## Math Olympiad in India

The **Math Olympiad Program in India** aims to encourage the students interested in Mathematics. It nurtures their talent through healthy competition among pre-university students in India. This programme is one of the major initiatives undertaken by the **National Board of Higher Mathematics (NBHM) **and is organized by **Homi Bhabha Centre for Science Education (HBCSE).**

In India, there are 25 regions designated for training and selection of students in these stages. Each of these regions is assigned to a Regional Coordinator (RC). The Indian National Mathematics Olympiad (INMO) leads the Indian Students to participate in the International Math Olympiad (IMO).

## Eligibility for the Math Olympiad

Candidates born on or after August 1, 2001 and studying in Class 8, 9, 10, 11 or 12 are eligible to write PRMO 2020. Further, the candidates must be Indian citizens. Provisionally, students with OCI cards are eligible to write the PRMO, subject to this condition: https://olympiads.hbcse.tifr.res.in/how-to-participate/eligibility/mathematical-olympiad/

## Stages of Math Olympiad in India

Math Olympiad in India is a six-stage process:

**Pre Regional Mathematics Olympiad (Pre RMO):**This is the first phase of the International Mathematics Olympiad, conducted in August. In this exam, there are 30 questions that the students need to solve in two and a half hours of examination. Answers are marked on a machine-readable OMR Sheet.**Students from Class 8 can enroll.****Regional Mathematical Olympiad (RMO):**This is the second phase of the International Mathematics Olympiad, conducted in October. The question paper contains six problems and the duration of the exam is three hours. The difficulty level of the exam is higher than in the first phase.**Indian National Mathematical Olympiad (INMO):**This is the third phase of the International Mathematics Olympiad, conducted in January. The students selected (approximately 900) in the RMO are eligible for the Indian National Mathematical Olympiad (INMO). It is held at 28 centers across the country.**S***uccessful candidates get direct entry in Indian Statistical Institute and Chennai Mathematical Institute interview pool for their prestigious bachelor’s program*.-
**IMO Training Camp**– Approximately best 35 students are invited to take training at HBCSE from April to May. In this camp, stress is laid on building the concepts and problem-solving skills of the students. Also, orientation is provided for the IMO. Students need to take several selection tests during this training period. Taking the performances of the students into consideration, only six students are selected to go for the IMO Examination. -
**Pre Departure Camp**– The selected students go through rigorous training of 8-10 days before the main Olympiad. -
**IMO**– A team of 6 candidates accompanied by 4 teachers or mentors represents India in the greatest mathematics contest of the world.

## What is not an actual Math Olympiad?

Many private organizations use the name of IMO to conduct their own contests. These include booksellers who are trying to sell books to coaching centers who use it as a marketing trick. Parents and teachers have requested them to not use the name of IMO.

These private contests are no way similar to the actual math olympiad which is organized by the department of atomic energy and Indian Statistical Institute. In fact, they can sometimes be counterproductive as they promote rote learning of formulas.

**In the actual International Math Olympiad**, students have 9 hours to solve 6 problems. These problems require special problem-solving skills and creativity. The fake olympiads usually kill this creative spirit and replace them with rote formula learning.

Here is a public petition against fake math olympiads in India.

https://www.change.org/p/organizations-bringing-down-the-prestige-of-olympiads-in-india

## How to prepare for Math Olympiad?

Math Olympiad has four core topics:

- Number Theory
- Geometry
- Algebra
- Combinatorics

The preparation involves months of problem-solving and concept building. The real math olympian is regarded very highly by the prestigious universities of the world. For example, an IMO medal is almost a sure shot entry to Ivy League universities like Harvard, MIT, Yale. Even an INMO level medal, lets the student take the interview of Indian Statistical Institute’s B.Stat – B.Math Program, and Chennai Mathematical Institute’s B.Sc. Math Program, bypassing the entrance tests.

## Cheenta Program for Maths Olympiad

Cheenta has a rigorous program for Maths Olympiad candidates starting as early as class 1. Our team consists of Olympians and researchers from leading universities in the world.

The unique feature of Cheenta program is that it has both one-on-one and group classes for every student, every week.

## Books for Maths Olympiad

### Miscellaneous

- Challenges and Thrills of Pre-College Mathematics by Venkatchala
- Excursion in Mathematics by Bhaskaracharya Pratishthana
- Problem Solving Strategies by Arthur Engel
- Test of Mathematics at 10+2 Level by East West Press
- IMO Compendium

### Number Theory

- Elementary Number Theory by David Burton
- Elementary Theory of Numbers by W. Sierpinsky

### Combinatorics

- Principles and Techniques in Combinatorics by Chen Chuan Chong and Koh Khee Meng
- Graph Theory by Harary
- Notes by Yufei Zhao

### Algebra

- Polynomials by Barbeau
- Inequality by Little Mathematical Library
- Secrets in Inequalities by Pham Kim Hung
- Complex Numbers from A to Z by Titu Andreescu

### Geometry

- Lines and Curves by Vasiliyev (something else)
- Geometric Transformation by Yaglom
- Notes by Yufei Zhao
- Trigonometric Delights by El Maor
- Trigonometry by S.L. Loney
- 101 Problems in Trigonometry by Titu Andreescu

