levels. In India, this is organized by National Board for Higher Mathematics (NBHM), since 1988.

NATIONAL BOARD FOR HIGHER MATHEMATICS (NBHM) This is a unit of the Department of Atomic Energy, Govt. of India which provide funds for various academic programmes related to Mathematics. NBHM awards scholarships for pursuing studies for MSc degree in Mathematics. Final year BSc students and those who have joined for MSc degree course are eligible to apply. The present scholarship amount is Rs. 4000/- per month.

Research awards for PhD in Mathematics: These awards are meant for motivated students with a MSc degree in Mathematics. Selection is made on the basis of a written test usually held in May followed by interviews. The scholarship amount is Rs. 8000/ per month.

The present National Coordinator of NBHM is Prof. V. M The present National Coordinator of NBHM is Prof.V.M.Sholapurkar Head of Department of Mathematics, S.P.College, Pune -411030 Contact No: 09922542713 Contact No. (O): 020-24331978 Extn. 2309 Email: deepaksholapurkar@yahoo.com

HOMI BHABHA CENTRE FOR SCIENCE EDUCATION Mathematical Olympiad Programme in India (Leading to participation in International Mathematical Olympiad) HOMI BHABHA CENTRE FOR SCIENCE EDUCATION TATA INSTITUTE OF FUNDAMENTAL RESEARCH (HBCSE) and NATIONAL BOARD OF HIGHER MATHEMATICS (NBHM) DEPARTMENT OF ATOMIC ENERGY

Homi Bhabha Centre for Science Education (HBCSE) is a National Centre of the Tata Institute of Fundamental Research, Mumbai. The broad goals of the Centre are to promote equity and excellence in Science and Mathematics education from primary school to undergraduate college level, and encourage the growth of scientific literacy in the country.

To these ends it carries out a wide spectrum of inter-related activities, which may be viewed under three broad categories: (a) Research and Development, (b) Teacher Orientation and Science Popularization, and (c) Olympiads and other Students' Nurture Programmes. It is India's nodal centre for Olympiad programmes in Mathematics, Physics, Chemistry, Biology and Astronomy.

Mathematical Olympiad in India This is conducted in three stages, the Regional Mathematical Olympiad (RMO) usually held on 1st Sunday of December every year in 25 Regions. The Indian National Mathematical Olympiad (INMO) usually held on 1st Sunday of February every year and then an International Mathematical Olympiad Training Camp (IMOTC) organized in April- May from where a team of the best six students is selected to represent India in International Mathematical Olympiad (IMO) usually held in July each year in a member country of the IMO.

MATHEMATICS OLYMPIAD PROGRAMME IN INDIA AND RELATED ACTIVITIES The Mathematics 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 of Higher Mathematics (NBHM) of the Department of Atomic Energy (DAE). This programme is one of the major initiatives undertaken by NBHM. Its main purpose is to spot mathematical talent among pre-university students in the country.

MATHEMATICAL OLYMPIAD PROGRAMME IN INDIA AND RELATED ACTIVITIES For the purpose of training and selection of students for the Olympiad contest, the country has been divided into about 25 regions and 03 Groups (KVS, NVS & CBSE). The Mathematics Olympiad programme consists of the following stages :-

Stage 1: Regional Mathematical Olympiad (RMO): RMO is held on the first Sunday of December each year in different regions of the country. The Regional Coordinator of a region is given the responsibility of conducting RMO in the region. All school students from Class IX – XII are eligible to appear for RMO. But the number of students selected from Class XII from each Region can be atmost 6.

Stage 1: Regional Mathematical Olympiad (RMO): Exceptionally brilliant students from lower standards may also take RMO at the discretion of the Regional Coordinator. RMO is a 3-hour written test containing 6 to 7 problems. On the basis of the performance in RMO, a certain number of students from each region is selected for the second stage (INMO). The Regional Coordinators may charge a nominal fee to meet the expenses for organizing the contest.

Stage 2: Indian National Mathematical Olympiad (INMO): INMO is held on the first Sunday of February each year at centres in the different Regions. Only those students who are selected in RMO are eligible to appear for INMO. This contest is a 4-hour written test. On the basis of the INMO, the 30- 35 students from all over the country are chosen as INMO Awardees and receive a Certificate of Merit. (a maximum of 6 students of class XII can be INMO Awardees)

Stage 3: International Mathematical Olympiad Training Camp (IMOTC) : The top 30-35 INMO awardees are invited to a month long training camp in April – May each year. The training camp is organised at HBCSE, Mumbai. In addition to these 35 students, a certain number of INMO awardees of the previous year who have satisfactorily gone through postal tuition throughout the year are also invited to a second round of training.

