# International Mathematical Olympiad Training Camp

The **International Mathematical Olympiad Training Camp** (**IMOTC** for short) is a month-long annual training camp held in India, intended to train Indian students in Olympiad-related problem-solving and select the six-member team to represent India at the International Mathematical Olympiad (IMO).

In recent years, the IMOTC has been held at Homi Bhabha Centre for Science Education (HBCSE), Mumbai, during the month of May. IMOTC is coordinated by the Mathematical Olympiad Cell.

## Selection

### Eligibility

The primary purpose of the IMO Training Camp is to select students for the IMO, so the same criteria of eligibility apply. Specifically, the student must be at most 21 years of age, and must not yet have joined any college or post-secondary institution.

### Selection procedure

First-time selection to the IMOTC is done using a two-stage procedure:

- Regional Mathematical Olympiad (RMO): These are conducted in the (approximately) 15 marked regions of India, during December of the previous year. Each region selects approximately 36 students using the results of the RMO, to represent it at the next stage. A region can send at most six students from Standard 12 (the final year of school).
- Indian National Mathematical Olympiad (INMO): This is conducted in late January or early February. Only students who have been selected by their respective regions through the RMO are eligible to write the INMO. A total of approximately 500 students write the INMO, and approximately 36 students are selected to attend the IMOTC. At most six students from the final year of school can be selected.

Students who have already been selected to the IMOTC once have the following options for subsequent years (while they still remain in school):

- The students are sent postal problem sets regularly (every fifteen days) in the time period July-December. If they submit solutions to the postal problem sets regularly, they are invited to attend the next year's IMOTC, without having to write RMO/INMO again
- If they do not submit solutions to the postal problem sets regularly, they need to write INMO again (they do not need to rewrite the RMO)

People attending IMOTC for the first time are called *juniors* while people attending a second time are called *seniors*. Typically, IMOTC has around 30-35 juniors and 20 seniors.

## Selection for the IMO

One of the key purposes of the IMOTC is to select the six-member team to represent India at the International Mathematical Olympiad. Selection is done through a series of *selection tests*. The six students with the maximum total score on the selection tests, are chosen to represent India. Factors like rank in INMO or performance in previous years' IMO or IMOTC are not usually given consideration (except possibly in the case of ties).

Since 2007, the selection test pattern has been as follows:

- There are four selection tests, each test being 4.5 hours long and featuring three problems. Each problem is evaluated out of 7 points.
- The answer sheets submitted by the students are corrected, shown to the students (allowing students to get their grievances redressed), and then taken back. The score awarded per problem is not revealed to the student.
- At the end of the selection tests, the total scores are revealed to students, and the six students with highest total scores are selected for the International Mathematical Olympiad.

This is a change from earlier years. Until 2006, the selection test pattern featured five selection tests, problems were evaluated out of 10 points, and the full scores were revealed to the students immediately after the test.

## Lectures

### Lecture topics

The IMOTC features regular lectures during weekdays (Monday-Friday), with separate lecture schedules for juniors (first-time attenders) and seniors. Lectures focus on both theory and problem-solving in topics closely related to Olympiad mathematics, including:

- Geometry: Topics covered may include triangle geometry, transformation geometry, inversion,
- Number theory: Topics covered may include congruences, Diophantine equations
- Combinatorics
- Algebra: Topics covered may include polynomials, functional equations and inequalities

There is no well-defined syllabus and the material covered varies from year to year, depending on who turn up to give the lectures.

### Regular lecturers

Regular lecturers at the IMOTC include: (fillin)

## Composition

Official statistics haven't been compiled, so the representation of composition given below is approximate.

### Regional composition

There are strong skews in the regional composition of students at the IMOTC. The Maharashtra region, and Pune in particular, has regularly sent a large number of students to the IMOTC. This has been attributed to Olympiad coaching activities conducted at the Bhaskaracharya Pratishthana. Since 2000, 2-4 people in the six-member team finally selected to the IMO have been from Pune.

In recent years, there has been an increase in the representation of Tamil Nadu at the IMOTC, which some have attributed to Olympiad coaching activities conducted by the Association of Mathematics Teachers of India (AMTI) as well as the efforts of individual Olympiad coaches. Orissa, too, has had a good representation in recent years, again attributed by some to coaching activities.

### Gender composition

The IMOTC has more boys than girls on average, with the number of girls ranging between 2 and 15 (out of the 50+ participants). 2003 was the first year where a girl (Shubhangi Saraf) mdae it to the IMO team. The teams for the IMO in 2004 and 2005 also had one girl each, while there were no girls in 2006 and 2007.

### Age composition

The bulk of students qualifying INMO do so while finishing Standard 11, so they get the opportunity to attend the IMOTC twice. Every year, there is a reasonable number (varying from 5 to 10) of students who qualify the INMO at the end of Standard 10. Approximately 1-2 students every year qualify the INMO at the end of Standard 9.

The youngest student to attend the IMOTC has been Swarnendu Datta, who attended it at the end of Standard 8 (i.e. he qualified the INMO while in Standard 8).

The composition of students making it to the team also varies from year to year. Usually, 3-4 of the people making it to the team are "seniors": people who've already attended the camp earlier. The rest are juniors, usually those attending at the end of Standard 11. Rishi Raj, Swarnendu Datta, and Abhishek Dang are three people who made it to the IMO team at the end of Standard 9.