## Maths Olympiad Curriculum at Cheenta

**Number Theory I**

This is the first course in elementary number theory:

**NT.I.1**Primes, Divisibility**NT.I.2**Arithmetic of Remainders**NT.I.3**Bezout’s Theorem and Euclidean Algorithm**NT.I.4**Theory of congruence**NT.I.5**Number Theoretic Functions**NT.I.6**Theorems of Fermat, Euler, and Wilson**NT.I.7**Pythagorean Triples**NT.I.8**Chinese Remainder Theorem

**Combinatorics I**

This is the first course in combinatorics and elementary counting techniques:

**Com.I.1**Multiplication and Addition rules**Com.I.2**Bijection Principles**Com.I.3**Combinatorial Coefficients**Com.I.4**Inclusion and Exclusion Principles**Com.I.5**Pigeon Hole Principle**Com.I.6**Recursions**Com.I.7**Shortest Route Problems

**Algebra I**

This is the first course is school algebra. (We assume that the student is familiar with algebraic expressions, and elementary algebraic identities)

**Alg.I.1**Algebraic identities (Sophie Germain, Cube of three etc.)**Alg.I.2**Mathematical Induction**Alg.I.3**Binomial Theorem**Alg.I.4**Linear Equations**Alg.I.5**Quadratic Equation**Alg.I.6**Remainder Theorem**Alg.I.7**Theorems related to roots of an integer polynomial

**Geometry I**

**Geo.I.1**Locus visualization**Geo.I.2**Straight Lines**Geo.I.3**Triangles**Geo.I.4**Geometric Constructions**Geo.I.5**Circles

**Trigonometry I**

**Trig.I.1**Angle and rotation**Trig.I.2**Half arcs and Half chords – Genesis of trigonometric ratios**Trig.I.3**Elementary ratios and associated angles**Trig.I.4**Trigonometric identities**Trig.I.5**Geometry and trigonometry**Trig.I.6**Basic properties of Triangles**Trig.I.7**Compound Angles**Trig.I.8**Multiple and Submultiple Angles**Trig.I.9**Trigonometric Series**Trig.I.10**Height and Distance

**Inequality I**

This first course in inequality must be preceded by a basic course in algebra.

**Ineq.I.1**Geometric Inequalities**Ineq.I.2**Arithmetic and Geometric Mean Inequality**Ineq.I.3**Cauchy Schwarze Inequality**Ineq.I.4**Titu’s Lemma

**Complex Number I**

**Complex.I.1**Geometry of Screw Similarity**Complex.I.2**Field Properties of complex Number**Complex.I.3**nth roots of unity and Primitive roots**Complex.I.4**Basic applications to geometry

Intermediate Curriculum

**Number Theory II**

**NT.II.1**Mobius Inversion Formula**NT.II.2**Greatest Integer Function**NT.II.3**Elementary Group Theory**NT.II.4**Primitive roots and indices**NT.II.5**Quadratic Reciprocity**NT.II.6**Representation of Integers as sum of squares**NT.II.7**Perfect Numbers

**Combinatorics II**

**Com.II.1**Chu Shih Chieh’ Identity (Hockey Stick)**Com.II.2**Multinomial Coeffiecients**Com.II.3**Advanced Pigeon Holes and Ramsay numbers**Com.II.4**Catalan Numbers (and advanced bijection)**Com.II.5**Stirling numbers of second kind**Com.II.6**Generating functions**Com.II.7**Non-linear recurrance

**Algebra II**

**Alg.II.1**Elementary ring and field theory**Alg.II.2**Eisenstein’s criterion

**Geometry II**

**Geo.II.1**Barycentric Coordinates**Geo.II.2**Miquel Point Configuration**Geo.II.3**Translation**Geo.II.4**Rotation**Geo.II.5**Screw Similarity

**Inequality II**

**Ineq.II.1**Schur’s Inequality**Ineq.II.2**Rearrangement Inequality**Ineq.II.3**Jensen’s Inequality**Ineq.II.4**Bernoulli’s Inequality and Power means

**Complex Number II**

**Complex.II.1**Cyclotomic Polynomials**Complex.II.2**Nine Point theorem and other geometric investigations using complex numbers

Advanced Curriculum

**Number Theory III**

**NT.III.1**Thue’s Theorem**NT.III.2**Square Free Numbers**NT.III.3**Diophantine Analysis of second and higher degrees**NT.III.4**Arithmetic Progression whose terms are primes.**NT.III.5**Trinomial of Euler**NT.III.6**Scherk and Richart’s Theorem**NT.III.7**Amicable Numbers**NT.III.8**Liouville function**NT.III.9**Roots of polynomials and roots of congruences**NT.III.10**Numeri Idonai

**Combinatorics III**

**Com.III.1**Graph Theory**Com.III.2**Invariance and Extremal Principles**Com.III.3**Combinatorial Geometry

**Algebra III**

**Alg.III.1**Polynomials

**Geometry III**

**Geo.III.1**Inversive Geometry**Geo.III.2**Advanced Application of complex numbers**Geo.III.3**Projective Geometry

**Inequality III**

**Ineq.III.1**Holder and Minkowski’s inequality