Stage 3: International Mathematical Olympiad Training Camp (IMOTC) : On the basis of a number of selection tests conducted during the camp, a team of the best six students is selected from the combined pool of junior and senior batch participants to represent India in the International Mathematical Olympiad (IMO).

Stage 4: International Mathematical Olympiad (IMO): The six member team selected at the end of IMOTC, accompanied by a leader and a deputy leader and an observer represents India at IMO. That is normally held in July each year in some country. The IMO contest consist of two 4-and-a-half hour tests held on two days. Travel to IMO venue and return takes about two weeks. The students of Indian team who receive gold, silver and bronze medals at IMO receive a cash prize of Rs. 5000/-, Rs. 4000/- and Rs. 3000/- respectively from NBHM at a formal ceremony at the end of the training camp during the following year.

Stage 4: International Mathematical Olympiad (IMO): MHRD finances international travel of the 8-9 members Indian delegation to IMO. While NBHM (DAE) finances the entire in-country programme and takes care of other expenditure connected with the International participation.

Syllabus for Mathematical Olympiad The syllabus for Mathematical Olympiad (regional, national, 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 combinations,

factorization of polynomials, 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 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 JMO RMO INMO IMO.

Mathematical Olympiad in KVS and Related Activities Kendriya Vidyalaya Sangathan ,a premier organization in the field of Secondary and Senior Secondary education. It has to achieve its mission of “To pursue excellence and set the pace in the field of school education.”

For last 15 years KVS has been conducting its own Mathematical Olympiad Programme which is supplemented by INMO Indian Mathematical Olympiad conducted by NBHM( National Board of Higher Mathematics), Deptt of Atomic Energy of India . KVS is nurturing the talent of students through this programme and students are producing very good result at National & International Level.

JUNIOR MATHEMATICAL OLYMPIAD (JMO) A Student studying in class X who secured A2 or higher grade in Mathematics in class IX examination and A student studying in class XI with Mathematics as an elective subject (irrespective of stream opted) who secured A2 or higher grade in Mathematics in class X examination can appear.

A student studying in class XII with Mathematics as an elective subject who secured 80% and above marks in class XI can also appear. Note- There will be a common question paper for all the participants.

The JMO is held on first Sunday of September everywhere The JMO is held on first Sunday of September everywhere. About 20,000 students participate in JMO every year. Out of these participants about 200 students are short listed for certification & awards. Merit Certificates are given to those students who secure at least 35 % marks in JMO.

SPOT EVALUATION / MERIT LIST The answer scripts of 16th KVS- JMO- 2013 will brought to KV, NFC, Vigyan Vihar Delhi (Spot Evaluation Centre) and be evaluated by the examiners (TGT/PGT – Maths) of Delhi and nearby Regions. A merit of about top100 students will be prepared. These 100 students will attend the training camp for KVS- RMO/INMO- 2013 for 10 days during winter break of the year-2013.

VENUE FOR TRAINING CAMPS INMO - 2014 Last year, it has been observed that the attendance of the participants in the training camps was increased from 65% to 84%. Further to motivate/ facilitate the participants, this year also it is proposed that 02 camps for 10 days during winter break may be organized at the following centres as per schedule given below: KV- IIT Chennai 26th December 2013 – 4th January 2014. KV NFC Vigyan Vihar, Delhi, 26th December 2013 – 4th January 2014.

KVS - RMO (Regional Mathematical Olympiad) On the last day of the INMO preparatory camp, a test of 3 hours for 100 marks will be conducted and evaluated at both the centres (Delhi/ Chennai). About top 30 students of RMO will be selected on the basis of combined merit of both the centres. They will then participate in INMO in the month of Feb.2014 conducted by NBHM. Selection at National level leads to participation at the International Mathematical Olympiad (IMO) through another round of training/test/orientation etc.

CERTIFICATES AND CASH AWARDS AT KVS LEVEL: KVS (HQ) confers the following Cash Awards and certificates as per the laid down criteria: Cash awards of Rs.10,000/-, Rs.8000/- and Rs.5000/- for securing first, second and third position respectively at KVS State Level. Cash awards of Rs.5000/-, Rs.4000/- and Rs.3000/- respectively for securing first, second and third position at Regional Level. Students eligible for State as well as Regional level awards shall be conferred the higher one alone.

Merit certificates are given to about top 200 students who secured atleast 35% marks in JMO. Apart from Awards at JMO level; each INMO Awardees gets a cash Award of Rs.20,000/- from KVS. The cash Award of Rs. 20,000/-for INMO Awardees at KVS Level is highest in the country.

KVS Leadership in INMO-2007 KVS secured best position all over the country in INMO-2007. Out of 34 INMO Awardees all over the country, 06 students were from KVS Group alone.

Name of student selected in INMO Year Name of student selected in INMO Name of KV Cash award from KVS 2005 Master Harshit G.Vashnav SAC Ahemadabad Rs. 20,000/- 2006 Master Rohit Singh ONGC Dehradun 2007 Sajiv Chandra Minambakkam Chennai M. Prasanna Ashok Nagar Chennai Ananth Shankar CLRI Chennai George Sebastian KV No1 CPCRI Kasaragod Bangalore Utkarsh Tripathi KV IIT Kanpur Senior Group 2008 Master Ajitesh Shrivastava   KV Ishapore No.1,  Kolkata Master M. Prasanna  KV Ashok Nagar Chennai Utkarsh Tripathi    2009 Manish Chawala KV.No.1 Ambala Cantt Master R, Bharadwa KV Anna Nagar Chennai Master Anshu Avinash KV ASC Centre Banglore

INMO AWARDEE 2011 The INMO was held on 18-01-2011. All over India about 650 students participated in INMO . 34 students selected as INMO Awardees. Out of these 34 students 03 Students were selected from KVS group alone.

International Mathematical Olympiad 2007- KVS Participation: In the history of KVS one student Master Utkarsh Tripathi of KV IIT Kanpur was first time selected to participate in IMO -2007. He won Honorary Mention in IMO-2007. He was one of the KVPY awardees.

International Mathematics Olympiad 2008- KVS Participation: Due to his overall performance in IMO-2007,Master Utkarsh Trpathi was again selected to participate in Indian team at IMO. He was awarded Bronze Medal in IMO-2008 held at Spain on 10-07-2008.

KVS PRIDE Master Anant Shankar – a student of class XII of KV CLRI Chennai – an INMO Awrdee-2008 participated in IMO -2009 held at Bremen Germany. He won Silver Medal at IMO-2009.

The performance of Indian team in IMO Year Host Country No. of Medals Rank (Unofficial) No. of Countries 1989 Germany 4 Bronze 25 50 1990 China 1 Gold, 1 Silver, 2 Bronze 17 54 1991 Sweden 3 Silver, 3 Bronze 10 56 1992 U.S.S.R. 1 Silver, 4 Bronze 22 60 1993 Turkey 4 Silver, 1 Bronze 15 73 1994 Hong Kong 16 69 1995 Canada 14 1996 India 1 Gold, 3 Silver, 1 Bronze 75 1997 Argentina 82

1998 Taiwan 3 Gold, 3 Silver 10 79 1999 Romania 3 Silver, 3 Bronze 17 2000 South Korea 5 Silver, 1 Bronze 14 82 2001 United States 2 Gold, 2 Silver, 2 Bronze 7 83 2002 United Kingdom 1 Gold, 3 Silver, 2 Bronze 9 84 2003 Japan 4 Silver, 1 Bronze 15 2004 Greece 4 Silver, 2 Bronze 85 2005 Mexico 1 Silver, 1 Bronze 32 92 2006 Slovenia 5 Bronze 35 90 2007 Vietnam 3 Silver 25 94 2008 Spain 31 97 2009 Germany 3- Silver 2 Bronze, 01 honourable 95 2010 Kazakhstan 2 Silver, 01 Bronze, 03 Honourable 53 98

Result of IMO & India’s position Rank 2013 2012 2011 I China Korea II USA III Singapore India’s Rank 29th 11th 23rd

The Olympiad books recommended by NBHM 1. Problem Primer for Olympiad C R Pranesachar, B J Venkatachala and C S Yogananda (Prism Books Pvt.Ltd,. Bangalore). 2. Challenge & Thrill of Pre- College Mathematics V Krishnamurthy, C R Pranesachar, K N Ranganathan & B J Venkatachala (New age International Publishers, New Delhi).

3. An Excursion in Mathematics Editors: M R Modak, S A Katre & V V Archarya (Bhaskarachary Pratishthana, Pune). 4. Problem Solving Strategies Arthur Engel (Springer- Verlag, Germany).

5. Functional Equations B J Venkatachala (Prism Books Pvt. Ltd., Bangalore). 6. Mathematical Circles Fomin & others (University Press, Hyderabad). …………………………………………….